Predictive Speed Control of PMSM Based on Circular Geometric Constraints

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Abstract
To address the predictive control problem of constrained control variables in practical applications and to avoid the drawbacks of nonlinear optimization numerical solutions, such as high computational burden and slow convergence speed, the constraints on the control variables are analyzed from a geometric perspective. The current and voltage constraints are represented as two circles in the $\boldsymbol{\Delta}$udm−$\boldsymbol{\Delta}$uqm plane. By analyzing the positional relationships between the current limit circle and the voltage limit circle, the feasible regions of the constraints under different positional relationships are identified. Subsequently, the cost function is expressed as a family of equipotential surfaces. In this case, the constrained optimization problem in the optimization space is transformed into the issue of where the elliptical surface is tangent to (or intersects with) the feasible region of the constraints. By calculating the tangency points between the ellipse and the intersecting circular arcs, the optimal solutions $\boldsymbol{\Delta}$udo and $\boldsymbol{\Delta}$uqo under the constraints are obtained. The reference voltages udref and uqref in the d–q coordinate are then calculated. Experimental verification indicates that this method not only effectively constrains the motor voltage but also is simple and easy to implement, avoiding the disadvantages of high computational burden and slow convergence speed associated with numerical solution methods.
Funding Information
  • Tianjin Education Commission Scientific Research Project (2024KJ074)

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