Sensitivity shaping with degree constraint by nonlinear least-squares optimization

Abstract

This paper presents a new approach to shaping of the frequency response of the sensitivity function. A sensitivity shaping problem is formulated as an approximation problem to a desired frequency response with a function in a class of sensitivity functions with a degree bound, and it is reduced to a finite dimensional constrained nonlinear least-squares optimization problem. A numerical example illustrates that the proposed method generates controllers of relatively low degrees.

Approximation of Achievable Robustness Limit Based on Sensitivity Inversion

“…Another difficulty may arise due to unnecessarily high order of the resultant controller. Nevanlinna-Pick interpolation theory is another branch of methods developed for more direct shaping of sensitivity magnitude without resorting to the frequency weighting function [7][8][9]. Analytic interpolation facilitates direct shaping of sensitivity magnitude profile while guaranteeing the constraints for internal stability and controller degree, however, this method has gained relatively a limited attention of practitioners.…”

Feedback sensitivity functions analysis of finite‐time stabilizing control system

“…The quantitative feedback theory (QFT) is one of popular techniques in order to design a robust control in the presence of plant uncertainties and disturbances (for example, [1][2][3][4][5][6][7]), where desired performance is completely characterized by six feedback sensitivity transfer functions called the Gang of Six (or the Gang of Four for a system with (pure) error feedback) [1,6,7]. In [3,8,9], QFT was developed for nonlinear systems.…”

“…One of ideas of these works is representation of nonlinear and multivariable systems as a parameterized family of linear time-invariant control systems and application of basic QFT approach afterwards. Nevertheless, this approach assumes to use mostly PID-based or lead-lag controllers [1][2][3] and other linear control techniques that are suitable for loop shaping [6,7,10].…”