HART protocol and control - Pure - Aanmelden · PDF fileHART protocol and control Ortmans, R.M.H.M. ... Center of Process Control / Engineering Stamicarbon of DSM made an experimental

HART protocol and control

Ortmans, R.M.H.M.

Published: 01/01/1996

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Citation for published version (APA):Ortmans, R. M. H. M. (1996). HART protocol and control. (DCT rapporten; Vol. 1996.057). Eindhoven:Technische Universiteit Eindhoven.

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ana Control Roy ûrtmans, id. 322004

NR rapport I943 WFW rapport 96.057

Stageverslag

Begeleiding:

* Ir. P.J. de Jong * Ir. B. Vissers . Prof. Dr. Ing. H.A. Preisig

DSM (Engineering - Stamicarbon) DSM (Engineering - Stamicarbon) TUE

R.H.M.H. Ortmans Faculteit Werktuigbouwkunde

Technische Universiteit Eindhoven Mei 1996

Summary

Digital Communication can send signals of several devices on one wire. This reduces the costs of wiring immensely. DIA and AíD converters are superfluous for digital communicatioQ because controllers are mostly digital and the mfonnation is already digital now. So this also reduces the costs. These advantages make digital communication attractive. The HART protml is wide spread digital communication protocol in process industry. At DSM many devices are HART compatible. In the multidrop mode the HART protocol can send signals of several devices on one wire. Because of the advantages and the unacquaintedness with the multidrop mode of the HART protocol, the Instrument Group, pari of the Center of Process Control / Engineering Stamicarbon of DSM made an experimental design to investigate the HART protocol and its multidrop mode.

Problems are expected for the HART protocol in DDC because of the sampiing time and time áelay that can cause undesirable behaviour. The sampling time can be varied by changing the number of devices to the multidrop line. The sa.mplq time is equal to number of devices times halfa second. Investigating if' the HART protocol is suitable for DDC is left to the Advanced Process Control Group, part of the Center of Process Control / Engineering Stamicarbon of DSM. This report is the result of a practical work period to investigate this.

A guidehe for the optimal controller gain setting for which the control performance in DDC is not significantly different then the performance in continuous control, is searched. In other words when the controller gain is lower than this optimal controller gain setting the HART protocol can be used in DDC. Such a guideline is found for h s t order processes with no dead time:

K,(optimal) < z / (5n)

Assumptions for this guideline are; the integration time must be equal to or larger than the time constant and adding derivative control action does not affect the difference in control performance much. This guideline does not take non- linearities into account.

This guideline is applied to the model of the experimental design in Simullak. The experimental design is a vessel with a warm and cold inlet flow and an outlet flow. Also some valves are in the experimental design to make it possible to control flow, level or temperature. From these simulations with Simulink it appears that the HART protocol can be used in level and temperature control. In plants the HART protml can also be used in level and temperature control, because time constants in plants are larger than in the experimental design. The HART protocol can not be used in flow control because even time constants of large valve in process industry are too small.

The guideline is not applied to the experimental design in the laboratory because the control possibilities were not h s h e d in time. Because flow control is the only control for that the HART protocol can not be used, it can be useful to investigate this also for the experimental design in the laboratory.

11

Table of Contents

1 In troduction 1

2 HART Protocol 2.1 Inti-oduction 2.2 Analog Communication 2.3 Digital Communication

3 Direct Digital Control 3. i ~toctuction 3.2 Sampling 3.3 The Discrete P D Alogorithm 3.4 Sampling Time Selection 3.5 3.6

Sampling Time Selection for Closed Loop Systems Influence of Tuning Parameters on Control Performance

4 Guideline for HART Protocol in DDG 4.1 Introduction 4.2 4.3 4.4 Remarks

Theoretical Optimal Contoller Gain Setting Practical Optimal Controller Gain Setting

5 Applications 5.1 Laboratory Experiments 5.2 Simulations with Sirnulink

5.2.1 Modelling the Vessel 5.2.2 Control Possibilities 5.2.3 Simdation Results Correctness of the Guideline in Applications 5.3

6 Conclusions and Recommendations 6.1 Conclusions 6.2 Recommendations

2 2 2 2

5 5 5 6 7 9 10

15 15 15 15 16

17 17 17 17 19 22 25

26 26 26

References 27

... 111

Appendices

A Simulations for a Guideline A. 1 A.2 Validation of the Guideline

Simulations to Determine a Guideline

B Implementation in Simulink Model of the Vessel B. 1.1 The Entire Vessel B. 1.2 B. 1.3 B. i .4

B.2.1 Control Possibilities B.2.2 Ratio Block B.2.3 The Continuous PID Controller Discretisation with the HART Protocol Initialisation and Parameters of the Model

B. 1

Model of the Level of the Vessel Model of the Temperature of the Vessel Model of a Valve of the Vessel

B.2 Control

B.3 B.4

c Simulations of the Vessel

28 28 28

33 33 33 33 34 34 35 35 38 38 39 40

43

iv

1 Introduction

Chemical plants exist of several processes and systems. The purpose of those systems and processes is to produce one or more products with a certain quantity and specdlcation. Many values and parameters have to be measured to control and monitor these systems and processes. The domation of these measurements is used by contro'llers, monitoring systems or other systems. It speaks for itself that communication between these systems is important.

Tlus communication can be realized analog or digital. Digital communication has the advantage that signals of several devices can be sent on one wire. This reduces the costs of wiring immensely. Another advantage is that nowadays most controllers in plants are digital controllers and with digital comunication many AD and DIA converters would be s ~ p d c o u s . These advantages make digitai communication very attractive. Xevertheiess, besides advantages digitai communication can have disadvantages. It causes a loss of information compared with analog communication. This loss of idformation is introduced by sampling. Another possible disadvantage of digital communication is that for digital communication it takes more time before the signal reaches its destination.

When the disadvantages of digital communication are negligible compared with analog communication, digital communication could be better applied than analog communication. The disadvantages of digital communication have the most effect in control loops. So the most important question for digital communication is:"What are the problems of digital communication in combination with control in process industry ?".

The HART protocol is a wide spread digital communication protocoi in process industry, 80 percent of the field devices are HART compatible. At DSM, the HART protocol is also applied a lot. Because of the advantages of digital communication and the unknown parts of the HART protocol, the Instrument Group, part of the Center of Process Control f Engineering Starnicarbon of DSM started to investigate the possibiliîy of the HART protocol to send signals of several devices on one pair of wires. An experimental design was made to get better acquainted with this possibility of the HART protml. In this expekental design several process values can be controlled to investigate the problems of digital communication in combination with control. The investigation and judgement if the HART protocol are suitable for control, is left to the Advanced Process Control Group, part of CPCRS.

This report is the result of the practical work period to investigate this. First an analytical study is done for the HART protocol in combination with PID controllers. PID controllers are chosen, because most controllers in process industry are PID controlIers or a variant of it. The results of this study are applied to simulations in SimuIuik. From these results conclusions are drawn for HART and control in process industry, where time constants are merent then in an experimental design. The results are not applied to the experimental design, because the possibility to control process values was not realized in time.

In Chapter 2 the HART protocol and digital communication are discussed. Digital control is the subject of Chapter 3, especially the sampling time selection for digital control.Using the HART protocol sampling time and time delay are Isno% so in Chapter 4 a guideline is tried to fmd for the optimal controller gain setting for a given ñrst order process and HART protml. This guideline is applied to the model of a vessel in chapter 5. In the fmaí chapter conclusions for digital control and the HART protocol are drawn.

I

2 M R T Protocol

2.1 Introduction

Nowadays much dormation of plants is available. Most of this information comes ffom measurements. This dormation can be used for several purposes, for example controlling or monitoring. To communicate efficiently with a range of Mèrent field devices, 5: communication standard is needed. HART, Highway Addressable Remote Transducer, is such a communication standard.

The HART protocol has the possibility to communicate analog and digital. it includes specfieations for the physical fom of transmission, transaction procd-mes, message sti?icturz, dûta formats, and a set of uo~m~mds to perf=nr, the required functions for digital communication. The HART protocol was originally developed by Rosemount Inc. Nowadays the HART protocol is open for use by everybody and supported by d e HART Communication Foundation. The HART Communication Foundation is an independent organization that operates as a not-for-profit corporation to coordmate and support the application of HART technology worldwide. Because of this openness and nonprofit support about 80 percent of the instruments used in process industry are HART-compatible instruments.

As mentioned the HART protocol has the possibility to communicate in dfierent modes; point to point, burst and multidrop mode. In the point to point and burst mode, digital and analog communication can be used together. Digital and analog signals coexist on the same pair of wires without disrupting the analog signal in this mode. In the third mode, the multidrop mode, digital communication is the only possibleway to communicate.

