Practicalities of Digital Control

A Survey

The Overall System

• The individual controllers• The interconnection• The central computer or computers• The transducers and actuators

The individual controllers

• P L C• General-purpose controllers• Purpose-built

More on the P L C

• Probably still ‘ladder logic’ -- good for on-off control but cumbersome for analogue --but ...

• Can incorporate analogue I/O• Can often include p.i.d. controller blocks and

routines in high-level languages• Most modern PLC types can be interfaced to

a SCADA system

Traditional example -- Mitsubishi F1/F2

• Basically ladder logic• Can do analogue quantities, but awkward• Good at on -- off control• An analogue ladder example follows• More modern networkable PLCs will be

described in a later lecture

General-purpose Controllers

• Most common type is PID but other strategies possible

• Parameters can be changed/downloaded by/from SCADA system

• Self-tuning types becoming more popular but care is still needed in their use

• Less good at on-off than the PLC• Better at ‘analogue’ control

DSP Possibility

• Can be based on DSP Chips• Very fast micros optimised for multiply-

and-add ... the sums of digital control• Some can operate in floating-point• Serial interface to I/O

How fast shall we sample ?

• Shannon/Nyquist Theorem -- we must sample at least twice the highest frequency present if we are not to lose information

• Actually we need to sample faster than this to avoid aliasing and because of noise

• 10 - 20 x highest frequency of interest is usual

Why ?

• Less than 10 x means it is difficult to produce an effective anti-aliasing filter

• More than 20 x leads to a double penalty ...• We have to do the sums faster ...• ... and more accurately if they are to work !• But what is this aliasing thing ?

Suppose we sample this signal every 14 s

0 20 40 60 80 100-10

-5

0

5

10

x

x

x

x

x x

x

“I’ve got aliasing, doctor.”

• We have ‘found’ a sine wave of much lower frequency than the actual one.

• The system may be able to respond to the lower frequency one ...

• ... even if the original was too fast for it to respond to.

“I’ll give you a prescription for ...”

• Some effective screening (the high-frequency signal is likely to be the mains or Radio 1/2/3/4/5/etc)

• An analogue low-pass filter on the inputs

The anti-aliasing filter

• Has to be analogue (it would itself be at the risk of aliasing if it were digital !)

• It must not appreciably affect signals within the normal frequency range of the controller but it must effectively remove everything above half the sampling frequency.

• The faster we sample, the easier it is to remove the aliasing signals.

A Sampling-rate Example

• Controller 0.1s + 1 +2/s• We have already digitised with a sampling

interval of 0.05 s• We will see what happens with 0.25 s ...• ... and 0.01 s. • Using the simple substitution.

We obtain with Ts = 0.25 s ...

• 1.9 - 1.8z-1 + 0.4z-2

• -----------------------• 1 - z-1

• This one causes very serious degradation of performance -- if not actual instability

What is happening ?

• The problem is that by sampling we are producing a Transport lag

• We remember from Analogue Control that a Transport Lag is a pure time delay ..

• ... and that it reduces system stability by increasing the phase lag in the loop.

• We introduce one by sampling ...

What is happening -- Continued

• ... because an event happening during a sampling interval is only detected at the next sampling instant.

• So the delay in detecting it can be anything between zero and a full sampling interval ..

• .. so it is Ts/2 on average.• This is the effective extra transport lag

introduced by sampling.

...So let us use Ts = 0.02 s ...

• 11.02 - 21z-1 + 10z-2

• ---------------------------• 1 - z-1

• If we do not do the sums very accurately, we entirely lose the integral term !

Ts = 0.02 s .. A Consequence

• We will lose the integral term entirely if we use 8-bit arithmetic.

• I will do the sum ...• ... in which we are only allowed integer

numbers between 0 and 255 (or probably between -128 and +127 in practice)

Interconnection

• Multi-line bus (VME etc)• Parallel or serial• Two-wire (FIELDBUS etc)• Systems often combine hardware and

software

Analogue Interfaces

• Voltage ranges (often 0 -> 10 V or -10 -> 10 V)

• Current loop (usually 4-20 mA)• So e.g. for 8-bit, 4 mA converts to 0 and 20

mA converts to 25510

• What would the values be for 12 and 16 bits ?

Arithmetic

• Now normally floating-point within the controller

• Fixed-point arithmetic is still used in some low-cost (often mass-produced) equipment

• It saves hardware cost but incurs extra development time

• Input and output are still fixed-point

Precision

• 8-bit I/O restricts us to 0-255 decimal• 12-bit often used in ‘good’ systems

Supervisory Control -- SCADA

• Central computer (or network) connected to local controllers, PLCs and data loggers

• Data recording as well as control -- often now with an economic process optimisation overtone

• Central control of parameters and setpoints but the local controllers and PLCs do the actual controlling

SCADA Continued

• Often able to do statistical analysis on the data collected

• Especially ‘trending’ to see if quantities are changing when they should be constant (or vice versa)

SCADA Continued

• Upmarket PCs often used now instead of minis/mainframes/workstations

• Examples follow ....

First -- just a PLC !

• Canal-lock control panel• Controlling two sets of gates and ..• ... two sets of paddles.• Needs to detect gate position and water

level on each side (done via pressure)• Hydraulics to operate gates and paddles

Again not SCADA -- Disk Head Drive

• Linear motor plus drive electronics• Must be fast, so DSP chip used• Position feedback from format track pattern

on disk

A Glassworks

• Central Computer -- high-spec PC (duplicated)

• “Hot End” -- GP Controller for zone temperatures and feed + PLC for batching

• “Cold End” -- PLC (mostly on-off)• Transducers -- mostly of the “on-off” type

apart from temperature

Transducers

• Analogue then A - D ...• or...• ... direct to digital

Example -- Position or Angle

• We can use a potentiometer or LVDT• to give a voltage dependent on the position

or angle to be measured• then digitise it

Position or Angle -- Continued

• Or we can use a Gray-coded disc or strip to give a digital reading directly.

Precision

• The control is only as accurate as our measurement of the quantity being controlled

• Our transducer must be accurate enough to fulfil the specification

Timing

• Interrupts• Real-Time Clock• Watchdog Timer

Real-Time

• Operating System or Language ?• Hierarchy of interrupts• Solves the sampling-interval problem• May need an arrangement for immediate

action in the event of problems during an interval

• Local or central ?