Hm Design using Normalized Coprime Factors an Application to

Hm Design using Normalized Coprime Factors an Application to

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Hm Design using Normalized Coprime Factors : an Application to an Electromechanical Actuator 0. MalassC (I), M. Zasadzinski (2), C. Iung M. Hayar (2), M. Darouach (2) CRAN, CNRS URA 821 (1) ENSEM. 2 Avenue de la for& de Have. 545 16 Vandeuvre-les-Nancv Caex EARAL. IUT de Longwy, Universitk de Nanci 1; 186 rue de Lorraine, 54400 eosnes-et-Romain FRANCE Abstract In this paper, we apply an H, control law to a testing bench composed by an electromechanical actuator. We present the plant model which takes into account external disturbances and uncertainties such as non-linearities and unknown parameters. The H, design is based on normalized coprime factor plant [l]. To define the frequency weighting functions, a loop shaping procedure is used to allow the specification of performance and robust stability characteristics [2]. The loop shape is used as a measure of the trade-off between closed loop performances and robust stability. The obtained results are compared with those given by LQG and LQGLTFZ designs. Key-words Electromechanical actuator, H, design, Robustness, Loop shaping. L INTRODUCTION Actually, the robustness is a key concept in modern control synthesis. Various optimization methods try to recover, in the multivariable case, the robustness obtained in the SISO case with classical design methods based on Nyquist and Bode plots. Like classical design procedures, the modem approaches of robustness use frequency domain optimization methods : quadratic and H, design strategies based on loop shaping. This paper is devoted to an application of the H, design, recently developed by McFarlane and Glover [1]-[3], to a testing bench. This method can be divided in two steps. Firstly, the robust stability and performance specifications are defined by shaping the singular values of an augmented plant. Secondly, a robust stabilization technique [ 11-[3], based on normalized coprime factor of the shaped plant, is used to control the process. Unlike the standard H, design with mixed sensitivity [4], [5], the procedure in the second step allows to obtain the design specifications (defined in the first step) in one time. In addition, this procedure permits to insert an integrator in the control law. In this work, the controlled plant of the testing bench is an electromechanical actuator with various disturbances and non-linearities. This paper is organized as follows. In section 2, we describe the electromechanical actuator. We give a linearized model of this process and we show its time and its frequency responses. In section 3, we give the design specifications to achieve the required performance and robust stability levels. In section 4, we compute the H, controller. In section 5, this design is applied to the electromechanical actuator and compared with LQG and LQGLTR control laws. The obtained robust stability and performances are illustrated with various frequency and time responses. The H, controller gives a better stability/perfomances trade-off.
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This note was uploaded on 05/08/2011 for the course MECHANICAL 203 taught by Professor Krishna during the Spring '11 term at Akademia Ekonomiczna w Poznaniu.

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Hm Design using Normalized Coprime Factors an Application to

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