Tuning of PID controllers Course PEF3006 Process Control Fall 2018 Tuning of PID controllers By Finn Aakre Haugen (finn.haugen@usn.no) PEF3006 Process Control. USN. F. Haugen. 2018

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

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

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

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

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

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

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. 2018.

Ex.: PI controller in simulated biogas control system Original ZN Repeated ZN Big improvement! F. Haugen. Process Control. NMBU. 2018.

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

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

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

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

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

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

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

PEF3006 Process Control. USN. F. Haugen. 2018

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