Sensitivity shaping with degree constraint by nonlinear least-squares optimization

This paper presents a new approach to shaping of the frequency response of the sensitivity function. In this approach, a desired frequency response is assumed to be specified at a finite number of frequency points. A sensitivity shaping problem is formulated as an approximation problem to the desired frequency response with a function in a class of sensitivity functions with a degree bound. The sensitivity shaping problem is reduced to a finite-dimensional constrained nonlinear least-squares optimization problem. To solve the optimization problem numerically, standard algorithms for an unconstrained version of nonlinear least-squares problems are modified to incorporate the constraint. Numerical examples illustrate how these design parameters are tuned in an intuitive manner, as well as how the design proceeds in actual control problems.