A general U-block model-based design procedure for nonlinear polynomial control systems

摘要

The proposition of U-model concept (in terms of “providing concise and applicable solutions for complex problems”) and a corresponding basic U-control design algorithm was originated in the first author’s PhD thesis (Zhu 1989). The term of U-model was the first time appeared (not rigorously defined) in the first author’s other journal paper (Zhu and Guo 2002), which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches  nonlinear polynomial plants). This paper represents the next milestone work --- using linear state space approaches to design nonlinear polynomial control systems (in brief, linear state space approaches  nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as U-Block model, which provides a generic prototype for using linear state space based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, Sliding Mode Control (SMC) design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present U-model oriented control system design in formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm based studies and simulation demonstrations. In some sense this paper can be treated as a landmark for U-model based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.