Tuning of PID controller added to state feedback control for unstable single-input multivariable plants

In this paper, a method to tune PID controller attached in series to state feedback gain for unstable single-input multivariable plants is proposed. To tune PID controller, the method requires only one-shot transient response data of the state feedback control system stabilized by an arbitrary stable feedback gain. The data is used in frequency domain for classical loop-shaping. The effectiveness and the simplicity of the proposed method are shown through simulations and experiments.