Parameter self-tuning of relay feedback PID controller

Today, we will introduce a method of automatic tuning of control algorithm parameters , This method is called relay feedback based self-tuning .

One 、 Relay feedback principle

By adding a non-linear link with relay characteristics to the circuit, a continuous and stable oscillation can be obtained , Then the intermediate parameters are obtained ： Critical gain and critical period , Combine with the setting formula to realize PID Parameter setting of . Generate continuous oscillation through relay feedback as a pair Z-N An improvement of critical proportionality method .

                                              chart 1.1 Structure block diagram of relay self-tuning

 ,

  h Is the relay amplitude ,a- Is the output signal amplitude .

                                              chart 1.2 Frequency domain response curve of relay and control object

 

From the Nyquist stability criterion ：

have to ：

The critical value can be roughly obtained ：

Two 、 be based on Z-N French PID Parameter setting

Controller type	KP	Tn	Tv	Ki	Kd
P	0.5*Kμ	---	---	---	---
PD	0.8*Kμ	---	0.12*Tμ	---	KP*Tn
PI	0.45*Kμ	0.85*Tμ	---	KP/ Tn	---
PID	0.6*Kμ	0.5*Tμ	0.12*Tμ	KP/ Tn	KP*Tn

3、 ... and 、 relay feedback PID Introduction to self-tuning process

1、 First use the relay to make the system vibrate , The process of oscillation is ： When feedback is less than expected , Output positive full control quantity ; When feedback is greater than expected , Output negative full control quantity , Force the system to vibrate .

2、 Measure the amplitude and period when the system vibrates , The critical gain and oscillation period of the system can be obtained （ The oscillation period is obtained from the adjacent peaks of the curve ）

3、 According to the obtained critical gain and oscillation period , from Z-N Table get the required PID Parameters .

                                      chart 3.1 Relay feedback self-tuning PID Controller rendering

                                                      chart 3.2 Effect diagram of system vibration

Four 、 summary

Relay feedback setting PID Parameters can be set PID Parameters , It is better to . But in the simulation process ,PI The effect is not satisfactory . The overall scheme is simple , Strong applicability . Relay feedback method self-tuning PID Parameters are widely used in temperature control systems , Other applicable scenarios are not clear .

relay feedback PID Controller parameter self-tuning - You know (zhihu.com)