Eigenstructure assignment and controller optimization for mechanical systems

A technique to assign a desired eigensystem to an actively controlled structure and to optimize the controller and structural parameters is presented. The technique explicitly parametrizes the feedback gain matrices in terms of the eigensystem and structural matrices and then optimizes the closed-loop system by minimizing some norm related to the feedback gain matrices. The technique can optimize design criteria such as gain suppression, actuator and sensor placement, minimum number of sensors, structural stiffness, and system sensitivity to parameter variations. The technique is computationally efficient by being developed in second order form using real arithmetic and with an analytic gradient supplied for the design variables. Two analytical example problems are presented in which active control systems are designed using eigensystem assignment with parametric feedback. The first example assigns eigenvalues and optimizes the controller design for a three-story scale model building. The second example assigns decoupled vibration modes to eliminate rotation of a gyro box