pid controller design,tuning and troubleshooting
DESCRIPTION
Lecture notes on how to design, tune and trouble shoot a proportion integral derivative controller.TRANSCRIPT
PID Controller Design, Tuning and Troubleshooting
Disturbance responses for a close loop system
Disturbance responses for nine combinations of the controller gain and integral time for a first order + time delay simple close loop system.
Aggressive response
Aggr
essiv
e re
spon
se
Performance criteria for closed-loop systemsIdeal performance criteria
β’ The close loop system MUST be stableβ’ Effect of disturbances are minimized,
providing good disturbance rejection.β’ Rapid and smooth response to the set
point changesβ’ Steady state error (offset) is eliminatedβ’ No excessive controlβ’ Control is robust. Insensitive to changes in
process conditions and to inaccuracies in the process model.
Performance
Robustness
Performance criteria for closed-loop systemsPerformanc
e Robust
Kc -> lowI -> large
Reasonable degree of model inaccuracy
Wide range of conditions
Smooth responses
Rapid response to changes
PID Controller settings
Techniques
β’ Direct Synthesis method (DS).β’ Internal Model Control method
(IMC).β’ Controller tuning relationsβ’ Frequency response techniquesβ’ Computer simulationβ’ On-line tuning after control system is
installed.
Computer simulation
Model Based Design MethodsDirect Synthesis Method π
π π π=
πΎππΊππΊπ£πΊπ
1+πΊππΊππΊπ£πΊπ
πΊβπΊππΊπ£πΊπ πΊπ=πΎπ
ππ π π
=πΊππΊ1+πΊππΊ
What is ?
πΊπ=1πΊ ( π /π π π
1βπ /π π π)
Model Based Design Methods
Lets see some options for
πΊπ=1πΊ ( π /π π π
1βπ /π π π)
A desired transfer function is used to make the problem simpler.
πΊπ=1~πΊ ( (π /π π π )π
1β (π /π π π )π )
( ππ π π )π=
1ππ π +1
πΊπ=1~πΊ
1ππ π is the desired closed-loop time constant
Direct Synthesis Method
Model Based Design Methods
Lest see some options for
( ππ π π )π=
πβππ ππ π +1
πΊπ=1~πΊ
πβπ π
ππ π +1βπβπ π is a term to include the time
delay
Direct Synthesis Method
πΊπ=1~πΊ
πβπ π
(ππ+π ) π
Model Based Design MethodsDirect Synthesis Method
Lets derive controllers for two important process models
First Order Plus Time Delay Model
πΊ=~πΊ=
πΎπβππ π π +1
πΊπ=1~πΊ
πβπ π
(ππ+π ) π
πΊπ=1
πΎ πβπ π π π +1
πβπ π
(ππ+π )π
πΊπ=πΎ π(1+ 1ππΌ π )
πΎ π=1πΎ
ππ+ππ
,ππ=π
Model Based Design MethodsDirect Synthesis Method
Lets derive controllers for two important process models
Second Order Plus Time Delay Model
πΊ=~πΊ=
πΎπβπ π
(π1π +1 ) (π2π +1 )
πΊπ=1~πΊ
πβπ π
(ππ+π ) π
πΊπ=πΎ π (1+ 1π πΌ π
+ππ·π )
πΎ π=1πΎπ1+π2π+ππ
π πΌ=π1+π 2 ππ·=π1π2π1+π2
Model Based Design MethodsDirect Synthesis Method
Example: Use DS method to calculate the PID controller settings for the process. Consider three values of the desired closed loop time constant
πΊπ=πΎ π(1+ 1π πΌ π
+ππ·π )
πΎ π=1πΎπ1+π2π+ππ
π πΌ=π1+π 2
ππ·=π1π2π1+π2
πΊ=2πβ π
(10π +1 ) (5 π +1 )πΊβπΊππΊπ£πΊπ
πΊπ=1~πΊ
πβπ π
(ππ+π ) π
Model Based Design MethodsDirect Synthesis Method
Example: Use DS method to calculate the PID controller settings for the process. Consider three values of the desired closed loop time constant
πΊ=2πβ π
(10π +1 ) (5 π +1 )
3.75 1.88 0.682
15 (1/15)* 15 (1/15)* 15 (1/15)*
3.33 3.33 3.33
=3.75=1.88
=0.682
Model Based Design MethodsDirect Synthesis Method : The problem with this method is that we need to guess
If the system can be simulated by then
1. and
Model Based Design Methods
πΊπ=πΎ π (1+ 1π πΌ π
+ππ·π )
ON-Line Controller TuningZiegler and Nichols (1942). Paper βContinuous cycling methodβ this is a trial and error method
