Power shaping control of nonlinear systems: A benchmark example

Abstract

It is well known that energy balancing control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, the authors recently proposed the alternative paradigm of power shaping - where, as suggested by its name, stabilization is achieved shaping a function akin to power instead of the energy function. In this paper we extend this technique to general nonlinear systems and apply it for the stabilization of the benchmark tunnel diode circuit. It is shown that, in contrast with other techniques recently reported in the literature, e.g. piece-wise approximation of nonlinearities, power shaping yields a simple linear static state feedback that ensures (robust) global asymptotic stability of the desired equilibrium. © Springer-Verlag Berlin Heidelberg 2007.