Directionality in input-constrained systems: its definition and optimal compensation

For discrete-time input-constrained systems, the notion of directionality is defined and an optimal directionality compensator is presented. According to the definition, a single-input single-output process may exhibit directionality. An example of such a process is given and simulated. Given an unconstrained controller output, the compensator calculates an optimal constrained (feasible) process input that results in a process output response as "close" as possible to the output response of the same process to the unconstrained controller output. The compensator can be used for both linear and nonlinear processes, irrespective of the type of controller being used. For processes whose nonsingular characteristic (decoupling) matrices are independent of manipulated inputs and can be made diagonal by row or column rearrangements, the optimal directionality compensation is identical to clipping; this class of processes do not exhibit the directionality over short time horizons. By two examples the performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation.