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We consider the problem of shaping the transient step response of nonlinearsystems to satisfy a class of integral constraints. Such constraints areinherent in hybrid energy systems consisting of energy sources and storageelements. While typical transient specifications aim to minimize overshoot,this problem is unique in that it requires the presence of an appreciableovershoot to satisfy the foregoing constraints. The problem was previouslystudied in the context of stable linear systems. A combined integral andfeedforward control, that requires minimal knowledge of the plant model, wasshown to make the system amenable to meeting such constraints. This paperextends that work to nonlinear systems and proves the effectiveness of the samecompensation structure under added conditions. Broadly, it is shown that theintegral constraint is satisfied when this compensation structure is applied tononlinear systems with stable open-loop step response and a positive DC gain.However, stability of the resulting closed-loop system mandates bounds on thecontroller gain.

Shaping the Transient Response of Nonlinear Systems to Satisfy a Class of Integral Constraints