2.2 Andog Communication

The HART protml uses a 4 to 20 mA signal for analog comunication. Before using analog communication the range of the measured value is determined per device and the maximum expected value is set to 20 mA and the minimum expected value is set to 4 mA. A measured value corresponds with a value between 4 and 20 mA, lmearly interpolated between maximum and minjmum expected value. A geater value than the maximum expected value will be 20 mA and a lower value than the minimum expected value will be 4 mA.

2.3 Digital Communication

The HART protocol has the possibility to use digital techniques to transport signals, digital comunication. Digital communication has the advantage that additional dormation of the field device can be sent. Digital communication of the HART protocol uses the Bell 202 standard frequency sh& keying (FSK) signal to communicate at 1200 baud, superimposed at a low level on the 4 to 20 mA analog measurement signal, see Figure 2.2.1.

. . . . . .

......

__... . ~ Time

Figure 2.2.1 HART digital communication

2

The 1200 Hz and 2200 Hz of Figure 1 correspond with the digital values "1" and "O".

Device 1 Device 2

The greatest advantage of digital communication is the possibility to transport signals of several devices on one pair of wires. Th~s is called multidrop mode in the HART protocol. In the multidrop mode it is possible to communicate with up to 15 devices connected to a single multidrop line. Figure 2.2.2 gives the communication scheme for the multidrop mode.

e . . . . Device n Device 3 I ~ I

Multiplexer

Figure 2.2.2 Communication scheme multidrop mode

Control System

The analog signal is no longer required in this situation to send information. However the transmitter analog output is set to 4 mA to provide power to the device. So an advantage of the multidrop mode is that it can reduce the cost of field wiring and the cost of host input interface electronics are an advantage.

When devices are connected to a multidrop line the communication is organized as follows. A device only gives mformation when it is asked for information. Consider one device Connected to a multidrop line, the multiplexer asks for the mformation of the device and writes this mformation to a register. To ask dormation and to write it to a register will take a certain time per device. This time TmT is determined by the baud rate. For the HART protocol this rate is 1200 baud, which corresponds with THART of about half a second. The information in the register of the device is not the current information, but is information of some moments before. This time delay is between zero seconds and T,, For the ease this time delay is assumed to be equal to half TmT Sending back information to a device takes place in the same way.

When several devices are connected to one mu1tidrop line, the multiplexer asks the information of the devices in series. So the information of a device is updated after the other devices connected to the same multidrop line are asked for mformation. This results in a sampling time equal to the number of devices multiplied by halfa second. when the control system and the Communcation with the control system take no time, the communication sequence of the multidrop mode can be represented as shown in Figure 2.2.3

3

2 HART Protocol

u,

Figure 2.2.3 Time scheme multidrop mode

Digital and analog mmmunication differ in several ways, The differences in equipment are not discussed. The difEerence in methods can be described by a few parameters of digital communication knowing: sampling time, time delay and shift time.

Time delay

In digital communication it takes some time before information reaches its destination. This kkod1uces a time delay in the control loop. The time delay of the HART protocol is equal to 2*Tm,./2 = TwT

t,,,(HART) = 0.5 seconds (2.2. I )

Samding time

As described the HART protocol imposes a sampling time. The number of devices connected to a multidrop line determine the samphg time. A multiplexer can have more channels acting independently from each other. This implies that a different number of devices could be connected to each channel. So the sampling time can vary per channel for the same multiplexer.

tsmpkJHART) = n"0.5 second (2.2.2)

With n the number of devices per channel.

Shifî time

Figure 2.2.3 shows that the measurements of the separate devices do not contain information taken at the same time. The difference in time of which the mformation is measured can be a complication when both measurements as-e used for one purpose. This shift time is determined by the sequence in which the devices are polled.

ts,(Hí4AT) = (m - n)*0.5 seconds (2.2.3)

The shift time can be abolished by putting the devices of that the measurements are needed at the same time on different channels. The sampling time of these camels must be attuned to each other with an acceptable sampling time to have the values at the same time.

4

3 Direct Digital Control

3.1 Introduction

Using digital communication digital control will save the investments of the converters and a part of the wiring. An advantage of digital communication in combination with digital control is the connection without the use of DIA and DIA converters. So the problems of digital communication in combination with digital control must be investigated.

Controlhg processes can be divided in two groups. These two groups are continuous (analog) controllers and discrete (digital) controllers. Since the emergence of digital control, from the time digital control provided suEcient computing power and reiiabiiity, both methods have been applied to process contro-ol next to each other.

Digital controllers are more flexible than analog controllers, because the controller is implemented as software. The controller algorithm and parameters can be changed easily. For an analog controller an electrical or pneumatic circuit must be made that obeys the control law. Regarding to the costs only simple, standard calculations can be implemented in such a circuit. Once it is made only the parameters can be changed, not the algorithm. So an analog controller is inflexible compared with a conîinuous controller.

In contrast with an analog controller the behaviour of a digital controller can be reproduced. Other advantages of a digital controller are flexibility and insensibility to drift. The advantage of flexibility has been suppressed a long time, digital controllers were given the same adjustment possibilities as malog controllers.

Despite the advantages of the digital controller, the analog controller still exists. The fact that analog controllers still exist is because control equipment has a long lifetime, so that equipment installed several years ago can still be in use. Another reason is that analog equipment has cost and reliability advantages in several applications. The most important reason that analog control is strll used may be due to the fact that the advantage of flexibility and larger possibilities have been suppressed for a long period.

Digital control and analog control use different concepts. The important difference is that digital control performs its calculations in series, so it has to perform its function periodically. When time-consuming steps are involved in the calculations, digital control might be too slow. The time that every period last is called sample time and depends on computation, communication and measuring. The difference between analog and digital control can be summarized as sampling.

When a controller must be applied to a process, the choice is fixed upon digital control, because reliability and computing power are no restrictions anymore and one is more aware of the flexibility advantage. So the differences between analog and digital control, with sampling as major difference, must be taken into account.

3.2 Sampling

A digital controller operates on discrete numerical values of the measured controlled variables. The values of these variables are obtained from sampling the signal. The smaller the sample time is, the closer the continuous case is approached. Sampling causes loss of dormation, because there is only information of the signal at the times the signal has been sampled. This causes the loss of high-frequency dormation and is called aliasing. According to Marlin El], an uidication of the information lost from sampling can be deterinined bough Shannon’s samphg theorem, which is stated as follows and is proved in many textbooks:

A continuous function with all Ii-equency components at or below w ’ can be represented uniquely by values sampled at a frequency equal to or greater than 2w’.

So according to Shannon’s tnieorem, a signaf can be perîèctly reconstructed when t h ~ s signal is sampled with a frequency of at least twice the highest frequency of the signal.

However for controlling a system ihe signal needs not to be reconstructed pedecfiy, but having sufficient ktomation

5

3 Direct Dieital Control

to achieve good dynamic performance is enough. Thus, using Shannon’s theorem as guideline for sampling gives a good dynamic performance, but often this can be achieved sampling less frequently. When the signal does have frequencies with a signlticant amplitude above the íì-equency range one is interested in, these frequencies appear in low-frequency mmponenis. Frequencies above the sampling frequency are folded back to a frequency below the sampling frequency. This can be avoided filtering the continuous signal before sampling it.

As mentioned before one does not need to reconstruct the signal perfectly to control a system. So for controlling an approximation of the signal from the sampled values is needed. This approximation of the signal from the sampled values ca? be done in mîîy wìys. In process control the =i& used nethod is the zero-order hold. The zero-order hold zssmes that &e va;labk is amstant between two samples. Reconstructing the signal from a zero-order hold affects the dynamics as shown in Figure 3 .Z. i .

ZOH-approximation of a sinewave

o 2 4 6 8 10 time [sec]

Figure 3.2.1 Reconstruction of a signal after zero-order hold

The reconstructed signal is the original signal with a time delay of AtíZ. According to Marlin [i] this explains the rule of thumb that the major effect on stability and control performance of sampling can be estimated by adding Atí2 to the dead time of the system. This additional delay negatively affects stability and performance of the process.

3.3 The Discrete PID Algorithm

For controlluig a process variable, a controller must be chosen. Continuous controllers can not be used in digital control, because analog and digital control use Wërent concepts. Continuous algorithms have to be modified for digital control. PID controllers are the most common controllers, so the modification of a PID controller is used as an example.

The continuous PID algorithm:

E(t’)dt’-Zd- dCV(t) dt ‘ O

(3.3.1)

The digital approximation of the continuous PID algorithm is as follows:

6


(3.3 -2)

In Equation 3.3.2 the subscript N denotes the current sample. So the ith previous sample is designated by the subscript N-i. The proporiional mode is self-explanatory, the integral term is derived by a simple rectangular approximation of the continuous signal and the derivative mode is approximated by a backward dflerence.

