Proceedings of the 8th

World Congress on Intelligent Control and Automation July 6-9 2010, Jinan, China

978-1-4244-6712-9/10/$26.00 ©2010 IEEE

Simulation of System Identification and Decoupling Control of Rotary Lime Kiln System *

LUO Xian-xi1.2.3 YUAN Ming-zhe1 and WANG Hong1 1.Key Laboratory of Industrial Informatics, Shenyang

Institute of Automation, Chinese Academy of Science, Shenyang, Liaoning Province, China

2.East China Institute of Technology,Nanchang , Jiangxi Province, China

3.Graduate School of the Chinese Academy of Science, Beijing,China Luoxx@sia.cn

1.Key Laboratory of Industrial Informatics, Shenyang Institute of Automation, Chinese Academy of Science,

Shenyang, Liaoning Province, China Mzyuan@sia.ac.cn

* This work is supported by a grant from the National High Technology Research and Development Program of China (863 Program)（No.2008AA042901）

Abstract: Lime is an important smelting raw material for iron& steel plants. Most of large and medium-scale iron& steel enterprises have their own lime works for self-supply. Reasonable control for the lime kiln is significant to reduce energy consumption and improve the pass rate of lime quality. In this paper, the model described in literature is applied to simulate the actual operating conditions of rotary lime kiln. The method of step response is adopted to identify the object with two inputs (the fuel flow rate and damper position) and two outputs (the temperatures in the front and the end of the kiln) into a first order, strong coupling linear system model and the validity of the model is verified as well. On the basis of the identified model, we design a decoupling controller. The simulation results show that the controller can accurately track the instructions to the temperatures at the front and the end of the kiln respectively with high stability and control accuracy. The method and conclusions of this paper may provide reference to the design of lime kiln combustion control system.

Index Terms- Lime Kiln, System Identification, Decoupling control

I. INTRODUCTION

Iron and steel production process consumes a lot of active lime as a supplementary raw material. Many steel companies have their own lime kilns to produce active lime. The implementation of reasonable control of lime kiln will effectively reduce energy consumption in the lime production process, improve the passing rate of final product, and thus improve the quality of steel, iron and steel products. It can also improve the economic performance and reduce pollutant emissions [1].

According to different structural characteristics, Lime kiln can be divided into rotary lime kiln and vertical gas firing kiln [2]. The control systems of different kilns vary a lot. However the overall of the control systems can be divided into feeding materials, discharging lime, combusting, cooling, cleaning dust, hydraulic station control sections. The object researched in this paper is the combusting control section of the rotary lime production process. The rotary lime kilns in iron& steel plants are fuelled with blast-furnace gas (BFG), coke oven gas (COG) or the mixture of different gases [2]. The kilns are heated to high temperature

and the raw lime stone begin to discompose into CaO(active lime) and CO2 . The temperatures of the front and the back of the kilns are controlled by the combusting control system. The performance of the control systems is vital to the consumption of energy and the passing rate of active lime. A rotary lime kiln is shown in Figure 1.

Fig. 1 The picture of rotary lime kiln

The schematic of lime kiln is also shown in Figure 2. There are two main manipulators: the fuel flow rate and the air flow rate at the entrance (the right side of figure 2). The fuel flow rate is controlled by control valve and the air flow rate is controlled by a damper. The target of the combustion control system is to regulate the temperatures at the front and the back of the kiln accurately within a certain range according to the production demands [3].

Fig. 2 Schematic diagram of lime kiln

Rotary kiln is important industrial equipment, and many related modelling and optimization control methods can be found in different literatures in China or abroad. References [3] [4] adopted the method of neural network to set up models

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and described the model with S function which can run in Matlab. Reference [5] model and optimize the system based on testing exhausted gases concentration, such as CO. Reference [6] established the static model of a lime kiln. Reference [7] [8] applied hybrid control and expert system to control lime kiln. These methods have positive meaning in improving the quality of lime production, reducing energy consumption. This paper studies the S-function model established by [3], using decoupling control method so as to achieve the closed-loop control on the temperatures of both sides of rotary lime kiln.

II. ROTARY KILN SYSTEM IDENTIFICATION AND MODEL VALIDATION

A. The Premise and Conditions Set for the Study Reference [3] has given the S-function code of the model of rotary lime kiln. This article assumes that the model can correctly describe the Kiln’s actual working conditions. This assumption is the starting point of the article. It is necessary to explain that even if the model and the actual working conditions are not fully fit, the presented method can also be useful. Because the model contains the object delay, coupling and coupling characteristics of the actuator, it is difficult to design a suitable controller directly from any descriptive models to achieve control targets. Therefore, we have to approximately identify the system into a linear system model, so the controller to the approximate linear system can be designed with the methods of linear systems. The problem of kiln temperatures closed-loop control can be successfully resolved. The S function model is treated as a “black box” to be identified, as shown in Figure 3.

