Nonlinear PI and gain scheduling

A general procedure is proposed for nonlinear IMC and PID controllers for single-input single-output nonlinear systems. The nonlinear IMC and PID controllers are designed to force the system output to track a desired linear closed-loop trajectory, which is tunable via a single, physically meaningful parameter: the trajectory filter time constant. Two illustrative simulation examples are presented, a highly asymmetric fourth order nonlinear process and a non-isothermal Van de Vusse reactor. The nonlinear PID controller performs as well as nonlinear controllers obtained by geometric methods.