Optimal control design for systems with collocated sensors and actuators

Donald J. Leo; Daniel J. Inman

doi:10.1117/12.240798

31 May 1996 Optimal control design for systems with collocated sensors and actuators

Donald J. Leo, Daniel J. Inman

Proceedings Volume 2715, Smart Structures and Materials 1996: Mathematics and Control in Smart Structures; (1996) https://doi.org/10.1117/12.240798
Event: 1996 Symposium on Smart Structures and Materials, 1996, San Diego, CA, United States

Abstract

Smart material systems enable near collocation of sensors and actuators for controlled structures. Distributed sensors and actuators, placed in close proximity to one another, yield high bandwidth control systems that exhibit passivity characteristics that can be exploited in the design of robust structural control laws. Transfer function properties of Single-Input- Single-Output (SISO) systems with collocated sensors and actuators are well understood. In this paper, analogies between the SISO case and Multiple-Input-Multiple-Output systems with collocated sensors and actuators are developed. The analogies are based on the eigenproperties of complex symmetric matrices; namely, that the eigenvectors of complex symmetric matrices are orthogonal to their simple transpose, and that the eigenvalues of complex symmetric matrices are bounded by the definiteness of their real and imaginary components. These theorems are derived and applied to the analysis and control of nongyroscopic, noncirculatory mechanical systems. Transfer matrices of mechanical systems with collocated sensors and actuators are shown to be complex symmetric matrices whose eigenproperties are determined by the type of collocated feedback. These properties are derived for both the general damping case and for the case of modal damping. An optimal control technique based on the eigenproperties of complex symmetric systems is developed. The technique is a constrainted convex optimization program that can incorporate many different types of performance and constraint specifications. The technique is derived in the paper and a design example is included.

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Donald J. Leo and Daniel J. Inman "Optimal control design for systems with collocated sensors and actuators", Proc. SPIE 2715, Smart Structures and Materials 1996: Mathematics and Control in Smart Structures, (31 May 1996); https://doi.org/10.1117/12.240798

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KEYWORDS

Sensors

Actuators

Control systems

Convex optimization

Matrices

Control systems design

Feedback control

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