Guaranteed stabilizing control strategies for boom cranes in marine applications

Abstract

The dynamics of many real-life control applications is influenced significantly by external stochastic disturbances. In the simplest case, these disturbances can be described by Gaussian probability distributions. In such cases, the corresponding continuous-time system models turn into systems of stochastic differential equations. Moreover, colored noise can be obtained by a suitable continuous-time filtering of white Gaussian noise. For that reason, it is often sufficient to limit the analysis and design of control systems with stochastic disturbances to the case in which the disturbance inputs can be described by a standard Brownian motion (standard Wiener process). Using suitable techniques for stability analysis of systems of stochastic differential equations, the robustness of linear and nonlinear control strategies can be evaluated and improved for many practical applications. In this paper, a stability and robustness analysis is performed for feedback linearizing controllers of crane systems in marine applications. In this scenario, external disturbances are mostly caused by the excitation of oscillations due to wind and waves. Representative simulation results and an investigation of different control procedures regarding their capability to stabilize the nonlinear closed-loop control system in the presence of stochastic disturbance inputs conclude this paper.