New Analysis/Design of Generalized Discrete PI Controller via Discrete Time Delay Control for Nonlinear Systems

Abstract

Abstract Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers are among the most common schemes for control since their formulation nearly a century ago. They have been very successful in many applications, even as we have migrated from analog implementations to digital control systems. While there is rich literature for design and analysis of PI/PID controllers for linear time-invariant systems with modeled dynamics, the tools for analysis and design for nonlinear systems with unknown dynamics are limited, despite their known effectiveness. This paper extends previous observations about a form of discrete Time Delay Control’s equivalence to a generalized PI controller for more general canonical systems, with additional complimentary feedback linearization of known dynamics, as desired. In addition, sufficient conditions for Bounded Input-Bounded Output (BIBO) as well as exponential stability are developed in this paper for the form of discrete TDC that is closest to generalized discrete PI equivalent controller, for multi-input multi-output nonlinear systems, including nonaffine cases. Accordingly, design procedures are suggested for such discrete TDC, and generalized discrete PI controller for nonlinear systems.