Fig. 3 Rotary Lime Kiln to be identified

From the figure we can see that the input variables of the

temperature control system of rotary kiln are the fuel flow rate and the damper position. Here, “u1” denotes the real fuel flow rate relative to the percentage of full flow rate, and “u2”denotes the percentage of the damper opening. The outputs of the system are the front temperature “T_fr” and the back temperature “T_bk.”

According to the information of production operating, the kiln has a balance operating point, namely: When [u10, u20] =[0.5, 0.5], [T_fr0, T_bk0] =[2225, 425]. Rotary kiln operation is performed in the vicinity of the point. Therefore, the linear object recognition may wish to use this point as the reference point for the establishment of an incremental mathematical model. Each variable is defined as:

1011 uuU −= (1)

2022 uuU −= (2)

0__ frTfrTTf −= (3)

0__ bkTbkTTb −= (4)

In this way, input and output variables are defined as the increment to the physical quantity of the balance point.

B. System Identification Method

If we assume that the relationship of the four variables of the system to be identified can be approximated as a linear time-invariant systems near the equilibrium point, we can describe the system with the transfer function matrix D (S).

)()()( sUsDsT = (5)

In the equation: TT

bf sUsUsUsTsTsT ))(),(()(;))(),(()( 21==

They denote the Laplace Transform results of the input and output variables, respectively.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

)()()()(

)(2221

1211

sDsDsDsD

sD (6)

In order to determine the transfer function matrix D (s), we have designed two experiments.

The first experiment is to keep U2 = 0 (i.e. u2 = 0.5), U1 = 0.5u (t) (i.e. u1 step 0 to 1 at the time of 0 second). The experimental results (simulation) are shown in Figure 4.

Fig. 4 The temperature curves whenU1 (t) = 0.5u (t), U2 (t) = 0

After the simulation, the precise data of T_fr (t) and T_bk (t) corresponding to time “t” can be seen in the workspace. These data can be transformed to increment data to the equilibrium point in accordance with equation (1) - (4) So, we get:

Tf (∞) = 165 (i.e. T_fr (∞) = 2390); To reach stable 65% of amplitude, the corresponding time is 35 seconds;

Tb (∞) = 34 (i.e. T_bk (∞) = 459); To reach a stable 65% of stable amplitude, the corresponding time is 5 seconds.

The trends of the curve can be approximated with first-order elements. In accordance with the characteristics of first-order elements, we can derive:

135330)(11 +

=s

sD (7)

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1568)(21 +

=s

sD (8)

The second experiment: to maintain the input U1 (t) = 0, U2 (t) = 0.5u (t), we can get the temperature curves shown in Figure 5.

Fig. 5 The temperature curves when U1 (t) = 0，U2 (t) = 0.5u (t)

According to the above methods we can derive:

12.4348)(12 +

−=s

sD (9)

13280)(22 +

=s

sD (10)

Till now, the transfer function matrix to express the mathematical model (5) has been worked out..

C. Model Validation

In order to verify whether the model identified out of the original system can describe the working process, we have designed a verification model diagram shown in Figure 6. The results of the simulation to the model with the S function and the identified model can be compared when they are inputted with the same signals.

Fig. 6 Block diagram to verify the identified model

We can take the slope signals for the test, 0.0025 increments per second for U1 and -0.025 for U2. When changes on U1 and U2 are not more than 0.5, the comparison of received waveform of T_fr with that of the identified model is shown in Figure 7, and the comparison of the waveform of T_bk is shown in Figure 8.

Fig. 7 Comparison of T_fr waveform and identified model waveform

Fig. 8 Comparison of T_bk waveform and identified model waveform

Through the test and analysis of the t waveforms, it can be deduced that the identified model can well reproduce the actual model. It confirms the validity of the identified model.

III DECOUPLING AND CONTROLLER DESIGN

From the equations (5) and (7) (8) (9) (10) , it can be seen that there are strong coupling relationship between the two inputs and two outputs. It is uneasy to design a suitable controller for such an object directly. Fortunately, there is an indirect method, which is decoupling first and later design. By decoupling, we can divide the object into two single input and single output (SISO) systems. Then we can design the controllers respectively.

Suppose there are a pair of input variables, R(s)=(R1(s), R2(s))T, and a diagonal matrix,λ(s)=diag(λ1(s), λ2(s)), furthermore:

)()()( sRssT λ= (11)

i.e. )()()( 11 sRssTf λ=

(12)

)()()( 22 sRssTb λ=

(13) By this way, the system changes into two SISO systems.

So the controllers can be designed. By equation (5) and (11) we can see;

)()()()( sRssUsD λ= (14)

Thus we can derive： )()()()()()( 1 sRsPsRssDsU == − λ (15)

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The input now is replaced by R (s), and we can transform R (s) into U (s) as shown in equation (15).

