بسم الله الرحمن الرحيم Advanced Control Lecture three Mohammad Ali Fanaei Dept. of Chemical Engineering Ferdowsi University of Mashhad Reference: C. C. Yu, “Autotuning of PID Controllers”, 2 nd ed., Springer, 2006

Off-Line Tuning of PID Controllers 1.Ziegler-Nichols(1942): Recommended for 0.2< D/  <2 ( ) About 250 tuning rules are exist for PI and PID Controllers What is the suitable tuning rule? It really depends on your process (Type, Order, Parameters, Nonlinearity, Uncertainty, etc)

Off-Line Tuning of PID Controllers 2.Tyreus-Luyben(1992): Recommended for time-constant dominant processes 3.Ciancone-Marlin(1992): Recommended for dead-time dominant processes

Off-Line Tuning of PID Controllers 4.PID tuning based on IMC (Rivera et al., 1986)

On-Line Tuning of PID Controllers  Ziegler-Nichols Test (1942) 1.Set the controller gain Kc at a low value, perhaps Put the controller in the automatic mode. 3.Make a small change in the set point or load variable and observe the response. If the gain is low, then the response will be sluggish. 4.Increase the gain by a factor of two and make another set point or load change. 5.Repeat step 4 until the loop becomes oscillatory and continuous cycling is observed. The gain at which this occurs is the ultimate gain Ku, and the period of oscillation is the ultimate period Pu.

On-Line Tuning of PID Controllers  Relay Feedback Test (Astrom &Hagglund, 1984)

On-Line Tuning of PID Controllers  Relay Feedback Test 1.Bring the system to steady state. 2.Make a small (e.g. 5%) increase in the manipulated input. The magnitude of change depends on the process sensitivities and allowable deviations in the controlled output. Typical values are between 3 and 10%. 3.As soon as the output crosses the SP, the manipulated input is switched to the opposite position (e.g. –5% change from the original value). 4.Repeat step 2 until sustained oscillation is observed. 5.Read off ultimate period Pu from the cycling and compute Ku from the following Equation: K u = 4h/(  a)

On-Line Tuning of PID Controllers  Advantages of Relay Feedback Test 1.It identifies process information around the important frequency, the ultimate frequency. 2.It is a closed-loop test; therefore, the process will not drift away from the nominal operating point. 3.The amplitude of oscillation is under control (by adjusting h ). 4.For processes with a long time constant, it is a more time-efficient method than conventional step or pulse testing. The experimental time is roughly equal to two to four times the ultimate period. 5.If the normalized dead time D /  is less than 0.28, the ultimate period is smaller than the process time constant. Therefore the relay feedback test is more time efficient than the step test.

On-Line Tuning of PID Controllers  Advantages of Relay Feedback Test

On-Line Tuning of PID Controllers  Process model identification from a Relay Feedback Test

Recommended Tuning Formulas The following formulas are recommended by Luyben and Yu for tuning The PI controllers:

Example 3: Using relay Feedback In this example for the system that described in example 2 a relay feedback test is used for on-line tuning of a PI controller