Time-optimal servomechanisms-discrete-time estimation of the optimum switching function

Time optimal control of a servomechanism requires a nonlinear control law based on a switching function. The switching function depends on the characteristics of the actuator, the inertia, and the disturbances which act on the system. In practical servomechanisms the actuator characteristics may be unknown. Also, the inertia and disturbances may be unknown and may change between moves. In such cases the optimal switching function is unknown prior to the start of each move. A continuous controller which estimates the optimum switching function during each move has been developed, and has been reported elsewhere. The complexity of this continuous controller means that a practical implementation is not feasible. This paper describes the means by which the continuous controller can be discretized to yield a practical controller