Robust Control Of Adaptive Predefined Space-Time Convergence For Piezoelectric Fast Steering Mirror

Nowadays,with the rapid development of technologies such as space laser communication and laser processing,traditional tracking control technologies fail to meet the high accuracy requirements.Hence,the composite tracking control technology,which consists of the coarse tracking and the fine tracking,has been developed.As the fine tracking subsystem of the composite tracking system,the control accuracy of the fast steering mirror system determines the ultimate accuracy of the composite tracking system.In order to optimize the system performance and achieve high-speed and high-accuracy control of the piezoelectric fast steering mirror,the main research contents of this paper are depicted as follows:Firstly,in consideration of the predefined time function and state-dependent upper bound assumption,the predefined space-time adaptive sliding mode control(PSASMC)method is proposed,which achieves the predefined space-time convergence of the piezoelectric actuator.Moreover,both the convergence time and accuracy are independent of the initial condition,lumped uncertainty,and other control parameters.Besides,by devising the state-dependent upper bound assumption,the proposed method removes the conservatism of the lumped uncertainty constant upper bound assumption.In addition,through the theoretical analysis,numerical simulations,and piezoelectric actuator experiments,the effectiveness of the proposed method is verified.Secondly,based on the saturation-tolerant factor and time-based barrier function,the saturation-tolerant predefined space-time adaptive super twisting control(SPSASTC)method is reported,which ensures the saturation-tolerant predefined space-time convergence of the piezoelectric fast steering mirror under input saturation.The saturation-tolerant factor generated by the auxiliary system constructs the relationship between the saturation-tolerant predefined space and input saturation.Then,by integrating the saturation-tolerant factor,the SPSASTC method can automatically adjust the saturation-tolerant predefined space according to the condition of input saturation.Besides,the proposed method not only reduces the overestimation of the control gain,but also avoids the segmentation of the control method.In view of the theoretical analysis,numerical simulations,and piezoelectric fast steering mirror experiments,the validity of the proposed method is verified.Finally,according to the reference convergence differential function,the saturationtolerant strict predefined time control(SSPTC)method is devised,which enables the saturationtolerant strict predefined time convergence of the nominal piezoelectric fast steering mirror system.Then,noting the SSPTC method and new-type barrier function,the saturation-tolerant strict predefined space-time adaptive sliding mode control(SSPSASMC)method is further designed,which achieves the saturation-tolerant strict predefined space-time convergence of the piezoelectric fast steering mirror with the existence of input saturation.In view of the theoretical analysis,numerical simulations,and piezoelectric fast steering mirror experiments,the superior properties of the proposed methods are tested.