Frequency-domain Analysis and Control of Linear Discrete-time System

In this paper, we present a new method for designing digital proportional-integral-derivative (PID) controllers for controller design problems in multivariable discrete-time control systems. Using the Kalman-Yakubovic-Popov (KYP) lemma, we divide the domain of the discrete system by the product scopes of the system frequency and sampling period. Then, based on the principle of approximate model matching, we convert the PID controller design problem to solve the optimization problem of the inequalities formed by the norm in the restricted areas. In addition, we solve the inequalities described in the form of coefficient matrices in the state space realization using linear matrix inequalities. Lastly, we provide a numerical example to illustrate that the proposed method enhances the robustness of the frequency and sample period values, and thus broadens the application scope of designed controller.