PMSM混沌系统无初始状态约束的固定时间有界控制

Fixed Time Bounded Control of PMSM Chaotic Systems without Initial State Constraints

永磁同步电机(PMSM)是一种多变量、耦合性强的非线性系统,在实际运行过程中会出现混沌振荡。为了抑制PMSM系统的混沌,本文设计一种无初始状态约束的固定时间有界控制器。首先根据PMSM系统各个子系统的虚拟误差设计虚拟控制器,通过反步法推导得出控制器具有较高的抗干扰性能和鲁棒性,并证明时变反馈参数能够保证系统在到达有限时间收敛的同时达到渐近稳定,且稳定时间只与规定的边界有关。最后数值仿真通过调整控制系数k使系统能够在不同的初始状态下快速达到稳定,验证了所设计的控制器无论系统的初始状态如何,都能够使系统在2.8 s内达到稳定状态且输出收敛于给定的边界。

Permanent magnet synchronous motor(PMSM)is a multivariable and highly coupled nonlinear system,which is subject to chaotic oscillations during practical operation.In order to suppress the chaos of the PMSM system,a fixed-time bounded controller without initial state constraints is designed,which can make the system reach a stable state within 2.8 s.Firstly,the virtual controller is designed according to the virtual errors of each subsystem of the PMSM system,and the controller is derived by backstepping to have high anti-interference performance and robustness.Secondly,it is proved that the time-varying feedback parameter ensures that the system achieves asymptotic stabilization while arriving at the finite-time convergence,and the stabilization time is only related to the prescribed boundary.Finally,numerical simulations are carried out by adjusting the control coefficients k so that the system can reach stability quickly under different initial states,and it is verified that the designed controller is able to make the system reach asymptotic stability and the output converge to the given boundary regardless of the initial state of the system.