Ziegler-Nichols ultimate sensitivity method

・In Japanese
＜Premise knowledge＞
・PID controller
・Scilab

■What is the Ziegler-Nichols ultimate sensitivity method?

This section describes the Ziegler-Nichols ultimate sensitivity method, which is one of the PID control gain setting methods. This is a method that can empirically determine the gain when the characteristics of the controlled object cannot be expressed by a physical model. In addition, this method is not limited to the control target of localization* like the step response method, and is also effective for non-localization. Furthermore, it cannot be used for controlled objects such as first-order delay and second-order delay, but it is effective for controlled objects of "dead-time and first-order delay element" or "dead-time and integral system". There is a pole arrangement method as another gain setting method.

* Localization is the property that when an input value is determined, the output value is determined accordingly. On the other hand, the property that the output value is not uniquely determined even if the input value is determined is called non-localization. An example of non-localization is a controlled object that includes an integrator.

■How to tune the ultimate sensitivity method.

Configure PID control for P control as follows.



When a step signal is input and Kc is gradually increased, it becomes a continuous vibration with a constant amplitude at some point. The vibration cycle at this time is Tc. If the object to be controlled is just a first-order delay system, it will not vibrate no matter how large the gain is, so it can be seen that the ultimate sensitivity method cannot be used for the first-order delay system.



Set the parameters as follows from the obtained Kc and Tc.



If this gain is set based on the following formula, the value will be different, but the result will be the same.

■Tuning the ultimate sensitivity method with Scilab

Use Scilab to tune the gain. The dead time L = 0.3 seconds, the Kp where continuous vibration occurs is 5.89, and the period Tc is 1.1 seconds.

■Confirm the operation result of PI control by the ultimate sensitivity method

The effect of the ultimate sensitivity method is confirmed by PI control.

＜Parameters＞
　Kp = 0.45*5.89 = 2.65
　Ki = 0.542*5.89/1.1 = 2.9
　Kd = 0

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