PMSM混沌系统的自适应反步控制

Adaptive backstepping control of permanent magnet synchronous motor chaotic system

基于永磁同步电机的混沌模型,当系统中含有不确定性参数时,设计一种自适应反步控制器,使系统从混沌状态中恢复过来,渐进跟踪期望速度并保持稳定。首先,对给定的期望转速和期望直轴电流,构造误差系统,用反步法设计子系统的控制器,在每个子系统中构造Lyapunov函数和虚拟控制量,获得使系统渐进稳定的期望的交轴电流的期望值。然后,当永磁同步电机混沌系统中的2个未知参数负载转矩和永磁磁通变化时,根据Lyapunov稳定性原理,用反步法设计出负载转矩和永磁磁通的自适应控制器,实现永磁同步电机混沌系统对速度的跟踪以及参数的一致收敛。数值仿真结果表明:所设计的自适应控制器是有效的,能使受控系统从混沌状态变成可控状态,并快速的跟踪期望速度,同时未知参数的估计值收敛达到了实际值。

A new type of adaptive backstepping controller was designed for the permanent magnet synchronous motor chaotic model with uncertain parameters when the system was in a chaotic state, allowing the system to recover from the chaos, keep asymptotic tracking of the desired speed and be stable. First, for a given expected speed and a direct axis current, error system was constructed. The controller of each subsystem was designed by backstepping method. The Lyapunov function and virtual control quantity was structured to obtain the expected quadrature axis current which made PMSM system asymptotically stable in each subsystem. Then, when load torque was unknown and permanent magnet flux changed in the PMSM chaos system, the load torque, and permanent magnet flux adaptive control law were designed by Lyapunov stability theorem. Next, the adaptive controller of unknown PMSM system was obtained to realize the asymptotic tracking of the speed reference and keep the uniform convergent to unknown parameters. Numerical simulation results show that the adaptive controller is valid. The controlled system can quickly track the desired speed and keep it stable, and estimation of unknown parameter has achieved the practical value.