Now the clBereme between the discrete and continuous algorithm can be exasnined. As mentioned before the major dif€erence between a discreet and a continuous controììer is sampling. Paying no aîîeniifon to this stLtteriieiit, m e could think that the settings for a continuous controller that gives a good control performance, give a good control Performance when used as settings for a discrete controller. This is not true, because sampling causes a loss of information and an addhonal time delay. So a discrete controller gives less control performance than a continuous controller.The optimal settings for a m h u o u s controller gives the best control performance that can be acchieved.. The question is how large the daerence in control performance is.

3.4 Sampling Time Selection

Selecting a sampling time asks for a criterion to decide whether a sampling time is acceptable or not. A criterion can be; sampling time is acceptable when the process is stable. This criterion can be used but often a certain control performance is wanted. The best achievable control performance is in the continuous case. A useful criterion is; the sampling time is acceptable when the effect of sampling in combination with digital control is not sipficant compared with continuous control.

For selecting the right samplmg time, several effects have to be taken into account. Franklin [ 3 ] describes some of these effects and the desired sampling time, see Table 3.4.1

Effect Desired sarnpiing time

aliasing At 2 tbf 2

smoothness tbf40sAts t ,16

delay At s tbf 20

disturbances At stb f 20 Table 3.4.1 Effects and desired sampling time

Aliasing has been mentioned already in Chapter 3.2. A response is wanted to be smooth so the Merences between two time steps are not to large. Reducing the time delay due to sampling is also an important issue. A command input can wur anytime throughout a sample period, what can give a delay up to a full sample period. Disturbances are difficult to take into account. Sampling too fast results in controlling the measurement noise. Sampling too slow results in reacting too late on a permanent disturbance. Reacting in time on disturbances is the intention, but not to control the disturbance.

t,, is the time constant that corresponds with the bandwidth eequency, in other words the maximum time constant of the process considered. So choosing tb equal to the aSl simcant effects are taken into account. Guidelines can be based on other known parameters other than t,,. Seborg [2] gives a number of other guidelines and rules of thumb shown in Table 3.4.2.

7


Approach and recommendation Comments

1. Type of physical variable

(a) Flow: At=l s

(b) Level and pr- bssuTe: A t = 5 s

(c) Temperature At=2Os

ignore specific process dynamics



2.Open-loop system

(a) At < O. 1 z,, z,, = dominant time constant

(b)O.2<At/G< 1.0

(c) 0.01 < At I z < 0.05

(d) ts/ 15 <At <tJ6

(e) 0.25 < At I f < 0.5

(Q O. 15 (At)o, < 0.50

For process model, G(s) = Ke-'"/ (zs + 1)

Based on (3b) and Ziegler-Nichols tuning

t, = settling time (95 % complete)

t, = rise time for open-loop system

o, = critical fiequency for continuous system (rad I s)

(g) 0.050 < (At)@, < O. 107 Table 3.4.2 Guidelines for the selection of sampling period for PID controllers

Table 3.4.2 is divided in two sections. Section 1 gves guidelines that ignore specific process dynamics. This means that time constant and dead time are not estimated, but these guidelines are based on the fact that flow has normally fast dynamics, level is slower and that temperature has very slow dynamics. In section 2 process dynamics of the open loop must be estimated and the guidelines are based on this estimation of process dynamics. The closed Imp dynamics are not taken into amount. In closed loop systems is tried to achieve better performance, the estimated time constant of the closed loop system is smaller than that of the open loop system. Guidelines for closed loop systems have probably to consider integration time, derivative time and controller gain, because the estimated time constant is aected by them.

From Table 3.4.1 and 3.4.2 it appears that the best possible sampling time is ambiguous. Even with the mentioned guidelines, choosing the correct sampling time is still difficult. Marlin [l] gives the following guideline that includes most guidelines for an approximation of the process by a first-order system with dead time:

At < (about O.OS($ + z) to O. l(G + z)] (3.4.1)

Here is 8 the dead time and z the time constant of an approximation of the process by a frst-order system with dead time. Remark that this guideline is based on open loop dynamics.

This guideline gives an upper boundary, but does not say a thing about the lower boundary. Corripio [4] says that sampling too fast makes no sense, because conirol performance does not improve much when the sampling time is r e d u d beyond one tenth of the time constant. So do not choose the sampling time too low when this is not necessary.

8


As mentioned before many guidehes for sampling time selection are available. Mostly the deadtime is small compared with the time constant. Independent of the dead time, Guideline (3.4.1) can safely be simplified to:

At < 0.05 z (3.4.2)

Au guidelines pretend when being used, the performance of sampling and digital control is not significantly worse than for continuous control. This indn-ectly implies that sampling affects the performance and stability negatively.

3.5 Sampling Time Selection fm Closed Leep Systems

The sampling time selection is mostly determined by the control performance. Before investigating how control performance can be aflècted by digital communication, someîhmg must be said about performance and what signifcantly different performance is. Performance and significantly dfierent performance are ambiguous, so a measure for the performance and a criterion for significantly different performance have to be defined. The definition of control performance according to Marlin [ 11 is:”Control performance is the ability of a control system to achieve the desired dynamic responses, as indicated by the control performance measures, over an expected range of operating conditions.” Measures of control performance can be determined in many ways.

In this report integral of the absolute value of the error (IAE) is chosen as indeation of control performance. This measure is chosen because it is based on the error whch can easily be calculated from measurements and other creterions are not significantly better. Mathematical operations as taking the absolute value and integrahg are simple operations. The IAE can clearly be visualized in a plot of the IAE versus the time. For a system with no offset the IAE converges to a constant. These constants can easily be compared.

Integral of the Absolute value of the Error: rn

IAE = S[SP(t) -PV(t)ldt O

(3.5.1)

In this report significantly different controi performance is deked as; control performance is significantly daerent when the IAE’s of the situations to compare differ more than 5 to 10 percent.

Systems with digital control are closed loop systems. In closed loop systems the time constant of the system is influenced by controller pameters. If the time constant of the closed loop system differs &om the time constant of the open loop system guidelines 3.4.1 and 3.4.2 have to be used meidly or need to be adjusted. In closed loop systems controller gain, integration time and derivative time affect the performance and stability of the process. Dependant on the performance and stability more or less destabilisation can be allowed before getting significant different control performance. This is shown by a first order process with a time constant of 3 seconds and no dead time with several PI-tunings in Figure 3.5.1.

9


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 ts [sec]

Figure 3.5.1 Drfference in IAE between continuous and discrete control

From Figure 3.5.1 it appears that Guideline 3.4.1 is not correct for any tuning, because the difference in IAE can be significant for t, smaller than 0.05 * z (O. 15). So the dflerence in IAZ strongly depends on the t"ng parameters. A guideline for closed loop systems based on process and tuning parameters is needed.

3.6 Influence of Tuning Parameters on Contrd Performance

A generally applicable guideline for any tuning of a closed loop system is difficult to give, because several parameters affect the performance of the closed loop system. In this report is tried to fmd a guideline for first order processes with no dead time. The guideline must be able to be used for simple controllers as P, PI and PID controllers. So it will be based on the same starting point as used for guideline 3.4.1; the performance of the digital controller does not signit;cmtly diner Erom the performance of the continuous controller. This criterion can be expressed in the difference in LAE of both controllers; the sampling time selection is acceptable when the relative error of the IAE, see Equation 3.5.5 islessthan0.05 toO.lO.

Relative error of IAE = (IAE( discrete) -LAE(conîinuous)) (3.6.1) IAE (continuous)

Soit is important to know how the IAE is aflècted by dead time, sampling, controller gain, integration time and derivative time.

Controller gain

For a first order system with no dead time controlled by a PI-controller the IAE decreases when the controller gain increases, see Figure 3.6.1

10


O 2 4 6 8 10 Controller gain

Figure 3.6.1 hfîuence of controller gain on the control perfomance for a fxst order process (z = 1) with no dead time controlled with a PI controller ( zi = i)

Dead time and sampling

Adding dead time to t h e w order system with a time constant of 1 second or sampling this system results in a different dependence between controller gain and IAE, see Figure 3.6.2.

o 2 3 4 5 6 7 8 Controller gain

Figure 3.6.2 Influence of dead time or sampling on the control performance for a first order process (z = 1) controlled with a PI controller ( xi = 1)

Two things can be seen in Figure 3.6.2. First the IAE of the system with dead time or sampling has a minimm far a certain controller gain. Second the IAE of the system with dead time or sampling is not significantly dBerent from the IAE of the system with no dead time till a certain value of the controller gain is passed. So when the controller gain is lower than a certain value for a given process, the performance between the continuous and discrete controller is not sigmñcantly different. Whithout other significant influences a guideline for the maximum controIler gain for a given process can be formulated. Because this is the maximum for the optimal tuning, this can be called the optimal controller gain setting. Other possible innuences are integral and derivative control action.

