1. Tuning of PID controllers
Course PEF3006 Process Control Fall 2018
Tuning of PID controllers
By Finn Aakre Haugen
PEF3006 Process Control. USN. F. Haugen. 2018

2. PEF3006 Process Control. USN. F. Haugen. 2018
Ziegler-Nichols'
closed loop method
PEF3006 Process Control. USN. F. Haugen. 2018

3. As fast control as possible, but with
Aim of tuning:
As fast control as possible,
but with
acceptable stability, i.e. ¼ decay ratio 3
Disturbance step:
A2/A1 = 1/4
Response in controlled
process output:
PEF3006 Process Control. USN. F. Haugen. 2018

4. Experimental setup in Ziegler-Nichols’ method:4
Experimental setup in Ziegler-Nichols’ method:
The PID controller is turned into a
P controller during the tuning
Oscillations with P controller
with critical controller gain, Kpu
PEF3006 Process Control. USN. F. Haugen. 2018

5. PEF3006 Process Control. USN. F. Haugen. 2018
Tuning procedure of Ziegler-Nichols’ method: 5
With controller in manual mode: Bring the process to the specified operating point by manually adjusting the control variable until the process variable is approx. equal to setpoint.
Turn PID controller into P controller with gain Kp = 0. (Ti = very large. Td = 0.)
Set the controller to automatic mode.
Increase gain Kp (you may start with Kp = 1) until there are steady oscillations in the loop due to a small setpoint step. This controller gain value is the ultimate gain, Kpu. Read off the period, Pu, of the oscillations.
Calculate controller parameters from the Z-N formulas:
Recommends "Relaxed ZN PI-tuning" (cf. article by FH og B. Lie in Modeling, Identification and Control):
Kp = 0,32*Kpu og Ti = Pu.
PEF3006 Process Control. USN. F. Haugen. 2018

6. Let’s try Z-N tuning of a PI controller on this simulator:6
Let’s try Z-N tuning of a PI controller on this simulator:
Temperature Control of Liquid Tank
PEF3006 Process Control. USN. F. Haugen. 2018

7. Repeated Ziegler-Nichols method (for PI contollers)7
Repeated Ziegler-Nichols method (for PI contollers)
PEF3006 Process Control. USN. F. Haugen. 2018

8. F. Haugen. Process Control. NMBU. 2018.
Assume that the PI settings are Kp0 and Ti0, and that the control system - unfortunately - has poor stability with these settings showing poorly damped oscillations with period Pu.
Improved PI setting can be obtained by applying ZN tuning assuming that these oscillations are true ZN oscillations:
Kp = 0.45Kp0
Ti = Pu/1.2
F. Haugen. Process Control. NMBU

9. Ex.: PI controller in simulated biogas control system
Original ZN
Repeated ZN
Big improvement!
F. Haugen. Process Control. NMBU

10. Let's try (assuming the initial PI tuning is with ZN):10
Let's try (assuming the initial PI tuning is with ZN):
Temperature Control of Liquid Tank
PEF3006 Process Control. USN. F. Haugen. 2018

11. (automatic PID tuning)11
Auto-tuning
(automatic PID tuning)
PEF3006 Process Control. USN. F. Haugen. 2018

12. PEF3006 Process Control. USN. F. Haugen. 2018
Example of auto-tuner: The Relay or On/Off tuner (by Åström and Hägglund). Sustained oscillations come automatically in control loop. From the amplitude and the period of these oscillations proper PID controller parameters are calculated by an algorithm in the controller.
Amplitude A
Amplitude Y
Period Pu
In Ziegler-Nichols’:
Use Pu and Kpu = 4*A/(pi*Y).
PEF3006 Process Control. USN. F. Haugen. 2018

13. Example: Relay-tuning of a PI temperature controller:13
Example:
Relay-tuning of a PI temperature controller:
Temperature Control of Liquid Tank
PEF3006 Process Control. USN. F. Haugen. 2018

14. PEF3006 Process Control. USN. F. Haugen. 201814
Skogestad's method
PEF3006 Process Control. USN. F. Haugen. 2018

15. simple step-response test on the process.
Skogestad’s method is a model-based method, but the model parameters may stem from a
simple step-response test on the process.
You must specify the time-constant Tc of the closed-loop system (illustrated below with setpoint step response):
tau is
process
time-delay
PEF3006 Process Control. USN. F. Haugen. 2018

16. Skogestad’s PI-tuning for a ”integrator with time-delay” process
Find model parameters K and tau from process step response
(or from a mathematical process model, if you have one):
(If time-delay is disregarded)
PI controller settings:
Kp = 1/[Ki*(Tc + tau)] = 1/(2*Ki*tau) if Tc = tau.
Ti = 2(Tc + tau) = 4*tau if Tc = tau.
Skogestad uses 4 in stead of 2 in the Ti formula, but you get faster disturbance compensation with 2.
If you do not know how to specify Tc, Skogestad suggests Tc = tau.
But if the process has negligible tau, you can not set Tc = tau. Then you must select Tc by yourself.
PEF3006 Process Control. USN. F. Haugen. 2018

17. PEF3006 Process Control. USN. F. Haugen. 2018

18. Temperature control of liquid tank18
Let’s try
Temperature control of liquid tank
PEF3006 Process Control. USN. F. Haugen. 2018