Constrained state-feedback control of an externally excited synchronous machine

State-feedback control of externally excited synchronous machines employed in applications such as hybrid electric vehicles and full electric vehicles is a challenging problem. Indeed, these applications are characterized by fast dynamics that are subject to hard physical and control constraints. The goal of this paper is to provide a controller synthesis method that can answer these challenges effectively. To this end, firstly, a linear control law is obtained for the unconstrained dynamics via a standard control Lyapunov function (CLF), along with an admissible basin of attraction. Then, a piecewise affine control law defined on a cubic partition of the state-space is obtained for the constrained dynamics via a flexible CLF. An a posteriori test for checking stability and invariance of a set of initial conditions for the resulting closed-loop dynamics is also proposed. The effectiveness of the developed synthesis method is demonstrated in a realistic simulation scenario.