Application of optimal polynomial controller to a benchmark problem

Abstract

In this paper, we investigate the performance of optimal polynomial control for the vibration suppression of a benchmark problem; namely, the active tendon system. The optimal polynomial controller is a summation of polynomials of different orders, i.e., linear, cubic, quintic, etc., and the gain matrices for different parts of the controller are calculated easily by solving matrix Riccati and Lyapunov equations. A Kalman-Bucy estimator is designed for the on-line estimation of the states of the design model. Hence, the Linear Quadratic Gaussian (LQG) controller is a special case of the current polynomial controller in which the higher-order parts are zero. While the percentage of reduction for displacement response quantities remains constant for the LQG controller, it increases with respect to the earthquake intensity for the polynomial controller. Consequently, if the earthquake intensity exceeds the design one, the polynomial controller is capable of achieving a higher reduction for the displacement response at the expense of control efforts. Such a property is desirable for the protection of civil engineering structures because of the inherent stochastic nature of the earthquake.