Torque ripple of permanent magnet synchronous motor (PMSM) will result in the distortion of current waveform and the load flexibility of spiral torsion spring (STS) will affect the control performance of driving system. This study focuses on a new control problem of simultaneous suppression of PMSM's torque ripple and flexible load's vibration. First, the Lagrange equation is used to establish the dynamic model of STS to describe its vibration mode. The overall model of STS directly derived by PMSM under stator current vector orientation is built. Then, based on the magnetic co-energy model of electromagnetic torque of PMSM, the constraint relation of optimal stator harmonic current under the condition of torque ripple minimisation is derived, and the controller based on stator current oriented closed-loop I/f control to suppress load vibration and torque ripple simultaneously is presented through backstepping control. A wide speed range identification method based on the least-square algorithm with a forgetting factor is also designed. The simulation and experiment show that the speed identification algorithm can estimate the speed accurately in a wide range. The proposed control scenario improves control performance, smoothes current waveform and inhibits torque ripple and load vibration effectively.

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The operational performance of the spiral spring energy storage system is affected by the vibration of the spiral spring and the electrical loss of the permanent magnet synchronous motor. It is important to eliminate vibration and reduce electrical loss. A unified control scenario for speed regulation and vibration suppression based on the minimum electrical loss is proposed. First, the spiral spring is equivalent to an Euler–Bernoulli beam and its dynamic model suitable for control is established via the Lagrange equation. Then, the unified control scenario is proposed through nonlinear backstepping control. The speed controller and current controller including modal vibration suppression and minimum electrical loss operation of the system are established, and the stability of the controller is theoretically proved. Moreover, for unknown vibration mode of the spiral spring, a vibration mode–based estimation method with the least-squares algorithm is designed. Aiming at the uncertainty of the permanent magnet synchronous motor’s iron loss resistance, an estimation algorithm based on an adaptive neural fuzzy inference system is designed. The experimental results verify the correctness and effectiveness of the proposed control scheme. In comparison with traditional backstepping control, the proposed control method can effectively suppress the vibration of the spiral spring and realize the stable and highly efficient energy storage operation of the system.

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Existing research studies on torque ripple suppression mostly ignore the electrical loss of PMSM. However, the electrical loss will not only decrease the operating efficiency but also adversely influence the suppression of torque ripple. This paper attempts to construct a unified framework to suppress torque ripple with consideration of electrical loss. Firstly, a dynamic mathematical model of PMSM under current vector orientation is established with a combination of electrical loss. The constraints that can achieve the control of both torque ripple and electrical loss for PMSM are derived. Then, on the basis of the backstepping control principle, a closed-loop I/f integrative control method under stator current vector orientation is proposed. Meanwhile, this paper also proposes a speed estimation algorithm of PMSM based on the least-squares method to realize wide-range speed identification and an online prediction algorithm for control parameters of backstepping control to enhance the stability of the motor in operation. Both simulations and experiments have been performed to verify the effectiveness of the proposed control method, and the results indicate that torque ripple is suppressed effectively, operating efficiency is significantly improved, and all variables are regulated to track their reference signals correctly and rapidly.