Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

Abstract

This paper presents a discrete-time state-space methodology for the digital modeling and design of an optimal digital proportional-integral-derivative (PID) plus state-feedback controller for multiple-input, multiple-output (MIMO) continuous-time systems with multiple time delays in states, inputs and outputs. To implement the digital design, first the Chebyshev quadrature formula together with a linear interpolation method is employed to obtain an extended discrete-time state-space model from the continuous-time multiple time-delay system. Then, a partially predetermined digital PID controller and the extended discrete-time state-space model are formulated as an augmented discrete-time state-space system utilizing state-feedforward and state-feedback linear-quadratic regulator (LQR) design. As a result, the parameters of the optimal PID controller and its associated state-feedback controller can be determined by tuning the weighting matrices in the LQR performance criteria. Further, an optimal discrete-time observer is jointly constructed for the multivariable system with multiple delays in states, inputs and outputs. The proposed design methodology can be applied to general MIMO continuous-time multiple time-delay systems for performance improvement and disturbance rejection. An illustrative example is given to demonstrate the effectiveness of the developed method.