11


Integral control action

As mentioned the integral control action infiuences the control performance. The integral action is the controller gain divided by the integation time. In Figure 3.6.3 the relative error of IAE (Equation (3.6.1)) is plotted against the controller gain.

Ccntroíler gain

Figure 3.6.3 Influence of controller gain on the control performance for a fvst order system (z = 1) controlled with a PI controller

From Figure 3.6.3 it appears that the lower the integration time becomes, the lower the optimal controller gain setting becomes before getting sisnificantly dflerent mntrol performance. The fact that controller gain and integration time both influence the control performance requires an assumption for the integration time. To make an assumption for the integration time, the dependence of the integration time is plotted in Figure 3.6.4.

1.61

, ~~ __._.. ~ ..........................

!

:- continu&Us process witb no &ad time .i .__...__.._...___._..._._____.__... I ................................... ............................... --. .~ Contin&us process with d d time ( id= i)

o 5 10 25 20 0.4 '

Integration time

Figure 3.6.4 Influence of integration time on the control performance for a fxst order system (z = 1 O) controlled with a PI controller ( K, =2)

From Figure 3.6.4 it appears that for a greater integration time than the time constant of the process, the difference

12


between a process with dead time and a process with no dead time is not significant. It also appears that the control performance is good for an integration time that is equal to the time constant of the process and does not improve much for decreasing integration time. This statement also counts for sampling, because sampling can be seen as an additional time delay.

So for the integral control action the following assrunption can be made; when the control performance of continuous and discrete control are not sipfkantly different for an integration time equal to the time constant of the process, the control performance of continuous and discrete control will not be significantly different for a higher integration time than the tiXe coristant of the process. h integation t i i e eqa l to the ikze constant of the process is chosen ôs limi< because for an integation time equal to the time constant of the process a good control perfomance is achieved.

Derivative control action

Derivative control action is used when the process estimated by a first order process with dead time has a dead time. These can be fust order processes with dead time or higher order processes. When the estimation of the process has no dead time, the derivative control action improves the paformance of the discrete case and will decrease the performance of the continuous case compared with only PI-control. So the derivative control action must be examined for processes with dead time. This makes the situation more compley now the pdormance depends on controller gain, sampling time, integration time, derivative time and dead time. How the control performance depends on the derivative time for the continuous and discrete case is plotted in Figure 3.6.5

0 0.5 1 1.5 2 2.5 Derivative time [sec]

Figure 3.4.5 Muence of the derivative time on a first order system with dead time. K, = 5, z = zi= 13 and dead time= 3.

In Figure 3.6.5 the derivative time for the continuous case is not increased more than 1.7 seconds because then simulations become unreliable. For the discrete case is the derivative time not increased more than 2.3 seconds, because then it is already shown that the discrete case has an optimum too.

The only conclusions that can be drawn &om Figure 3.6.4 are that both cases have an optimum at a different derivative time and this optimm for the discrete case is at a higher derivative time. It is ambiguous to say that for adding derivative control action to the controller the difference in control performance decreases or increases. The difference in control performance for derivative control action is determined by controller gain, integration time, derivative time, sampling time, dead time and time constant In combination with the fact that no assumptions can be made for the derivative time and dead time, d e h g a guideline based on two parameters, time constant and sampling time, is not possible. The best alternative for a controller with derivative control action is to use the guideline determined for PI controllers.

13


All actions together

From the previous only for a PI controller it is clearly possible to determine a guideline for the optimal controller gain setting. For this guideline the assumption has to be made that the integration time is not larger than the time constant of the process. For a P controller the IAE does not converge to a constant value, because of the absence of integral control action. For a P controller the guideline for the PI controller is used too, with the assumption that the control performance is affected for a P controller in the same way as for a PI controller.

Derivative controi is only added when the estLï&m ofthe process by a frst order process with dead tine h a ;? dead &ze. This dead h e is additional parameter that affects the control performance. Besides this, with derivative action the optimal tuning setting has more interaction So the controi performance becomes dependant oîmore parameters. This additional complexity makes it impossible to determine a simple guideline for a controller with derivative control. Using the guideline based on PI control for controllers with derivative control implies that the deerence in control performance is not guaranteed to be not significantly different.

So for PID control a guideline for the optimal controller gain setîing can be given based on a fist order process with no dead time with PI control with an integral time not larger than the time constant of the process. For PI control the difterenee between discrete and continuous control will not be sigmficantly different. For P, PID and PD control this difference can not be guaranteed to be not significantly Merent.

14

4 Guideline for HART Protocol in DDC

4.1 Introduction

From the previous chapter it seems diacult to formulate a guideline for closed loop systems that is applicable for any tuning. Chapter 3 also showed that the performance of the closed loop system controlled by an analog or digital controller is not sigaUicantly Merent until1 the controller gain crosses a certain value. From now this certain value is called the optimal controller gain setting. A useful guideline for the optimal controller gain setting can be determined for a fkst order process with no dead time and PI control. For the HART protocol sampling h e and dead time are fixed and known which simphñes determining a guideline. The shift time that the HART protocol can produce for a controller that uses severai measmements CXI Ge neglecied aad is expected tû be iìeglected.

4.2 Theoretical Optimal Controller Gain Setting

Guideline 3.4.2 is used as a base for the theoretical approach of a guideline for a PI controller of an open loop system. The thought is that this guideline can be expanded by multiplying it with a function dependant of the controller gain. Guidehe 3.4.2 is a guideline for the samphg time selection. The sampling time, At, can be considered as an additional time delay.

additional time delay = At I2 (4.2. i)

With guideline 3.4.2 this gives:

2 * additional time delay < 0.05 z (4.2.2)

When the sampling time is written as an additional h e delay, the time delay of the HART protml can be added to &us additional time delay of the sampling.

additional time delay = 0.5 * At + time delay (4.2.3)

For the HART protocol At is equal to the number of devices times THART (0.5 seconds) and the time delay is equal to THART In combination with Equation 4.2.3 this gives:

additional time delay = 0.5 * n * 0.5 + 0.5 = 0.25*( n + 2 ) (4.2.4)

Equation 4.2.4 and 4.2.2 give:

z >5*n+ 10 (4.2.5)

This is a guideline based on the time constant of an open loop system. For the closed loop it is assumed that guideline 4.2.4 has to be modified by multiplying it by a function of the controller gain. The additional time delay decreases for increasing controller gain, so guideline 5.2.4 has to be multiplied by a function of (I/ Kc), f (I/ K,). This gives:

z*f(l/K,) >(5*n+10) (4.2.6)

f (I / K,) can not be determined analytically and will be determined practically in the next section.

4.3 Practical Optimal Controller Gain Setting

f (1 /KJ is determined by simulating a frst order system with no dead time and a PI controller. In each simulation the integration time is equal to the time constant. The only parameters left are the controller gain (Kc) and the number of devices (E). The optiz121 ccntroller gain setting is r e d x d fclr a difference in contro! perSomance of about 5 to 10 percent.

15

4 Guideline for HART Protocol in DDC

Assume f (1/ IQ is al %. From simulation a appears to be not a constant value and appears to converge to 2, see Table A. 1.1. Thus, this is no good guideline. A better guideline can be found by leaving the dead time out of Equation 4.2.6:

z *f (UKc) > 5% (4.3.1)

From simulations, Appendix A. 1, f (I/ K,) appears to be K,. Thus Equation 4.3.1. can be written as:

‘G K,( optunal) - 5 *n

(4.3.2)

With this Equation the optimal controlIer gain setting is calculated for fist order processes with dserent time constants and the HART protocol. These processes have been antrolled with a PI controller and the calculated optimal controller gain setting. The results of these simulations are shown in Appendix A.2. These results show that the difference in control performance is about 5 to 10 percent when using Guideline 4.3.2 for the optimal controller gain setting. So Guideline 4.3.2 is a useful guideline for the optimal controller gain setting of a PI controller.

4.4 Remarks

Guideline 4.3.2 is a guideline detennined €or a very idealized situation. The processes considered are fist order processes with no dead time. In practice higher order processes can occur as well as first order processes. A higher order process can be estimated as a fvst order process with dead time. In literature guidelines valid for first order process are asmd to be valid for higher order processes estimated as a first order process with the same parameters. Dead time is also a well-known phenomenon in process industry. For a process with dead time a PID controller is mostly used. As mentioned before the difference in performance can not be guaranteed to be not significantly different.

Most processes contain non-linearities. Such non-linearities as limitation of controller output, vake limitations or equipercentual valves are not considered. Presence of these non-linearities make it not possible to guarantee the difference in control performance to be not significantly different.

