Analog/digital PID-based sliding-mode controller design for nonlinear processes with long time delays

This paper presents a methodology for the design of a cascaded analog/digital proportional-integral-derivative (PID)-based sliding-mode controller for continuous-time multivariable linear/nonlinear processes with long time delays. The optimal linear model (OLM) for an input/output time-delay nonlinear system is utilized to design the analog controller by using the dominant pole-assignment and the linear quadratic regulator (LQR) approaches. The Chebyshev quadrature digital redesign method is extended to convert the designed analog controller into the digital counterpart. Thus, the developed controllers exhibit the advantages of both the PID and sliding mode controllers regarding the tracking, robustness, and computer control of real processes affected by bounded uncertainties, unmodeled dynamics and disturbances. Furthermore, the ideal state reconstruction methods are newly developed for the input/output time-delay plants from the input-output data. Thus, the state-feedback controller can be designed for the input/output time-delay plant with in-accessible states. Two illustrative examples are given to show the proposed method.