So, the decoupling matrix is： )()()( 1 ssDsP λ−=

(16) It should be pointed out that: a reasonable choice ofλ(s) is

very important, because the matrix P(s) must be physically achievable, or the degree of numerator polynomial of each element in the matrix should not higher than that of the numerator polynomial. Therefore, the design should take into account of the compromise between system simplification and realization.

Now we select properλ(s)according to the actual situation as follows:

⎟⎠⎞

⎜⎝⎛

++=

131

1351)(

ssdiagsλ

(17) This just can eliminate a factor section from each

numerator of the elements in the inverse matrix of D (s). After the final solution, we get:

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++++

++++

×++

=

1)5)(5s(21s48115)1)(21s(3s

36017-

1)1)(35s(5s24291)5)(5s(21s

367

403)6074s(15365s1)( 2sP

(18) The decoupling matrix can be described as figure 9：

Figure 9: Decoupling Matrix Diagram

If we combine this section with Figure 6, the system

would change to having the inputs of R1 (s) and R2 (s) and the outputs of Tf (s), Tb (s). And the system has been decoupled into two independent sections. According to equations (12), (13) and (17), we can see the new mathematical model of the system can be described by formula (19):

⎪⎩

⎪⎨

⎧

+=

+=

)(13

1)(

)(135

1

2

1)(

sRs

sT

sRs

T

b

sf

(19) After decoupling, the two sections of the system both are

first-order objects. Regulators are easy to design, and we can predict to gain a good performance system.

If we design the system into typical I-type system, all we need are two integrators, just as shown in figure10. That makes the system fast adjusting with no error. The parameters k1,k2 of the integrators can either be preset or tune according to the production demands.

The final design of the control system model block diagram is shown in Figure 10, and its equivalent block diagram shown in Figure 11.

Fig. 10 Block diagram of control system

Fig. 11 The equivalent block diagram of control system

IV SIMULATION OF THE DECOUPLING CONTROL SYSTEM

Suppose the instruction of the system changes from the balanced state [2225, 425] to the target state [2225, 445] on the 5th second, and to another target state [2245, 445] on the 100th second, we can see the results of simulation which are shown as Figure12.

Fig. 12 The simulation results of decoupling Control

We can compare the results with the PID control system

without decoupling (i.e. removing P(s) from Figure 10 and substitute PID controller for the integrators). We can tune the parameters of each PID carefully. However we can get no better results than which is shown in Figure 13.

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Fig. 13 simulation results of normal PID control

From the Figure 12 and the Figure13, we can get such

conclusions: 1) PID controlled system without decoupling has larger

fluctuation. It is difficult to accurately track the temperature changes of instruction. However, the decoupling control system can accurately track the changes in instruction. It can achieve the target state within 1 minute. The dynamic performance of the system is much better.

2) When the instruction of the back kiln temperature changes, there is attenuation of oscillation, and the period of time for the transition process is short. It’s an obvious second-order system response. The front Kiln temperature fluctuates with small-scale amplitude and damps out quickly.

3) The response to the instruction of the back kiln temperature is much slower. That is because this section has a larger time constant (35 seconds) in the design. We can adjust the parameter k1 for better performance.

4) When the back kiln temperature is regulated, the front kiln temperature fluctuations in a small range (the period of time from the 0 to 50th second). When the front kiln temperature is regulated, there is no obvious change on the back kiln temperature (from the 100th to150th second). In the ideal decoupling control system the two should not affect each other. It Occurs like Figure 12 because there is some error between the real system and the identified model. However, from the simulation results we consider the error is acceptable.

V CONCLUSION In this paper, rotary lime kiln and the kiln temperature

control problem has been studied. A model described by the S-function in Matlab is treated as a “black box” on behalf of real lime-kiln, and the method of step response is applied to identify the system with two inputs and two outputs. The mathematical model with a transfer function matrix is derived to describe system. Based on this model, we design a decoupling controller in accordance with decoupling control method.

Through the previous discussion we get the following conclusions:

Lime-kiln temperature control systems can be described with a first-order, coupled two-input two-output mathematical model.

Decoupling control method can effectively solve the lime-kiln burning controller design problems. The simulation results are excellent. The performance is much better than normal PID control.

The elements in the diagonal matrix λ(s) should be chosen properly. If the selection is too simple, the decoupling matrix would be a physically unachievable one.

The accuracy of identified model has impact on the performance of decoupling controller. So the identification error should be limited into a certain range.

The research method and conclusions of this paper can provide helpful reference to the combustion control system design of rotary lime kiln.

ACKNOWLEDGMENT This work was supported by a grant from the National

High Technology Research and Development Program of China (863 Program) (No.2008AA042901).

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