Syrichronsation of the controller with the HART protocol is not needed, because Guideline 4.3 2 counts also for a dead time of 1 second. So the only requirement of the synchronisation between controller and HART protocol is that the controller performs at least 1 calculation per sample time. Otherwise the optimal controller gain setting is lower than determined with Guidehe 4.3.2, because then the sampling time is determined by the cyclus time of the controller that is higher than n*OS seconds.

16

5 Applications

5.1 Laboratory Experiments

An experimental design, called the vessel, is built to investigate the HART protocol. This experimental design exists of a vessel with several measurements and two control valves, see Figure 5.1.1.

Y ” I I

Hot

@-

@ @ (E$

Flow 1

Valve 1

Vaive 2

Figure 51 .1 Schematic representation of the vessel

This experimental design has the possibility that several process values can be controlled. The control part is implemented in a PLC. However the experimental design was not fintshed in time, so no experiments has been done.

This experimental design is small in size and values compared to real processes in process industry. Time constants of temperature, level and valves are small compared to time constants of real processes. The time constant of the valve in the experimental design is about 0.1 seconds. A valve in process industry has a time constant of 1 to 3 seconds. So when processes in the experimental design cause no problems with HART and control, no problems will occm in similar processes in plants.

5.2 Simulations with Sirnulink

This vessel is also modelled and implemented in SIMULINK for both continuous and discrete case. Controllers are selected, modelled and attached to this model to control several values of the vessel. In the discrete situation the discretisation is modelled to be the HART protocol and the sampling time can be variable. Simulations for the discrete and continuous case with this model are compared to ven@ Guideline 4.3.2.

5.2.1 Modelling the Vessel

The vessel can be suEciently modelled by solving the mass and energy balance of the vessel. Equations 5.2.1.1 and 5.2. I .2 give the general mass and energy balance.

General mass balance

d(pV) = piF,- pjFj dt iïnlet j:outlet

(5.2.1.1)

17

5 Applications

General energy balance

+ + = ~ i F i - PjFj - Q - Ws

dE d(U+K+P) _ - dt dt tiniet j:outlet

(5.2.1.2)

Mass balance of the vessel

The densiîy of the water in the vessel does not d8er much due to different temperatuïes. Thus the density G f the xateï ui the iil- tìiìd catlet flc~ws a d U; the wsse! C ~ E be corsiderrb pnlld. -3-

pvessei c p % p c p 5 p 1 2 3

The density of the water can even be considered constant in time.

d p = * at

With these assumptions the mass balance of the vessel is:

dh dt

A- = F, +F2-F3

Energy balance of the vessel

The total energy of the liquid in the vessel is:

E = U + K + P

But since the vessel does not move, dK/dt = dF'/dt = O and dE/dt = duldt. For liquid systems,

(5.2. I .3)

(5.2.1.4)

(5.2.1.5)

(5.2.1.6)

(5.2.1.7)

Where H is the total enthalpy of the liquid in the vessel. Furthermore,

H = p VcP (T - Tref) = p Ahc, (T - Tref) (5.2.1.8)

With these assumptions ((5.2.1.3) and (5.2.1.4)) and if TZef is equal to zero, the following energy balance of the vessel is derived:

(5.2.1.9)

Filling in Equation 5.2.1.5 gives:

18

5 Applications

F, +F, A -F3 Tvesiei+h---- *Tvessei - - ;T,+-T F2 --T F3

dt A 2 A 3 (5.2.1.1 O)

With Equations 5.2.1.5 and 5.2.1.10 The vessel is modelled in SJMULINK, see Appendix B. 1.

5.2.2 Control PossibiIities

__ lhe vessei has severai vaiues that can be controlled in severai ways. Güideline 4.3.2 is deteïìììiiìec! foï sLq!e PIC! controllers. Some possible P D controllers are applied to the model of the vessel. Feedforward control is a control that can not be expressed in a controller gain. However fèedforward control in combination with feedback control is applied to the vessel. Advanced controllers are not applied because Guideline 4.3.2 is determined for simple, most common, ControIlers.

The following ControIlers are implemented to apply Guideline 4.3.2. No derivatice control action is added because all processes to control are first order processes with no dead time. And the optimal controller is in the continuous case.

Feedback control

Feedback control can be represented as shown in Figure 5.2.2.1.

PV Process

Figure 5.2.2.1 Feedback control

The feedback controls applied to the vessel are; temperature, level and flow control. In the situation of Figure 5.2.2.1 the process value (PV), is the controlled value (CV).

Temperature control

Temperature control is a PI controller. The CV is the temperature ofthe vessel and the MV is the position of valve 1, see Figure 5.2.2.2.

Flaw 1

Cold r 1

7 I Vdve 1

Figure 5.2.2.2 Temperature control of the vessel

19

5 Applications

Level control

Level control is a PI controller. The CV is the level of the vessel and the MV is the position of valve 2, see Figure 5.2.2.3.

I I

Vessel I SP

I L 2- Flow3

valve 2

Figure 5.2.2.3 Level control of the vessel

Flow control

Flow control is a PI controller. The CV is flow 3 and the MV is the position of valve 1, see Figure 5.2.2.4.

I ‘I 7

valve 2

Figure 5.2.2.4 Flow control of flow 3

Cascade control

A special case of feedback control is cascade control. Cascade control is a control existing of two feedback controllers. These two controllers are called master and slave controller. The master controller gets its setpoint external and provides the setpoint of the slave controller, see Figure 5.2.2.5.

Figure 5.2.2.5 Cascade control

20

5 Applications

A cascade control with level control as master and flow control as slave is applied to the vessel, see Figure 5.2.2.6. The master controls the level of the vessel and the slave controls flow 3.

I - Flow3

Valve 2

Figure 5.2.2.6 Cascade control for the level of the vessel

Feedforward control

Feedforward is based on the fact that disturbances are detected before they can affect the process, so control action can prevent these disturbances to affect the process, see Figure 5.2.2.7.

Figure 5.2.2.7 Feedforward Control

Only feedforward is not applied to the vessel. However, feedforward in combination with feedback control is applied. The chosen feedtlorward control is ratio control.

Ratio control is a special type of feedforward control. In ratio control two disturbances are measured and held in a constant ratio to each other. Realizing a certain temperature in the vessel can be done by satis-g to:

From this ratio flow 1 can be calculated:

(5.2.2. i)

(5.2.2.2)

The calculated flow 1 is the setpoint for the flow control, see Figure 5.2.2.8.

21

5 Applications

Ratio ca lda t i on & SP(fl0W 1)

+, valve 1

Figure 5.2.2.8 Ratio and feedback control

5.2.3 Simulation Results

The control possibilities described in the previous section are implemented in SIMCTLINK for the continuous and discrete case, see Appendix B.2, B.3 & B.4 Judging from simulations with this models Guideline 4.3.2 is verified. The plots of the results of the simulations are in Appendix C.

The initial values of the model are chosen equal to the values of a steady state situation of the temperature and level. The steady state value of the level is set to 0.7 m. The other parameters are calculated to realize steady state of flow and temperature, see Appendix B.4.

In Guideline 4.3.2 the optimal controller gain setting is based on the time constant of the process and the number of devices connected to the multidropline. So the time constants of the model are important.

First order processes with no dead time can be represented as follows:

Kp TPS + 1

H(s) = - (5.2.3.1)

Where zp is the time constant of the process.

Level control

The level seems a pure integrator and no time constant can be determined.. However, flow 3 depends on the square root the Ievel of the vessel and linearizing at h, results in a first order process for the level of the vessel. Then the level time constant of the vessel will be:

(5.2.3.2)

The controller gain is set to 10, because the time constant is expected to be large. From Equation 5.2.3.2 the time constant of the level at this steady state appears to be about 3000 seconds and the integration time is set at 3000. At a

22

5 Amlications

n

time of 50 seconds the level setpoint is changed from 0.7 m to 0.8 m. The level responds as shown in Figure C. 1. For the setpoint-change of the level, flow 3 is manipulated as shown in Figure C.3. As expected the temperature does not change, see Figure (2.2, because the inlet Bows are Constant.

IAE ( discrete} - IAE (contirnious ) optimal controller gain setting

IAE( continuow)

The results for the discrete case are almost the same. For a sampling time of 20 seconds the flow is plotted in Figure C.5. The difference between discrete and continuous case must be found by comparing the IAE of both cases. However nothmg can be said about the difference in IAE of discrete and continuous case, because for both cases the IAE has no constant value at 5000 seconds. The development of the Merence in IAE of a first order process with constant time ccnstant is shown in Figure C.7. It is not to say if the dBerence in IAE is larger or smaller-, because this development can not be plotted. The development can not be plotted because the number of datapoints of both simulations are not equai. Simulating for a longer period to get a coïìstaat M is not possible, became d m m h g o& of memory for larger simulations.

