Computationally efficient design of optimal strategies for controllable damping devices

Abstract

SUMMARY The development of control strategies for controllable passive dampers — ‘semiactive’ damping devices — is complicated by the nonlinear and dissipative nature of the devices and the nonlinear nature of the closed-loop system with any form of parametric feedback control. Control design for nonlinear systems is often achieved by designing a control for a linearized model since strategies for linear systems are straightforward. One such approach is clipped-optimal control in which the desired damper forces are determined from an optimal controller (e.g., linear quadratic regulator, linear quadratic Gaussian, H2 and H∞), which is designed assuming that the damping devices are fully linear actuators that can exert any forces (dissipative or nondissipative), and a secondary bang–bang controller commands the controllable damper to exert forces as close as possible to the desired forces. However, designs using any linearized model generally result in suboptimal (and sometimes very poor) performance because the linear actuator assumption differs from the actual implementation with a dissipative damping device. Thus, one must generally resort to a large-scale parameter study in which the nonlinear system is simulated many times to determine control strategies that are actually optimal for the nonlinear controlled closed-loop system. This paper demonstrates how an approach developed by the authors, which can reduce the model of a system with local modifications to a lower order set of Volterra integral equations in the modification forces, can significantly decrease the computational burden of a complex control design study for controllable dampers. The approach is first adapted to use a state feedback control with a bang–bang on–off secondary controller. Then, the structural and damping device models are detailed. The optimal semiactive control design is demonstrated via both a parameter study and an optimization algorithm. Numerical examples demonstrate that the approach is effective and, compared with a conventional simulation approach, can reduce computation time by two orders of magnitude. Copyright © 2014 John Wiley & Sons, Ltd.