A Feedback Systems Approach to Copper-Loss Minimization of Anisotropic Synchronous Machines

A feedback-systems-based approach for real-time copper-loss minimization of nonlinear anisotropic permanent magnet synchronous motors (PMSMs) considering saturation and cross coupling is proposed. The procedure is based on a feedback systems formulation of the underlying optimization problem for maximum torque per current (MTPC) control. A nonlinear dynamical system is derived that describes the scalar product of the tangent of the torque curve and the gradient of the current circle. By a suitable feedback design, a closed expression of the control input of the nonlinear current dynamics in the direct-quadrature (<inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>)-axis is obtained. As a result, the solution of the differential equations of the nonlinear current dynamics yields the desired optimal setpoint <inline-formula> <tex-math notation="LaTeX">$d/q$ </tex-math></inline-formula> currents. The stability of the designed feedback system for MTPC control is thoroughly examined by Lyapunov’s direct method. Comparative studies for measured data as well as an analysis of computational runtimes confirm the effectiveness of the proposed method.