Shaping transient response of nonlinear systems to satisfy a class of integral constraints

We consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While typical transient specifications aim to minimize overshoot, this problem is unique in that it requires the presence of an appreciable overshoot to satisfy the foregoing constraints. The problem was previously studied in the context of linear systems and this article extends that work to nonlinear systems. A combined integral and feedforward control, that requires minimal knowledge of the plant model, is shown to make the system amenable to meeting such constraints. Broadly, the compensation is effective for nonlinear plants with stable open-loop step response and a positive DC gain. However, stability of the resulting closed-loop system mandates bounds on the integral gain. In this regard, we state and prove generalized stability theorems for first and higher-order nonlinear plants.