Speed Control of Permanent Magnet Synchronous Motor with State and Input Constraints

This paper researched in tackling with paradox between celerity and saturation constraints in the speed control of PMSM. The state variable cannot be in the desired boundary if only considering the saturation of input for its nonlinear. So it is necessary to draw into state constraints. According to the relativity of the system being 2 and the system can be described as the cascaded former, the paper proposes a backstepping approach. Firstly by constructing Lyapunov function to design the control law without saturated, this is to ensure that the system asymptotically stable. Then the control law is extended to the condition of the saturation of input and state by drawing into low-pass filter. It is proved that the expanded control law under the saturation constraints can also make the system asymptotically stable strictly through the reconstruction of Lyapunov function, while it can eliminate expansion of calculation caused by the differentiation of virtual control law. Finally the simulation shows the validity of this method.