UoL--paper7 - Design of Flight Controllers based on...

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Design of Flight Controllers based on Simplified LPV model of a UAV Kannan Natesan, Da-Wei Gu, Ian Postlethwaite and Jianchi Chen Abstract —In this paper, two strategies for the design of controllers based on a simplified LPV model of a UAV (longitudinal flight dynamics) are presented. The simplified LPV model is first derived from a UAV LPV model over the entire range of the cruise speed. The dependence of the LPV model on the varying parameter is reformulated in terms of a μ synthesis problem. A straight μ design and a gain-scheduling μ control scheme have been considered. Simulation results of the closed loop system comprising the controllers and original state-space models are presented and compared. I. INTRODUCTION ain scheduling is an important and intrinsic part of any flight controller design process. While the classical gain-scheduling techniques use a family of equilibrium operating points for obtaining the corresponding controllers, the alternative continuous gain scheduling approach has gained increasing attention in recent years. This approach directly exploits the dependence of the linear state-space models on the scheduling parameter. Such systems known as Linear Parameter-Varying (LPV) systems can be expressed as: () () ( ) ) u t D x t C y u t B x t A x θ + = + = & ( 1 ) where θ (t) is the varying parameter [1]. The main aim in the control of LPV systems is to guarantee closed-loop stability and performance for all possible varying parameters. In [2,3], the scaled small gain theorem is used for the design of controllers for LPV systems that can be expressed in LFT form. While [2,3] use a modification of the small gain theorem to prove stability, performance in the sense of L 2 norm is guaranteed in [4,5] by obtaining a single quadratic Lyapunov function for all possible variations of the plant. It is however assumed that the parameters enter the LPV model in an affine fashion. In [6], the derivation technique is extended using the bounded real lemma formulation of H performance. The controller is then obtained by solving a system of Linear Matrix Inequalities (LMIs). Again the parameter dependence is assumed to be affine and the time- varying parameter θ is assumed to vary over a polytope of vertices. Recent approaches to controller synthesis for LPV systems include the use of unstructured scaling matrices at different vertices of the parameter region [7] and quadratic LFT Lyapunov functions and full-block multipliers [8]. Manuscript received March 8, 2006. This research work is supported by the BAE Systems and UK Engineering and Physical Sciences Research Council. The authors are with the Department of Engineering, University of Leicester, LE1 7RH, UK. Phone: +44-116-2560; fax: + 44-116- 2522619 ; e-mail: [email protected] While the satisfaction of robust stability and performance for LPV systems is the ultimate goal in controller synthesis, the modeling of LPV systems in itself is an important task.
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This note was uploaded on 02/04/2012 for the course ECE 445 taught by Professor Hert during the Spring '11 term at Maryland.

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UoL--paper7 - Design of Flight Controllers based on...

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