Abstract As the model predictive control (MPC) is conceptually clear and simple to implement with the ability to control several nonlinear objectives simultaneously, it is the preferred control method for permanent magnet synchronous motors (PMSM). However, the resistance, inductance, and other parameters in the current prediction model are vulnerable to nonlinear factors and changes in the load, resulting in model parameters mismatch, ultimately weakening the robustness and dynamic response ability of the MPC. Recently, although many papers have analyzed the influence of inductance and resistance mismatch on control performance, the influence of flux mismatch has yet to be considered. Additionally, the Euclidean norm, Euclidean norm square, and modular sum cost functions commonly used in MPC systems are considered equivalent. However, more theoretical analysis and experimental verification of the difference and relationship between the three cost functions are still necessary. Therefore, a visual analysis method is proposed to study the effects of different parameter mismatches on the MPC system of PMSM under different cost functions. Firstly, the reference voltage that meets the control requirements is calculated based on deadbeat control principle. Secondly, the influence of parameters such as resistance, inductance, and flux linkage on the reference voltage is analyzed. The change of the reference voltage spatial position due to different parameter mismatches is determined. Then, based on the mismatched reference voltage, the optimal voltage vectors of different cost functions are obtained. Finally, the Matlab algorithm is used to visually express the selected optimal voltage vectors under all reference voltages. The influence and difference of parameter mismatch on the selection of optimal voltage vectors under different cost functions are analyzed by visualization method, which provides a solid theoretical basis for error compensation control methods. The experiments of inductance and flux mismatch in the speed loop show that when the load torque is set to 10N·m, and the reference speed is stepped up from 150 r/min to 1 000 r/min, the inductance mismatch has an impact on the selection times of zero vector. Thus, the effective value of the total current error is greater than when the inductance is matched. Meanwhile, at low speed, the current ripples when the flux linkage is mismatched are similar to when the one is matched. However, at high speed, the current ripples and effective value of the total current error when the flux linkage is mismatched are significantly larger than when the one is matched. When the speed is set to 1 000 r/min and the load torque is changed from no-load to full load (25 N·m) and then to no-load, the current ripples and total current error when the inductance and flux linkage are mismatched are larger than those when the parameters are matched. Additionally, under the same conditions, the current ripples and the effective values of total current error under the two Euclidean norm cost functions are smaller than those under the modular sum cost function, indicating that the Euclidean norm cost functions have better control effects. The experimental results are consistent with the visualization analysis results, which shows the correctness and effectiveness of the proposed visualization method. The following conclusions can be drawn from the theoretical and experimental analysis: (1) Parameter mismatches will affect the optimal voltage vector selection for the MPC method. (2) The MPC methods based on different cost functions have different parameter sensitivities. (3) The two Euclidean norm cost functions are preferred for MPC as they have smaller control errors when the parameters are mismatched.
Guo Leilei,Wang Pengshuai,Li Yanyan等. Visual Analysis of Parameters Mismatch in Model Predictive Control for Permanent Magnet Synchronous Motor Under Different Cost Functions[J]. Transactions of China Electrotechnical Society, 2023, 38(4): 903-914.
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