Robustness analysis of flexible structures: practical algorithms

Abstract

SUMMARYWhen analysing the robustness properties of a flexible system, the classical solution, which consists of computing lower and upper bounds of the structured singular value (s.s.v.) at each point of a frequency gridding, appears unreliable. This paper describes two algorithms, based on the same technical result: the first one directly computes an upper bound of the maximal s.s.v. over a frequency interval, while the second one eliminates frequency intervals, inside which the s.s.v. is guaranteed to be below a given value. Various strategies are then proposed, which combine these two techniques, and also integrate methods for computing a lower bound of the s.s.v. The computational efficiency of the scheme is illustrated on a realworld application, namely a telescope mock-up which is significant of a high order flexible system.

Stability and performance analysis for linear systems with actuator and sensor saturations subject to unmodeled dynamics

“…with matrices A 0 , B 01 and C 02 defined in (7). Relations (13), (14) and (15) are obtained by considering the quadratic Lyapunov function V (ξ) = ξ ′ Q −1 ξ, with matrix Q defined in (19), and by invoking similar arguments like in Proposition 1 with respect to the complete closed-loop system (6):…”

“…In a linear context many methods exist among which µ-analysis is one of the most popular [7]. The In a nonlinear context however, the subject has received less attention.…”

Structured Singular Value and Applications: Analyzing the Effect of Linear Time-Invariant Uncertainty in Linear Systems

“…as an additional real parameter (since M.j!/ is an LFT of 1 ! ) (Ferreres et al 2003). This is a generalization of the Hamiltonian methods to compute the H 1 norm of a linear system without a frequency grid, coupled with an alternative form of the upper bound (Young et al 1995).…”

Efficient convex design of robust feedforward controllers

“…Let us now state the general problem solved by the µ frequency sweeping technique [5], [6], [7]. µ test problem: Let a given transfer matrix N (s) and ∆ an LTI structured model perturbation.…”

“…This is nevertheless a difficult optimization problem, with an infinite number of optimization parameters and frequency domain constraints. The principle is to solve it first on a frequency gridding with an LMI solver, and then to validate the result with a µ frequency sweeping technique [5], [6], [7], even when time-varying uncertainties are accounted for: remember that the structured singular value (s.s.v.) µ is used to analyse the robustness properties in the face of LTI model uncertainties.…”