Plotting the IAE for the continuous case, see Figure C.8, the IAE seems to be close to a constant value. Thus the difFerence in IAE at 5000 seconds will not M e r much from the final difference in IAE. Some differences of IAE are plotted in Table 5.2.3.1.

Table 5.2.3.1 Difference in IAE for level control

In spite of the controller gain being smaller than the optimal controller gain setting, the difference in IAE is sigdkant for n is 30 and 40. This occurs because the integration time is not always larger than the time constant. This is due to the fact the time constant depends on the position of the valve. The valve position is zero for a period and in this period the integration time is significantly smaller than the time constant which is infiite. However the maximum number of devices connected to a multidropline for the HART protocol is 15. For 15 devices the dlfference in IAE is acceptable. So remembering îhat the experimental design has small time constants compared to processes in plants, the HART protocol can be applied for level control.

This all is for a setpoint-change. Normally process value must be held on a setpoint and then the valve position does not vary much and the Guideline satisfies.

Temperature corztroi

The temperature time constant of the vessel can be derived -from Equation 5.2.1.1 0:

Ah T~ (temperature) =

F, +F2-F3 (5.2.3.3)

The controller gain is set to 10. The controller gain is chosen that high because the time constant is also expected very high. The time constant ofthe temperature of the vessel depends on all three flows, see Equation 5.2.3.3. The temperature is conîroiieci by one flow, so rhe time constant changes constantly. h the steady state sitdatioiì &e + h e constant would be infinite, because (fi + f2 - f ) is zero. The integration time is set 2000 seconds. The time constant of the temperature for the controlled situation is plotted in Figure C. 12. Directly can be seen that most of the time the

23

5 Amlieations

integration time is smaller than the time constant.

The temperature of the vessel is plotted in Figure C.10. The temperature is controlled by manipulating flow 1. By manipulating flow 1, the three flows are out of balance and the level changes, see Figure C.9. Flow 1 is plotted in FigureC.11.

For the temperature the IAE’S of the discrete case and continuous case do also have no constant value. And the same assumption as for the level can be made gom Figure C . 13 ; the difference in IAE at 1 O000 seconds will not differ miich &OE the fad eerenCe in M E For a sampling time of 20 seconds (n=40) the dinerence of IAE at 10000 seconds is 4.2 %, in spite of the integration time being smaller than the time constant for much of the time. But the optima: controolieï gain s e ï í g increases wiit iiìcïeasig &ie ~ ~ ~ ~ t t i i i t , bUt then the integration t i e becomes relatively smaller. The IAE normally converges to a constant and in the beginning the difference is the largest. In this situation the integration time is larger than the time constant in the beginning. From 2000 seconds the integration time is too small compared with the time constant and this results in an oscilating flow 1, see Figure C.14. This oscilating can be undesirable and starts at about a sampling time of I5 seconds (n=30). This results in an undesired behaviour of the temperature, see Figure C. 15.

This undesirable behaviour starts &om 30 devices which is double the number that can be maximally attached to a multidropline. Together with the fact that the experimental design has small time constants compared to processes in plants, the HART protocol can be applied for temperature control.

For flow control the time constant is the time constant of the valve. This time constant is exactly known and is O. 1 second, which is for a fast valve. The integration time is also set to 0.1 seconds, to satisfy to the fact that the integration time must be equal to or larger than the time constant of the process. The controller gain is set to 1, because the time constant is small.

The flow to control is flow 3. At 10 seconds the setpoint changes &om steady state flow to 90 percent ofthat value. In the continuous case the flow reacts as shown in Figure C. 16. In the discrete case the flow is already unstable for a sampling time of 0.5 seconds. This was to be expected according to Guideline 4.3.2, the optimal controller gain setting is 0.02.

For the flow is searched for a combination that satisfies to Guideline 4.3.2. For ‘ure time eonsWL is chosen 3 seeods. 3 seconds is chosen because this is the time constant for a Iarge valve. For a sampling time of 0.5 seconds the optimal controller gain setting would be 0.6. With these values the discrete and continuous case are compared. For 0.5 seconds the difference in IAE is neglectible. A sampling time of 3 seconds give a difference in IAE of about 8 percent. So for a sampling time of 0.5 seconds the controller gain can be increased. For a controller gain equal to 3 together with a sampling time of 0.5 seconds, the difference is 3 percent and for a sampling time of 1 second equal to 17 percent.

So a controller gain of 5 times the optimal controller gain setting gives no sigiitficantly different control performance. The question is where this factor comes &om. The only difference between a first order process are valve characteristic and the dependence of the level. In other words the process gain depends on the valve position and level.

24

(5.2.3.4)

(5.2.3.51

5 Applications

So the optimal controller gain setting for this situation can be about 5 times the optimal controller gain setting calculated from Guideline 4.3.2. The effect of reaching the maxunUm valve position is still not considered and this effect is not known.

For small valves as used in the experimental design the HART protocol can not be used in DDC. For large valves with an equiperentual charcteristic, the HART protocol can be used in DDC, but the controller gain and the number of devices connected to the muitidrop line are smdl. For large vaives with a linear characteristic the HART protocol can not be used in DDC. So the HART protocol is not suitable to use in flow control, because the situations it can be used are exceptional cases.

Cascade Control

The master controller is a level controller. This is a P controller with a controller gain op 1. The slave controller is a flow controller. This flow controller is a PI controller with an integration time of O. 1 second and a controller gain of 1. The controller gain is chosen not to high because of the small time constant of O. 1 second.

In the continuous case the level is stable for a setpoint-change from 0.7 m to 0.8 m, see Figure C. 18. Sampling with 0.5 second (n=l) results in an unstable behaviour, see Figure C.22. This is expected because the controller gain is higher than the optimal controller gain setting for the slave. In cascade control both controllers must satisfy to Guideline 4.3.2. When the time constant of the slave was 5 seconds the optimal controller gain setting is 1 and the behaviour is stable, see Figure (2.23.

Ratio Control

Ratio control is nothing else than a PID controller that gets its setpoint &om a calculation based on other values. In this case the ratio control must keep both inlet flow in a ratio to realize a desired temperature in the vessel. The flow controller has a controller gain of 1 and a integration time of 0.1 second. For the continuous case the desired behaviour is realized, see Figure C.26. In the discrete case with a sampling time of 0.5 second (n=l), the flow becomes unstable as expected according to Guideline 4.3.2. The effect on the temperature is not plotted because the simulation runs out of memory before the temperature significantly changes. The effect of the unstable behaviour of the flow will probably not be seen in the temperature, because the temperature has a relative high time constant.

5.3 Correctness of the Guideline in Applications

From simulation with a model of the vessel in SIMULINK Guideline 4.3.2 appears to be a usefull guideline when having a known constant time constant. For changing time constants that become very large and the integration time is not equal to or larger than the time constant the Guideline can not be used. This is can be explained, because for the integration time the assumption is made that the time constant is equal to or smaller than the integation time. Guideline 4.3.2 is for first order processes with no dead time, so nothing is said about nodinearities. However some non-linearities such as for flow control with a valve with an equipercentual characteristic can be linearized and the effect can be expressed in a different real controller gain.

So the HART protocol can not be used for flow control, because large valves have a time constant of 3 seconds which results in a optimal controller gain setting of 0.6 when one device is connected. Normally controller gain of 1 to 5 are used. For processes with large time constants the HART protocol can be used when the optimal controller gain setting satisfies to Guideline 4.3.2 and the integration time is nearly always larger than the time constant of the process.

25

6 Conclusions and recommendations

6.1 Conclusions

For first order processes with no dead time it is possible to formulate a guideline, (4.3.2), that determines when the tunings of a PI controller for the continuous case can be used in digital control with the HART protocol with no significantry different control performance. This guideline is a guideline for the optimal controller gain setting and is based on the number of devices connected to the multidrop line and the time constant of the process to control with the assumption that the integration time is equal to or larger than this time constant.

'p1 i ne ';iK;IT protoed can be üsed UI DDC fûï pïûcesses with h g e c~nstmts. So !eve! md tempaz@m .,̂ ??trol give no problems in DDC with the HART protocol. The HART protocol can not be used for flow control, because time constants of valves in plants are too small.

6.2 Recommendations

The guideline, (4.3.2), is verified for simulations with a model in SIMULINK. No experiments are done with the experimental design in the laboratoq. Because flow is the only control that gives no good behaviour with HART protocol, it is useful to investigate flow control and HART protoCO€ at the experimental design.