1. After process reaches steady state, eliminate the integral and derivative control actions. and (large value).
2. Set to a small value. Then set the controller in automatic.
3. Introduce an small set point change. Gradually increase until a sustained oscillation with constant amplitude occurs. This value of is called Ultimate gain. The period of the oscillation is the ultimate period,
4. Use the table to calculate 5. Evaluate the system by introducing a small set point
change. You may need fine tunning. Lower
Zeigler-NicholsP 0.5 --- ---
PI 0.45 ---
PID 0.6
πΊπΆ=πΎ π (1+ 1π πΌ
1π +π π·π )
ON-Line Controller TuningUse the Ziegler and Nichols method to tune the following system
ON-Line Controller TuningUse the Ziegler and Nichols method to tune the following system
1. After process reaches steady state, eliminate the integral and derivative control actions.
ON-Line Controller TuningUse the Ziegler and Nichols method to tune the following system
2. Set to a small value. Then set the controller in automatic.
3. Introduce an small set point change. Gradually increase until a sustained oscillation with constant amplitude occurs. This value of is called Ultimate gain. The period of the oscillation is the ultimate period,
.0
πΎ ππ’=10
ON-Line Controller TuningUse the Ziegler and Nichols method to tune the following system
4. Use the table to calculate
Zeigler-NicholsP 0.5 --- ---
PI 0.45 ---
PID 0.6
π πΌ=0.5ππ·=1/8
πΊπΆ=πΎ π (1+ 1π πΌ
1π +π π·π )
ON-Line Controller TuningUse the Ziegler and Nichols method to tune the following system
5. Tune the controller trial and error if it is necessary
πΊπΆ=πΎ π (1+ 1π πΌ
1π +π π·π )
ON-Line Controller TuningDisadvantages
1. It is time consuming.2. There are many applications where this system do not
work as expected. In case of a chemical reaction it may cause a βrunawayβ.
3. It is not applicable to unstable systems.4. For first and second order models the ultimate gain do
not exist.
ON-Line Controller TuningProcess Reaction Curve Method
1. After process reaches steady state2. Place the system in manual mode3. Adjust the controller out put signal to the values that
were working in automatic mode.4. Wait for steady state5. Introduce an step change in set point.6. Record the response of the variable as shown in the
plot.7. Return the controller to the initial values.8. Calculate the new set up of the parameters according
to the table.
Zeigler-NicholsP --- ---
PI ---
PID 0.5
Model Based Design MethodsTuning with Matlab
Example:
πΊ=2πβ π
(10π +1 ) (5 π +1 )
Model Based Design MethodsTuning with Matlab
Example:
πΊ=2πβ π
(10π +1 ) (5 π +1 )
Model Based Design MethodsTuning with Matlab
Example:
πΊ=2πβ π
(10π +1 ) (5 π +1 )
WorkshopNow you have time to solve the following question
WorkshopUse the Ziegler and Nichols method and the curve response method to tune the proportional, proportional integral and PID controlled systems indicated below. Compare your results with the tuning results calculated by using Matlab.
πΊ=2
(π +2 ) (0.18 π 2+0.6 π +1 )
πΊ=2πβ 2π
(10π +1 ) (5 π +1 )