Control of Complex Nonlinear Dynamic Rational Systems

Nonlinear rational systems/models, also known as total nonlinear dynamic systems/models, in an expression of a ratio of two polynomials, have roots in describing general engineering plants and chemical reaction processes. The major challenge issue in the control of such a system is the control input embedded in its denominator polynomials. With extensive searching, it could not find any systematic approach in designing this class of control systems directly from its model structure. This study expands the U-model-based approach to establish a platform for the first layer of feedback control and the second layer of adaptive control of the nonlinear rational systems, which, in principle, separates control system design (without involving a plant model) and controller output determination (with solving inversion of the plant U-model). This procedure makes it possible to achieve closed-loop control of nonlinear systems with linear performance (transient response and steady-state accuracy). For the conditions using the approach, this study presents the associated stability and convergence analyses. Simulation studies are performed to show off the characteristics of the developed procedure in numerical tests and to give the general guidelines for applications.