A state space modeling and control method for multivariable smart structural systems

A system identification technique for the derivation of minimal, continuous time state variable models for multivariable smart structural systems is presented. The structural identification technique is based on the measurement of eigenvalues and eigenvectors of the structure. Two sensors are required for each mode included in the structural system model. Unlike computational system identification techniques, the relatively large number of sensors simplifies the identification process making it ideal for systems with several inputs and outputs. Additionally, the identification technique allows the implementation of multi-input multi-output full state feedback controllers with simple analog hardware. The amount of hardware required for the implementation of an analog linear quadratic regulator is significantly reduced from standard discrete control implementation methods and stability margins are retained. The eigenvectors of distributed parameter structural systems are examined. For a general unknown system, the eigenvalues and eigenvectors cannot be directly measured. For the lightly damped structural systems considered in this paper however, it is shown that these measurements are possible. Eigenvalues are conspicuous in the frequency domain and the eigenvectors exist at near steady state conditions. By utilizing a priori knowledge of the structural system, the eigenvectors can be estimated from steady state sinusoidal amplitude measurements. The identification procedure utilizes n measurement variables of the structural system with n/2 modes to produce a nth order model. This allows for the measurements to be defined as the model states. It is shown that an array consisting of n/2 sensors on the structure and some simple analog hardware suffice for the identification. For symmetrical systems, it is shown that the number of sensors required for the model identification is reduced further. A variety of measurement devices and techniques are discussed in relation to the proposed system identification technique. A sensor array consisting of shaped and segmented polyvinylidene fluoride film is presented as an inexpensive and practical measurement device. A procedure for the generation of distributed sensors for state variable measurement is presented. Identification and control are successfully implemented on a multivariable cantilever plate system and experimental results are presented.