State-space digital PID controller design for multivariable analog systems with multiple time delays

This paper presents a discrete-time state-space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time-delayed multivariable. analog systems are formulated in a state-space generic form so that the exact discrete-time state-space model can be constructed. Then, the optimal digital PID controller is designed via a state-feedback and state-feedforward LQR approach. The developed PID controller can be applied to a general time-delayed multivariable analog system represented by a semi-proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.