Optimal actuator design for vibration control based on LQR performance and shape calculus
For control engineers, it provides a novel method to design actuator shapes for optimal closed-loop performance, but the numerical example is limited to a simple beam model.
This paper optimizes actuator shape for vibration control using LQR performance and shape calculus, demonstrating the method on an Euler-Bernoulli beam model.
Optimal actuator design for a vibration control problem is calculated. The actuator shape is optimized according to the closed-loop performance of the resulting linear-quadratic regulator and a penalty on the actuator size. The optimal actuator shape is found by means of shape calculus and a topological derivative of the linear-quadratic regulator (LQR) performance index. An abstract framework is proposed based on the theory for infinite-dimensional optimization of both the actuator shape and the associated control problem. A numerical realization of the optimality condition is presented for the actuator shape using a level-set method for topological derivatives. A Numerical example illustrating the design of actuator for Euler-Bernoulli beam model is provided.