Nonlinear Control of Chaotic Systems in Permanent Magnet Synchronous Motors
Summary
Permanent magnet synchronous motors (PMSMs) are widely employed in industrial drives, electric vehicles and precision positioning systems due to their high efficiency and power density. Under certain operating conditions, these motors can exhibit complex chaotic dynamics arising from nonlinearities in magnetic saturation, inverter delays and feedback loops. Effective control of such chaotic behaviour is crucial to ensure stable torque production, minimise vibration and suppress torque ripple. Recent advances have focused on designing robust nonlinear controllers that can stabilise chaotic trajectories within a desired operating envelope, guarantee convergence in finite or fixed time and compensate for uncertainties arising from parameter variations and external disturbances. Techniques such as sliding mode control, disturbance observers, fuzzy modelling and fractional-order controllers have been adapted to the PMSM context, enabling real-time estimation of unmeasured states and adaptive adjustment of control gains. These methods strive to reconcile rigorous Lyapunov-based stability proofs with practical implementation constraints, delivering improved dynamic response, enhanced robustness and reduced energy losses in applications where chaotic oscillations would otherwise degrade performance.
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Nonlinear Control of Chaotic Systems in Permanent Magnet Synchronous Motors publication trend
The graph below shows the total number of articles in nonlinear control of chaotic systems in permanent magnet synchronous motors across all publications each year (not limited to Nature Index journals).
Technical terms
Permanent magnet synchronous motor (PMSM): An AC motor with a rotor fitted with permanent magnets, known for high torque density and efficiency.
Chaotic system: A deterministic nonlinear system whose trajectories exhibit extreme sensitivity to initial conditions and apparent randomness.
Lyapunov stability: A mathematical criterion ensuring that system trajectories remain arbitrarily close to an equilibrium under small perturbations.
Sliding mode control: A robust control method that forces system states onto a predefined sliding surface and maintains motion along it.
Takagi–Sugeno fuzzy model: A framework that represents a complex nonlinear system as a weighted combination of linear models based on fuzzy membership functions.
References
- Dynamical analysis of the permanent-magnet synchronous motor chaotic system. Advances in Continuous and Discrete Models (2017).
- Path Tracking of Permanent Magnet Synchronous Motor Using Fractional Order Fuzzy PID Controller. Symmetry (2021).
- Fixed‐Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control. Mathematical Problems in Engineering (2017).
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