Advanced Design Techniques in Linear Parameter Varying Control

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Title: Advanced Design Techniques in Linear Parameter Varying Control
Author: Dong, Ke
Advisors: Gregory D. Buckner, Committee Member
Stephen L. Campbell, Committee Member
Paul I. Ro, Committee Member
Fen Wu, Committee Chair
Abstract: To improve the analysis and control synthesis approach of linear fractional transformation (LFT) parameter-dependent systems, two types of non-quadratic Lyapunov function and switching control scheme are introduced and studied in this thesis. A gain-scheduled controller with parameter variation rate, a nonlinear gain-scheduled controller and an online switching linear parameter varying (LPV) controller are derived, and the advantages of proposed LPV control techniques are demonstrated through numerical and physical examples. In the first part of this thesis, we introduce a quadratic LFT parameter-dependent Lyapunov function, which includes affine parameter-dependent functions as special cases. Using full-block S-procedure, new LPV synthesis conditions have been derived in terms of finite number of linear matrix inequalities (LMIs). The constructed controller depends on parameters and their variation rate in general form compared with traditional LFT form. It is shown that the proposed approach can achieve better performance in a ship steering example by exploiting parameter variation rates. In the same spirit of exploiting more general type of Lyapunov function to achieve better controller, an analysis and synthesis algorithm for LPV systems using convex hull Lyapunov function (CHLF) and maximum Lyapunov function is presented. Using duality of LPV systems and conjugate properties of CHLF, sufficient LPV analysis and synthesis conditions have been derived in terms of LMIs with linear search over scalar variables. Because of the special structure of CHLF and maximum Lyapunov function, the output feedback controller turns out to be a nonlinear gain-scheduled controller. A second-order plant is used to demonstrate advantages and benefits of the new approach. The other main contribution in this thesis is the application of switching control to LPV systems with online optimization method. Arbitrary switching among subsystems is achieved, as well as performance improvement using multiple Lyapunov functions. A gain-scheduled controller working for the next switching interval is designed at each switching instant. A bumpless transfer compensator is also designed to minimize the output jump caused by switching. The synthesis conditions for both switching controller and bumpless transfer compensator are formulated as LMIs. The new LPV switching control scheme is applied to an uninhabited combat aerial vehicle (UCAV) problem. All our proposed approaches are efficient in computation, where the conditions are all formulated as LMIs or LMI-like ones. With slightly increased computational complexity, the proposed new approaches for analysis and synthesis of LFT parameter-dependent systems can achieve significant performance improvement comparing to existing approaches.
Date: 2006-08-10
Degree: PhD
Discipline: Mechanical Engineering

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