Practicalities of Digital Control

1
Practicalities of Digital Control

• A Survey

2
The Overall System

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

3
The individual controllers

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

4
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

5
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

6
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

7
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

8
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

9
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 ?

10
Suppose we sample this signal every 14 s
x
10
x
x
5
0
x
x
-5
x
x
-10
0
20
40
60
80
100
11
Ive 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.

12
Ill 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

13
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.

14
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.

15
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

16
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 ...

17
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.

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...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 !

19
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)

20
Interconnection

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

21
Analogue Interfaces

• Voltage ranges (often 0 -gt 10 V or -10 -gt 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 ?

22
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

23
Precision

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

24
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

25
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)

26
SCADA Continued

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

27
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

28
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

29
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

30
Transducers

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

31
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

32
Position or Angle -- Continued

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

33
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

34
Timing

• Interrupts
• Real-Time Clock
• Watchdog Timer

35
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 ?