Shaping the 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 stable linear systems. A combined integral and feedforward control, that requires minimal knowledge of the plant model, was shown to make the system amenable to meeting such constraints. This paper extends that work to nonlinear systems and proves the effectiveness of the same compensation structure under added conditions. Broadly, it is shown that the integral constraint is satisfied when this compensation structure is applied to nonlinear systems with stable open-loop step response and a positive DC gain. However, stability of the resulting closed-loop system mandates bounds on the controller gain.