Machine learning techniques for vector control of permanent magnet synchronous motor drives

Figures & data

Figure 1. Conventional vector control.

Figure 2. Proposed ML-based control method.

Figure 3. Proposed ML model framework.

Figure 4. Layout of proposed ML model.

Table 1. Hyperparameter settings for ML models.

ML model	Hyper-parameter	Selection
LR	Learner	svm
	Solver	BFGS
	Regularization	Ridge
	Lambda	1 / (Training sample size)
SVM	Kernel function	Linear
	Kernel scale	1
	Solver	SMO
NN	No. of hidden layers	2
	Size of hidden layers	10 + 2
	Activation function	Sigmoid function (hidden layer), linear function (output layer)
	Training algorithm	Levenberg-Marquardt algorithm

Figure 5. NN architecture.

Figure 6. Layout of an artificial neuron.

Figure 7. Conventional vs. ML-based controller performance: dq-axis reference voltages: (a) v_sd-ref and (b) v_sq-ref.

Table 2. PMSM parameters in Simulation model (Qutubuddin and N. Yadaiah, 2018, 2017).

Parameter	Description	Value	Units
R	Resistance	2.85	Ω
Ld, Lq	Inductance	0.0085	H
Ba	Friction coefficient	1 e-4	N.m-s
Jeq	Inertia	8 e-4	kg-m^2
P	Pole pairs	4	–
Ψf	Mutual flux linkage	0.1548	Wb-turns
ωm	Rated speed	300	rad/s

Figure 8. Conventional vs ML-based controllers: Motor speed response.

Figure 9. Conventional vs ML-based controllers: Motor torque response.

Figure 10. Conventional vs ML-based controllers: Current response of motor drive.

Figure 11. Conventional vs ML-based controllers: dq-axis currents (i_d, i_q) of PMSM drive.

Table 3. Comparison of speed response under rated conditions (Figure 8).

Description	PI	LR	SVM	NN
Peak overshoot (%)	1.15	1.13	1.13	1.17
Settling time (s)	0.017	0.02	0.02	0.022

Table 4. Comparison of current control performance (Figure 11).

Settling time	PI	LR	SVM	NN
For id = 0 A	0.01	0.025	0.025	0.06
For iq = 5.5 A	0.02	0.022	0.022	0.03

Figure 12. Conventional vs ML-based controllers: Motor speed response.

Figure 13. ML-based vs. Conventional controllers: Torque response for speed variations.

Figure 14. ML-based vs Conventional controllers: Motor current response for speed variations.

Figure 15. ML-based vs. Conventional controllers: Torque response for load disturbances.

Figure 16. ML-based vs. Conventional controllers: Speed response for load disturbances.

Figure 17. ML-based vs. Conventional controllers: Motor current response for load disturbances.

Figure 18. ML-based vs. Conventional controllers: Motor speed response for larger J_eq and B_a.

Figure 19. Metrics comparison of speed response (Table 5).

Table 5. Evaluation metrics for speed response under rated conditions.

	Metrics	PI	LR	SVM	NN
Rated conditions	MAE	10.9072	11.2512	11.1903	11.9194
	RMSE	40.6125	40.8831	40.8455	40.9932
	SMAPE	5.0976	5.2276	5.2072	5.4389
Speed variations	MAE	7.5233	10.0333	9.1848	8.3171
	RMSE	18.2025	19.7951	19.3128	19.0128
	SMAPE	7.9562	15.6132	12.1241	8.2194
Load disturbances	MAE	12.5194	12.6716	12.6216	15.3829
	RMSE	40.3287	40.8510	40.8211	41.0977
	SMAPE	5.5002	5.5565	5.5402	6.4487

Figure 20. Metrics comparison of reference voltage output under rated conditions (Table 6).

Table 6. Evaluation metrics (v_sd-ref, v_sq-ref)—rated conditions.

	Metrics	PI	LR	SVM	NN
vsd-ref	MAE	23.444	21.888	21.519	25.564
	RMSE	79.294	55.034	54.870	64.101
	SMAPE	20.733	27.639	27.521	30.166
vsq-ref	MAE	32.084	31.447	31.159	42.235
	RMSE	153.166	138.953	137.574	163.905
	SMAPE	7.216	7.466	7.415	12.048

Figure 21. Metrics comparison of reference voltage output under speed variations (Table 7).

Table 7. Evaluation metrics (v_sd-ref, v_sq-ref)—speed variations.

	Metrics	PI	LR	SVM	NN
vsd-ref	MAE	15.0201	21.7482	19.9905	18.3291
	RMSE	44.5536	41.6567	40.3158	46.2872
	SMAPE	25.2853	58.2353	54.4894	31.9344
vsq-ref	MAE	14.9334	22.6870	19.9989	20.2859
	RMSE	53.3610	53.7285	51.3261	60.3123
	SMAPE	8.3370	30.3406	23.1005	10.8283

Figure 22. Metrics comparison of reference voltage output under load variations (Table 8).

Table 8. Evaluation metrics (v_sd-ref, v_sq-ref)—load disturbances.

	Metrics	PI	LR	SVM	NN
vsd-ref	MAE	25.641	28.041	27.498	40.942
	RMSE	83.990	66.513	66.205	77.545
	SMAPE	18.567	26.414	26.164	44.119
vsq-ref	MAE	32.951	33.323	33.099	60.823
	RMSE	155.075	141.378	140.103	171.853
	SMAPE	8.422	9.426	9.399	27.867

Qutubuddin, M. D., & Yadaiah, N. (2018). A new intelligent adaptive mechanism for sensorless control of permanent magnet synchronous motor drive. Biologically Inspired Cognitive Architectures, 24, 47–58. https://doi.org/10.1016/j.bica.2018.04.003

 Google Scholar

Qutubuddin, M. D., & Yadaiah, N. (2017). Modeling and implementation of brain emotional controller for permanent magnet synchronous motor drive. Engineering Applications of Artificial Intelligence, 60, 193–203. https://doi.org/10.1016/j.engappai.2017.02.007

 Web of Science ®Google Scholar

Data availability statement

The data that support the findings of this study are available from the corresponding author, J. L. Febin Daya, upon reasonable request.