Noncausal robust set-point regulation of nonminimum-phase scalar systems

In this paper we propose a method, based on dynamic inversion, for the set-point-regulation of uncertain nonminimum-phase scalar systems. In particular the worst-case settling time is minimized taking into account an amplitude constraint on the control variable and limits on the overshoot and undershoot of the output function. The application of the devised methodology yields to the connected design of both the controller and the reference command input. The latter is obtained by solving a special stable inversion problem on the nominal dynamic system that leads to a noncausal signal, causing the preaction control. Eventually, an optimization problem arises and its solution is gained by means of genetic algorithms. A simulation example shows the effectiveness of the overall methodology, despite the inherent difficulty of the addressed problem.