26

References

[i] [2] [3]

[4]

Marlin, T.E., Process Control, McGraw-Hill, 1995 Seborg, D., T. Edgar, and D. Mellichamp, Process Dynamics and Control, Wiley, New York, 1989 Fr&, G., J. Powell, and M. Workman, Digital Control of Dynamic Systems (2nd Ed.), Addison-Wesley, Reading, MA, 1990 Corripio, Armando B., Tuning of Industrial Control Systems, ISA, 1990

27

Appendix A - Simulations for a Guideline

a - 5n n K

A.1 Simulations to Determine a Guideline

Relative error K C ( t S ' 2 t d J 0 f - E [%] a =

0.05~

In these simulations the process is a first order process with no dead time is controlled with a PI controller. The integration time of the controller is equal to the time constant of the process and the controller output is not limited. The control pe&ormance of the continuous case is compared with the discrete control performance. In the discrete case the HARS protocol is uesd which imposes samphg time and time delay. The sampling time of the HART protocol is n"0.5 seconds, where n is the number of devices connected to that multidrop line. For safety the time delay of the HPLRT protocol (tae) is chosen 2"realtime delay.

8.2 Validation of the Guideline

Guideline 4.3.2 has to be validated. This is done by aplying this guideline to first order systems with different time constants. These process have been controlled with a PI controller. The integation timeof the controller is equal to the time constant of the process. For this validation counts the daerence in control performance between the continuous case and the discrete case. In the discrete case the sampling time and a time delay imposed are by the M T protocol. The time delay is equal to the real time delay (0.5 seconds) of the HART protocol now.

28


n

Table A.2.1 First order process witb a time constant of 1 O seconds

Relative error of IAE [%I z K = _

5n

8

11

7 0.0086 2.3

0.0075 2.0

0.0055 1.5

I 15 I 0.004 1.1 I Table A.2.2 First order process with a time constant of 0.3 seconds

29


2

- 1 0.2 4.8

0. I 1 5.4

15 0.013 2.0 Table A.2.3 First order process with a time constant of I seconds

n Relative error

of IAE [“hl z K = _ 5n

I 1 I 0.6 I 4.9 I 2

3

0.3 5.1

0.2 5.2

11 0.055 4.2

Table A.2.4 First order process with a time constant of 3 seconds

15

30

0.04 3.7

Amendix A - Simulations for a Guideline

1 2.8 6.3

i 2 I 1.4 i 5.4

3 0.93 4.7

4 0.7 4.9

1 7 I 0.43 I 5.2

8 0.35 5.0

12 0.23 4.9

15 0.19 4.9 Tabie A.2.5 First order process with a time constant of 14 seconds

Relative error of IAE [%] z K = _ n

5n ~~

I 1 I 10 I 5.9

2 5 5.7

4 2.5 5.5

~

0.67 4.9 Table A.2.6 First order process with a time constant of 50 seconds

31


Table A.2.7 First order processes with several time constants

32

Appendix B - Implementation in Sirnulink

B.1 Model of the Vessel

B.1.1 The Entire Vessel

This is a model of the cornplete vessel. Piping resistance and dynamics of measurement devices are not taken into account, because piping resistance and the dynamics of the measurement devices are not known. Controllers are considered in Appendix €3.2 and discretisation in Appendix B.3.

Figure B. i. i. i gives the ShíLuIE\l block ofthe complete vessel Iri the cmtinüoüs case wit level cûï~kû!. The variable parameters of this model and the following models are defined in VAT-PAR.M and explained in Appendix €3.4.

Pcold

pmsure

To Workspace

I vahe 1

Mode14 IeYel ietpoint?

V I

I e tempembim model

Figure B.l.l.l SIMULDIK block of the vessel

B.1.2 Model of the Level of the Vessel

The level of the vessel can be described as Equation . Equation is implemented Ui S&lUL,IMK as shown in Figure B.1.2.1.

I

I: in-3

Integrabr $%2 - Area

I

Figure B.1.2.1 SIMIJLINK block of the level of the vessel

The in- yid out-ports can be read &om Figure B. 1.1.1 ;

in-1 = flow 1 in-2 = Bow 2

33

Appendix B - Implementation in Simulink

in-3 = flow 3 Out-3 = level of the vessel (h)

The saturation is implemented so the level can not exceed real values. The lower bound is set to 0.05 m to avoid numerical problems for the temperature model (uses Ik). The initial level is defined in the integrator with the initial value ho.

The temperature of the vessel can be descrilied as Equation . Equation is implemented Figure B.1.3.1.

SlMUJINK as shown i?

Figure B.1.3.1 SIMULINK block of the temperature of the vessel

The in- and out-ports can be read from Figure B. 1.1.1 ;

in-1 = " 2 = in-3 = in-4 = in-5 =

in-7 = in-6 =

ou t3 =

temperature of flow 1 temperature of flow 2 temperature of flow 3 (assumed to be equal to the temperature of the vessel) flow 1 now 2 Row 3 level of the vessel temperature of the vessel (T)

The initial temperature is defuied in the integrator with the initial value TO.

B.í.4 Model of a Valve of the Vessel

The vessel has two valves which position can be used as manipulated variable. Both valves have an equiprocentual characteristic:

(l3.1.4.1)

34


Where

f(x) = R, @. 1.4.2)

The dynamics and valve characteristic are implemented as shown in FigureB. 1.4.1.

Look-Up Table

I

Figare B.P.4.? SIMCTLINK block of a valve of the vessel

The switch is used to describe the valve correctly for small valve position. Otherwise the valve would Ieak ( RA(- l)*Fcn i) instead of not l e h g .

Sometimes the valve has to start with the correct flow. This can not be realized with a Transfer Fcn and the first order dynamics has to be built with a SIMULINK block as shown in Figure B.4.2.

I I Figure B.4.2 SIMULINK block of first order process with initial value

This SIMULINK block contains an integrator, that can be provided with an initial value.

B.2 Control

B.2.1 Control Possibilities

First the control possibilities are shown for the continuous case. The continuous PID controller and the ratio block are shown after the control possibilities.

Temperature Control

The temperature control of the vessel is implemented in SIMIJLINK as shown in Figure B.2.1.1.

35


vas 1 1 I M@d3 lwei sapim

'igure B.2.1.1 Temperature control ofthe vessel

Level Control

How the level control of the vessel is implemented in SIMULINK is already shown in Figure B. I . 1.1.

Flow Control

The flow control for the outlet flow is implemented in SIMULINK as shown in Figure B.2.1.2.

- cior

1

%gure B.2.1.2 FIow control for the outlet flow

36

Appendix B - Implementation in Sirnulink

Cascade Control

The cascade control is implemented in SIMULINK as shown in Figure B.2.1.3. The level control is the master and theflow control is the slave.

I I I I I

'igure B.2.1.3 Cascade control

Ratio Control

The ratio control is implemented in SIMSJLINK as shown in Figure B.2.1.4

t si6rppnI I II I I

1

'igure B.2.1.4 Ratie cmtrd

37


B.2.2 Ratio Block

In the ratio block is the setpoint calculated for flow 1, according to Equations 5.4.1 and 5.4.2. This is impplemented in

I

0-n

Figure B.2.2.1 Ratio block in SIMüLINK

B.Z.3 The Continuous PID Controller

The PID controllers can be represented as shown in Figure B.2..3.1.

I

control performance

PID controller in-2 w with initial value

Sum

I PigiaSe B.2.3.1 PID controller (continuous)

This representation is the same for the discrete and the continuous case. Only the PID block will be a discrete PID block for a discrete controller.

in-i = setpoint in-2 = measured value out-1 = controller output

The PID algorithm for the continuous case is shown in Figure 2.3.2.

38

Anaendix B - Imalementation in Sirnulink

I

2 + -

DI integrator

1 Figure B.2.3.2 PID controller (continuous)

The D proceeds the derivative block, the I the integrator and the P stands alone. In the integrator the initial value for the controller output is set.

B.3 Discretisation with the HART Prsto-ocol

Discretisation with the HART protocol is the same as adding a time delay of 0.5 seconds and sampling the values from and to the controller with a ZOH. In Figure 3.1 is this shown for the cascade control.

I l o I I

T O

Figure B.3.1- Discrete cascade control

In the transport delay block must be the correct initial value inserted. In this case this is the value of the steady state value ofthat signal.

The discrete PID algorithm is almost the same as the continuous algorithm, see Figure 3.2.

39


El- in-i

i

-43 out-I

Gain2

Figure B.3.2 P D controller (discrete)

In the discrete time integrator the initial value is set to the initial controller output

B.4 Initialisation and Parameters of the Modd

Initialisation and parameter declaration takes place in the MATLAB file vatpar.m. In this file all values rue explained.

