Optimization approach to controlling constrained nonlinear systems

The authors discuss the results of using the input-output geometric transformation method in the development of an efficient controller for nonlinear systems with constraints, while being easy and intuitive to tune and requiring minimal computational effort. While dynamic matrix control (DMC) and quadratic DMC (QDM-C) have been successfully applied in optimal control of industrial processes, they are restricted to linear/near-linear processes. An approach combining the transformation method with DMC for nonlinear systems with constraints that require low computational effort is reported. Using input-output linearization, a pseudolinear model of the system is derived that is valid for the entire region of operation. DMC is designed on this system, ignoring constraints. The DMC-computed input is checked for constraint violation, and a pointwise optimal feasible input is generated if such violation occurs. The performance of the proposed control scheme is demonstrated via simulation of two processes: a continuous stirred tank bioreactor (CSTBR), and an exothermic continuous stirred tank reactor (CSTR)