Affiliation:
1. Senior Lecturer in Flight Control Systems Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU UK
Abstract
Frequency response finds a wide range of applications in many engineering sectors. When variations and uncertainties exist during the operation and lifetime of an engineering system, the calculation of frequency response for an uncertain dynamic system is required in order to assess the worst cases in terms of various criteria, for example gain and phase margins in control engineering, or peak magnitude at different modes in the finite element analysis of structures. This paper describes an analytical approach toward the identification of critical interior lines that possibly contribute to the boundary of the frequency response. It is allowed that uncertain parameters perturb transfer function coefficients in a nonlinear form. Conditions for critical interior lines contributing to the boundary of the frequency response are presented. An invariant property of these critical lines under open-loop and closed-loop configurations augmented by control systems or compensators is established, which greatly simplifies the analysis, design, and verification process when using frequency domain techniques. A procedure for computing frequency response and identifying the worst cases is then developed based on the combination of symbolic and numerical computation.
Subject
Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering
Reference25 articles.
1. Radially Truncated Uniform Distributions for Probabilistic Robustness of Control Systems;Barmish
2. Worst-Case Properties of the Uniform Distribution and Randomized Algorithms for Robustness Analysis;Bai
3. The Uniform Distribution: A Rigorous Justification for Its Use in Robustness Analysis;Barmish;Math. Control, Signals, Syst.
4. A Fast Algorithm for Computing Parametric Rational Functions;Bailey;IEEE Trans. on Autom. Control
5. Computing the Frequency Response of Linear Systems With Parametric Perturbation;Fu;Syst. Control Lett.