NASA Technical Reports Server (NTRS) : Robust pdf

NASA Technical Reports Server (NTRS) : Robust

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The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered.

A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds

• Creator/s: NASA Technical Reports Server (NTRS
• Date: 1/1/1993
• Year: 1993
• Book Topics/Themes: NASA Technical Reports Server (NTRS), CONTROL STABILITY, CONTROL SYSTEMS DESIGN, CONTROL THEORY, NONLINEAR SYSTEMS, OPTIMAL CONTROL, ROBUSTNESS (MATHEMATICS), SYSTEMS STABILITY, ACTIVE CONTROL, ALGORITHMS, FEEDBACK CONTROL, LIAPUNOV FUNCTIONS, RICCATI EQUATION, How, Jonathan P., Hall, Steven R

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