Robust Fault Tolerant Control Method Research For Over-Actuated Nonlinear Systems

The characteristic of the over-actuated system is that the number of actuators is greater than the number of controlled outputs,and extra actuators increases the redundancy of the system to a certain extent.At the same time,there are many complex non-linear items in the over-actuated system,which brings great difficulties to the system controller design.The T-S fuzzy model is a fuzzy system model proposed by Takagi and Sugeno in 1985.The fuzzy model uses many linear sub-models and corresponding membership functions to equivalently represent complex nonlinear systems.Based on this system,some mature linear system controller design methods can be used for nonlinear over-actuated systems.The main work of this paper is as follows:Aiming at the problem of robust fault-tolerant control of over-actuated nonlinear systems,a new robust control method is proposed.Firstly,the over-actuated nonlinear system is modeled as a T-S fuzzy system with actuator configuration matrix,and then the actuator fault is regarded as unknown signal superimposed on the controller channel,and then a robust performance index considering actuator failure,initial state and external interference is proposed.A nonlinear polynomial approximation method is used to approximate the nonlinear term in the thruster configuration matrix,and a new linear conversion method is used to convert the nonlinear polynomial into the corresponding linear function,and then perform robustness analysis to obtain the linear matrix Stability conditions in the form of inequalities(Linear Matrix Inequality,LMI).Finally,the effectiveness of the method is verified by the simulation of ship dynamic positioning.In order to reduce the conservativeness of the above method,the corresponding T-S fuzzy model is converted into a more general polynomial fuzzy model by approximating the nonlinear polynomial matrix obtained by the actuator configuration matrix.Subsequently,a robust performance index considering external interference,initial state and actuator failure is introduced,and the robust stability analysis is carried out with this performance index,and the stability conditions in the form of SOS are obtained.Compared with other methods,it is less conservative and has better control effect.Finally,a simulation example is used to verify the effectiveness of the method.