Parameter space approach based state feedback control of LTV systems

Abstract

The calculation of all stabilizing controller parameters with the parameter space approach is a well-known method. Based on the determined stabilizing parameter space, there exist various analysis and fine-tuning tools for the design of controllers. Unfortunately, only for PID controller (of LTI systems) the parameter space approach is developed and implemented systematically now a days. This work expands the syntheses step of the classical parameter space approach to the LTV system class. It is realized by using a transformation method to bring a LTV system into a LTI system description as well as a frozen time eigenvalue based method. Therefore, this paper presents an overview of the parameter space method to design LTI state feedback controllers. After that, a short survey of LTV stability analyse methods and the transformation based method to extend the parameter space approach to LTV is given.

A new methodology to compute stabilizing control laws for continuous‐time LTV systems

“…There exists in the literature a fair amount of techniques for the design of controllers guaranteeing the uniform asymptotic stability of LTV systems. A classical approach consists in pole placement either directly to the time‐varying representation or to an equivalent linear time‐invariant one . However, such techniques demand the differentiation of the system matrices, which can be a problem if the information is available only via sensor measurements.…”

k P ‐stable regions in the space of PID controller coefficients

“…For the case of uncertain delay, the stable regions are determined in the common space of the delay and the controller coefficients in [18,19]. The parameter space method is extended to linear time variant systems in [20] In this paper, a method is presented to compute the stabilising PID set without needing to sweep the proportional gain. In this method, the regions for which a stable interval exists are computed in the k I /k P -k D /k P plane.…”

“…Now, consider the case of n = m + 1. In this case, from(20) the Nyquist plot H( jω, a, b) tends to a real value. Hence, the Nyquist plot intersects itself at this point on the real axis, if the following equations have real solutions for frequency,H r ω, a, b = a m a( − 1) ((3m + n − 1), 2) H i ω, a, b = 0 .…”