25.7 : PID制御

A PID controller thermostat adjusts heating or cooling based on the temperature gap between actual and desired levels.

A PD controller, found in car speed systems, can manage sudden speed changes but struggles to maintain constant speed.

Conversely, a PI controller, used in voltage regulation, enhances stability and reduces steady-state error but increases the time to reach the desired voltage.

A PID controller merges the features of PD and PI attributes, offsetting their individual shortcomings.

In the design of a PID controller, it is first considered as a PI part connected in cascade with a PD part. The proportional constant of the PD part is set to unity, as only three parameters are needed in the PID controller.

Next, only the PD component is active. The derivative gain value is chosen to achieve some desired stability, gauged by a maximum overshoot in the time domain and phase margin measurements in the frequency domain.

Finally, the integral gain and proportional gain for the PI part are selected to meet the total requirement of relative stability.