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EEB5213 / EAB4233 Plant Process Control Systems
Digital Implementation of PID Controller
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Objectives
At the end of this lecture, students should be able to: identify digital application in process control
computation and signal transmission program PID algorithm in digital controllers select a proper execution rate for a digital PID
controller
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Digital Feedback Control
Digital controlcalculation
D/A andhold
Sampleand A/D
4 - 20 mA
Process
Digitalvalue
Digitalvalue
mV
Thermocouplein thermowell
4 - 20 mA
Compressed air
3 - 15 psi
TTI/P
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Digital Control Digital control employs a distributed control network
(DCS).
D/A D/A
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Benefits of Distributed ControlFeature Effect on process control
Calculations performed in parallel by multiple processors.
Calculations are performed faster.
Limited number of controller calculations performed by a single processor.
Control system is more reliable since a processor failure affects only few control loops.
Control calculations and interfacing to process are independent of other devices connected to LAN.
Control is more reliable since failure of other devices does not immediately affect a control processor.
Small amount of equipment required for the minimum system.
Only the equipment required must be purchased and the system can be easily expanded.
Each type of processor can have different hardware and software.
Hardware and software can be tailored to specific applications like control, monitoring, operator console and general data processing.
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Digital Control
The techniques presented will be applicable for digital sampling and control calculation. Transmission can be either digital or electronic.
Periodically, the measurement is sampled and a calculation is performed.
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Digital Control - Sampling
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Digital Control - Sampling
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Digital Control - Sampling The last sampled value is kept constant between
control executions by using zero-order hold.
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Digital Control - Sampling The red line is the continuous approximation of the
signal after the sample & hold. This shows that the effect is to introduce a “dead time” of about t/2.
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Digital Control Performance What is the effect of digital execution of the PID
controller on tuning and performance ?
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Digital Control Performance
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Digital Control TuningGuideline for selecting execution time To prevent degradation of control loop performance,
select a controller execution time / sampling period of
Note: Typical sampling period for chemical process control is 1/3 – ½ sec. Much faster is possible, if needed.
)(05.0 t
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Digital Control Tuning Steps to tune a PID digital controller using open-loop
tuning methods:
1. Obtain process model.
2. Determine the sampling period or maximum execution period, t 0.05( +).
3. Recalculate new dead time, ’ = + t/2.
4. Applying the new dead time, ’, calculate PID tuning constants using any of the open-loop tuning methods used for analog PID controller.
5. Implement and fine-tune as needed.
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Digital Control Tuning
Let’s apply this guideline for the three-tank mixer with a long sampling period = 15 min.
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Digital Control Tuning
The performance is about as good as possible with the very long sampling time ! Would you fine-tune further ?
Tuning from chart
KC = 26
TI = 13
TD = 0.8
IAE increased from 12.2 to 20+
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Discrete PID Controller
The measured CV is sampled, giving values of CV1, CV2, CV3,........,CVN.
How would we estimate each mode of the PID controller in discrete equations ?
Idt
tdCVTdttE
TtEKtMV
t
D
I
C
0
)(')'(
1)()(
Proportional
Integral
Derivative
? ? ?
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Discrete PID Controller
The measured CV is sampled, giving values of CV1, CV2, CV3,........,CVN.
Idt
tdCVTdttE
TtEKtMV
t
D
I
C
0
)(')'(
1)()(
Proportional
Integral
NCalproportionN
NNN
EKMV
CVSPE
)(
N
ii
I
CintegralN E
T
tKMV
1
)(
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Discrete PID Controller
The measured CV is sampled, giving values of CV1, CV2, CV3,........,CVN.
Idt
tdCVTdttE
TtEKtMV
t
D
I
C
0
)(')'(
1)()(
Derivative
t
CVCVTKMV NNDCderivativeN
)(
)( 1
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Discrete PID Controller – Bumpless Transfer
Bumpless transfer: No change to the MV when controller first executed
Idt
tdCVTdttE
TtEKtMV
t
D
I
C
0
)(')'(
1)()(
Initialization / Bias
t
CVCVTEKMVI dc
)( 0111
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Types of Discrete PID Algorithm
Positional form or full-position algorithm of digital PID calculates the actual controller output to the final element at each execution.
ICVCVT
TE
T
tEKMV NN
dN
ii
I
NCN
)( 1
1
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Types of Discrete PID Algorithm
Velocity form of digital PID calculates the change in the controller output at every execution.
NNN
NNNd
N
I
NNCN
MVMVMV
CVCVCVT
TE
T
tEEKMV
1
211 )2(
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Digital Control If the PID controller performs no better in its digital
form, why did we spend decades in engineering time and billions of dollars converting the world’s process control to digital?
Complex controllers - Improved performance can be achieved with algorithms that optimize the path to the set point, every controller execution!
Process monitoring – We have digital history of measurements for:a) Troubleshootingb) Calculation of process performance indicators eg. reactor yield, energy efficiency per kg of product etc.c) Excellent graphical display
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What Next ?
Next Lecture : Practical Implementation Issues for PID Controller (Marlin, Chapter 12)