An integrated scheme of speed control and vibration suppression for spiral spring energy storage system driven by PMSM based on backstepping control with minimum electrical loss

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.