An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

Abstract

This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.