Stability Analysis Of PMSM With Time-delayed Fractional-order PID Controller

Permanent magnet synchronous motor(PMSM)is the most competitive driving motor,which is widely used in high performance driving systems for the advantages of high efficiency,high power density and high torque inertia ratio.At present,the motor control system and digital active control technology for PMSM has become a mainstream direction of the development of motion control system.The time-delay effect will occur in the small time-delayed link of digital active control technology,but the inherent time-delay effect of this control system often affects the stability and the control performance of the control system.Aim to current loop of PMSM under PI control,the inherent delay of current loop digital control is analyzed,and the mathematical model of fractional differential equation with time delay is established.The stability of the difference equation of current loop PI control system is analyzed,based on the stability theory of difference equation.Extending synchronous controller to asynchronous PI controller,asynchronous PD controller and asynchronous PID controller,the stability of the system with asynchronous controller is analyzed respectively.Based on the stability theory of fractional differential equation with time delay,the time-delay parameter stability regions of current loop for PMSM with time-delayed asynchronous PI~?and PI~?D~?controller are analysed by using the fractional integral upper bound method.The influence of fractional order of?and?on the stability region of time-delay parameters in control systems is analyzed.The relationship between the number of delay periods and the stable region of delay parameters in asynchronous control is found.The gain parameter stability region of time-delay fractional-order current loop control system is obtained by using fractional-order stability switching theory.And the difference of parameter stability region of asynchronous control mode is analyzed.The influence of fractional order of?and?on the parameter stability region of current loop control system is analyzed.Finally,the simulation model of permanent magnet synchronous motor is established by using MATLAB to verify the analysis results.