Calculation of optimal feasible controller output in multivariable processes with input constraints

Presents an optimal directionality compensator for multivariable processes with actuator saturation nonlinearities. Given an unconstrained controller output and the characteristic (decoupling) matrix of the process under consideration, the compensator calculates an optimal constrained (feasible) plant input that once applied to the process, the resulting process response is as close as possible to the response of the same process to the controller output. The compensator can be used for both linear and nonlinear processes, irrespective of the type of controller being used. When the characteristic matrix is diagonal, the optimal directionality compensator is identical to a series of limiters (clippers). The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation approaches, by numerical simulation of a linear example under decentralized PID control and a nonlinear bioreactor under input-output linearizing control.