Transient Response of Linear Systems Under Integral Constraints

Abstract

The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.