Model‐Based PID and Resonant Controller Design

The models used in the design of proportional integral derivative (PID) controllers are limited to two particular types. One is a first order model while the other is a second order model. If the plant dynamics yield a higher order model, an approximation is often involved to obtain a first order or a second order model so that a PID controller can be designed using a model based approach. When using model based design methods, a desired closed‐loop performance specification is required before commencing. The resonant controller, different from the PI or PID controller, incorporates the factor in the denominator of the controller. With the embedded mode, the closed‐loop feedback control system is designed to be stable, and at the steady‐state the output of the control system will completely track the sinusoidal signal and/or reject a sinusoidal disturbance signal that contains the frequency without any steady‐state errors.