% initial values

ho = 0.7; % basin level

% general settings

% accuracy

tend = 5000; mis = le-12; mas = 2el; tol = le-10; % tolerance n = le6;

% stop time % minimum stepsize % maximum stepsize

% maximum number of datapoints

% basin

AV = 0.23; hlow = 0.05; hhigh = 1 .O;

% basin area % minimum level % maximum level

% constants

rhow = 998; g= 9.81;

T1= 10; T2 = 20;

% density of water at 20 degrees % gravity constant

% temperature cold water % temperature hot water

40


'YO valve 1, output

cvout = (17.2/3600)/1.17; R1= 50; linl= 1Rl; tau1 = 1 .Oe- 1 ; f3max = cvout*sqrt(rhow*g*hgh* le-5);

% Cv(max) valve-out (m"31s) % relation between valve position and flow, f = RI "(x- 1) % lower than lin valve is linear % tau of valve dynamics (first order) % maximum flow-out

% valve 2, inpit

Pcold = 5.5e5; cvin = (1.2/3600)/1.17; R2 = 50; lin2 = 1 m ; tau2=0.1; v2 = .5;

% presure ciinrerence (in Fa) % Cv(max) valve-in (mA3/s) % relation between valve position and flow, f = E"(x-1) % lower than lin valve is linear % time constant valve 2 (first order) % input valve for steady state

% flow in

F1 = 0.5; % Bow cold water (50 % open) F2 = 0.5; % flow hot water (50 % open) flmax = 1000*(1/3600)*(1/1000>; % maximumumflow 1 Qmax = 100*(1/3600)*(1/1000); % maximumum flow 2

% controller settings temperature

Pt = -10; % P-value It = Pt4f2000; % I-value Dt = Pt*O; % D value

% controller settings level

P1= 10;

D1= P1*0; n = ~2/2000;

% controller settings flow

Pf= 1*1e3; If= PYO. 1 ; Df = PPO;

% Cascade control

Pcm= l*le-3; Icm = O; Dcm = O;

Pes = l*le3; ICs = Pcsl. 1 ; Dcs = o;

% HART-protocol

th = 0.5; nn= 1; ts = nn*th;

% P-value % I-value % D value

% P-value % I-value % D value

% P-value master % I-value master % D-value master

% P-value slave % I-value slave % D-value slave

% transport time HART % number of devices on the multidrop line % sampling time

41

Annendix €3 - Imdementation in Sirnulink

% initializing valves

fì2 = F2*Qmax; ffl = (R2"(V2-l))*cvin*sqrt(Pcold*1e-5);

% real flow 2 % real flow 1

Lci = (log((ffl+ff2)/(cvout*sqrt(rhow*g*hO* le-S}))/log(R1))+1; VI =Lci; Tci = 0.5;

Bset = ffl+m; Fci = Lci; Csi = Fci; Cmi = f3set;

% steady state input valve 1 % initial value IC = steady state input valve 1 % Equal to V2

% steady state value for ffl & ff2 % initiai vaiue fc = initial value ic % initial value CC slave = initial value IC % initial value cc master = steady state flow 3

% setpoints

tstep = so; h e t = 0.8;

% step time, can be modified in block (0.2"tstep) % level setpoint

TO = (TI *fn+T2*ff2)/(ffl+B}; Tset = 13; ra = ((T0-20}/(10-T0));

% steady state temperature for h0,fi ,f2 & f3 % temperature setpoint % initial value ratio

42

Appendix C - Simulations of the Vessel

In this appendix the results of some simulations of the model with SIMLTLINK are shown.

........... ._ .....

............ : _ _ _ _ ........

.........................

............ i_____ ......

.........................

O 1 O00 2000 3000 4000 5000 Time [SI

0.68

Figure C. 1 Leve! of the vessel for continuous level control

Figure C.2 Temperature of the vessel for continuous level control

43


1.2

1

-0.8 c E o I

0.6

- z lL

0.4

o .2

I

O i O00 2000 3000 4000 5000 Time Is]

O

Figure C.3 Octlet flow f=f rcntinuous level control

t-

I

0.2 ..

O O i 200 400 600 800 1000

Time [s]

Figure C.4 Outlet flow for continuous level control (zoomed in at O - I O00 sec.)

44


Time [SI Figure C.5 QGtlet flow fo? discrete ievel control ( ~ 3 0 )

Time [SI Figure C.6 Outlet flow for discrete level control (n=30, zoomed in at O - 1000)

45


K=.1 ,Ti=l O,Tau=IO,ts=lO -

...... P .......

.......

.......

O 100 200 300 400 500 600 700 800 Time [SI

Figure C.7 Developmeat of the difference in IAY for a first order process with aPIcontroller(z= 1O,Kc= l ,z ,= 10,ts=0.5)

20

18

16

14

12

2 10

8

6

4

2

O I

1 O00 2000 3000 4000 5000 Time [s]

Figure C.8 IAE of the level of the vellel for level control (continuous)

46


0.8

0.7

0.6

- ED.5 - al > 0; 0.4

0.3

0.2

................

................ \

..................

........... ~~ , ....

.......

.......

.......

.......

......

......

..... i

......

.............

.............

....................

....................

.....

.....

.....

.....

i I I

10080 0.1

O 2000 4000 6000 8000 Time [SI

Figure C.9 Level of the vessel for CQ~~~IIUOUS tenperature contrd

47


...........

O 2000 4000 6000 8000 1 O000 Time [SI

Figure C. 11 Wet flow for continuous temperriture control

48


3000

2500

2000

2 1500

IO00

500

Q

cc

............ :. ...........

.....................

....................

............ :.__ .........

.........................

2000 4000 6000 8000 10000 Time Is]

Figure C.13 L4E of fie temperature of the vessel for coatixu~xs temperature co~t1-01

............ j ................. ..

I I I

O 2000 4000 $000 8000 10000 -0.5'

Time [SI Figure C.14 Inlet flow for discrete temperature control (n=40)

49


Figure c.15 Temperature of the vessel for discrete temperature control (n=40)

50


.........................

.........................

....................

...................

.........................

....................

I

0 10 20 30 40 50 0.98’

Time [s]

Figure C.16 Outlet flow of the vessel fer contimow BOW control ( z = O . ~ , K C = ~ O , Z , = O . ~ , 100%-90%)

51


.....................................

I

5000 0.68'

O 1 O00 2000 3000 4000 Time [SI

Figure C.18 Level of the vessel for continuous cascads control

O I O00 2000 3000 4000 5000 Time [SI

I 1

Figure C.19 Temperature of the vessel for continuous cascade control

52


'.*I-- ..... .:. ...........

........................

........................

...... .:. ...........

....................... .......................

- O 1 O00 2000 3000 4000 5000

Tíme [SI Figure C.20 Ottlet flow cf the vessel for contimoius casczde cmtfol

i

O 1 O00 2000 3000 4000 5000 -0.2 '

Time [SI Figure C.21 (ûutlet flow - SP)/outlet flow, for continuous cascade control

53


0.8 ........

o . 8 2 ~ .......

.......

.......

.......

.......

~-.rl .............

...............

.......

.. ......,...

................

...............

.......

.......

.......

_ _ _ I .....

.........

.........

.......

.............

..........

.............

.......

038 O 500 1000 1500 2000 2500 3000 3500

Time [s]

Figure C.22 Level of the vessel for discrete czscade control (z (va1ve)=0.l,ts=0.5)

I

............ : _ _ _ _ ..................................

............ : _ _ _ _ _ .................................

...................................................

......

..................... ....,.........................

O 1000 2000 3000 4000 5000

Figure C.23 Level of the vessel for discrete cascade control (z (valve) = 5, t, = 0.5)

54

Amendix c - Simulations of the Vessel

................

............

........

........... _ ?

...............

........... .:

.............

.............

.......

.......

.......

.......

.......

.......

.......

.......

........................

......................

........................

........................

.......................

........................

........................

........................

L

O 1 O00 2000 3000 4000 5000 Time [SI

Figure C.24 Outlet flow of the vessel for discrete cascade control (z (valve) = 5, ts = 0.5)

-0.4‘ o 1 o00 2000 3000 4000 5000 Time [SI

Figure C.25 (outlet flow - sp)/outlet flow, for discrete cascade control (z (valve) = 5, t, = O 5)

55


3 O 1 O00 2000 3000 4000 5000

Time [SI Figure 6.26 Met flow of fie vessel for ccntiriuous ratio control

9

6.5

6

5.5

- 5 A

.g 4.5 2

4

3.5

3

2.5

........................

.........................

.........................

.........................

.........................

.........................

. ........................

.... .....................

............ :_ .....

O I O00 2000 3000 4000 5000 2

Time [s] Figure 6.27 Ratio for continuous ratio control

56

7

6

5

4

3

2

1

O

-1

I

O 200 400 600 800 1000 1200

Figure C.28 Inlet flow of the vessel €or discrete ratio control (n=l>

7

6.5

6

5.5

Ï 5 - .g 4.5

c4

3.5

3

2.5

- ...

...

...

...

...

...

...

...

...

2 O 200 400 600 800 1000 1200

Time [SI Figure C.29 Ratio for discrete ratio control (n=i>

57

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