Stability analysis of BLDC motor speed controllers under the presence of time delays in the control loop

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Stability analysis of BLDC motor speed controllers under the presence of time delays in the control loop

Pimentel, Julio C. G. / Gad, Emad / Roy, Sebastien

This work discusses the stability issues of PI-based brushless DC motor (BLDCM) speed controllers under the presence of strong time delay in the controller loop. Understanding of the time delay effect is of paramount importance to increase performance, quality and productivity in important modern applications. Unfortunately, the time delay effect in the speed controller asymptotic stability has not been well studied in the existing literature. In this work, we present an algebraic technique to calculate the maximum time delay that can be accepted in the control loop of a BLDCM speed controller before the response becomes unstable. Initially, we derive an analytical model for the set point tracking (SPT) and the load disturbance rejection (LDR) responses taking into account the various sources of time delay. Using a recently proposed stability analysis methodology, we derive accurate stability conditions for the BLDCM speed controller. The results show that tuning the PI controller for very fast response causes the time delay to significantly affect the system stability. As an example, the asymptotic stability of the LDR of a sensored controller is analyzed. The method proposed here can be easily extended to analyze the stability of the SPT response and the stability of sensorless controllers such as the direct Back EMF.