Synthesis of state feedback regulators for nonlinear processes

Abstract The present work proposes a new approach to the state feedback regulator synthesis problem for multiple-input nonlinear processes. The problem under consideration is not treated within the context of exact feedback linearization, where restrictive conditions arise, but is conveniently formulated in the context of singular partial differential equations (PDE) theory. In particular, the mathematical formulation of the problem is realized via a system of first-order quasi-linear singular PDEs and a rather general set of necessary and sufficient conditions for solvability is derived. The solution to the above system of singular PDEs can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package such as MAPLE. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback control law that is computed through the solution of the above system of singular PDEs, both feedback linearization and pole-placement design objectives can be accomplished in a single step. Finally, the proposed nonlinear state feedback regulator synthesis method is applied to a continuous stirred tank reactor (CSTR) in non-isothermal operation that exhibits steady-state multiplicity. The control objective is to regulate the reactor at the middle unstable steady state by manipulating the dilution rate. Simulation studies have been conducted to evaluate the performance of the proposed nonlinear state feedback regulator, as well as to illustrate the main design aspects of the proposed approach. It is shown that the nonlinear state feedback regulator clearly outperforms the standard linear one, especially in the presence of adverse conditions under which linear regulation at the unstable steady state is not always feasible.