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 ?