Optimal inversion-based control for the set-point regulation of nonminimum-phase uncertain scalar systems

In this note, we propose an optimal inversion-based control for the set-point constrained regulation of nonminimum-phase uncertain scalar systems. This approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion. Essential constituents of the architecture are a parameterized family of “transition” polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle. The methodology is then centered on the optimal combined design of the feedback controller and of the inversion-based command signal in order to minimize the worst-case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds. Finally, an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained with genetic algorithms. A worked example highlights the effectiveness of the overall methodology.