Dynamically equivalent outputs and their use in nonlinear controller synthesis

Abstract

A new notion, dynamically equivalent outputs, is developed to aid in controller synthesis for nonlinear systems. A dynamically equivalent output simplifies the controller design problem and, when controlled to its set point, guarantees that the system's primary output is also controlled to its set point. The use of this notion is demonstrated for three classes of systems. For systems with linear state equations but a nonlinear state/output map, conditions are derived for the existence of a linear dynamically equivalent output. Analogous conditions are derived for nonlinear systems for which the state equations can be made linear by means of a coordinate transformation and state feedback. Design of a controller in terms of the new output is straightforward, leading to a response which is nonlinear in the primary output. Simulations for a chemical reactor system using a coordinate transformation, state feedback, and a dynamically equivalent linear output are given. Finally, for general nonlinear systems, the use of input/output linearizing feedback in terms of a dynamically equivalent output is explored. Another chemical reactor system is simulated to demonstrate this approach.