Exhaustive Search-Based Multi-Criteria Optimization of the Anti-Windup Gain for PMSM Speed Control
Keywords:
Permanent Magnet Synchronous Motor (PMSM), Anti-windup Control, PI Controller, Exhaustive Search Optimization, Wolfram Mathematica, Speed ControlAbstract
Current and voltage saturation can significantly degrade the dynamic performance of permanent
magnet synchronous motor (PMSM) drive systems by causing integrator windup in proportional–integral
(PI) controllers. This paper explains an exhaustive search optimization approach for determining the
optimal anti-windup gain of a PI-based PMSM speed controller formulated in the synchronous d-q
reference frame. The dynamic model here incorporates the electrical and mechanical equations of the
PMSM together with cross-coupling compensation, current limitation, voltage vector saturation, and a soft
speed-limiting mechanism. A weighted multi-criteria objective function is formulated by combining the
Integral of Time-Weighted Absolute Error (ITAE), maximum overshoot, steady-state speed error, and
speed-limit violation. The objective function is evaluated for each candidate anti-windup gain within a
predefined search space using an exhaustive search optimization procedure, and the gain corresponding to
the minimum objective value is selected as the optimal solution. The complete mathematical modeling,
numerical simulation, performance evaluation, and optimization framework is developed and implemented
in the Wolfram Mathematica environment. Simulation results demonstrate that the optimized anti-windup
gain significantly improves the transient response, reduces overshoot and steady-state error, mitigates
integrator windup under saturation conditions, and effectively enforces the prescribed speed limit. The
proposed optimization framework provides a simple, systematic, practical, and computationally efficient
methodology for tuning anti-windup PI controllers in PMSM drive applications operating under current
and voltage constraints.
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