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Nonlinear Optimal Control of Magnetically Geared Induction Motors Cover

Nonlinear Optimal Control of Magnetically Geared Induction Motors

Power Electronics and Drives
Volume 10 (2025): Issue 1 (January 2025)
By: G. Rigatos,  P. Siano,  M. Abbaszadeh,  G. Cuccurullo and  K. Ouahada  
Open Access
|Aug 2025

Figures & Tables

Figure 1.

Diagram of the traction system of an EV based on a MGIM. EV, electric vehicle; MGIM, magnetically geared induction motor.
Diagram of the traction system of an EV based on a MGIM. EV, electric vehicle; MGIM, magnetically geared induction motor.

Figure 2.

Diagram of the control scheme for the MGIM. MGIM, magnetically geared induction motor.
Diagram of the control scheme for the MGIM. MGIM, magnetically geared induction motor.

Figure 3.

Tracking of setpoint 1 by the MGIM with the use of non-linear optimal control: (a) convergence of state variables x1 to x3 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering (b) convergence of state variables x4 to x6 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering. MGIM, magnetically geared induction motor.
Tracking of setpoint 1 by the MGIM with the use of non-linear optimal control: (a) convergence of state variables x1 to x3 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering (b) convergence of state variables x4 to x6 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering. MGIM, magnetically geared induction motor.

Figure 4.

Tracking of setpoint 1 by the MGIM with the use of non-linear optimal control: (a) variations of the control inputs u1 and u2 (blue lines) (b) variation of the tracking error variables ei, i = 1,…,6 associated with the state variables xi, i = 1,…,6. MGIM, magnetically geared induction motor.
Tracking of setpoint 1 by the MGIM with the use of non-linear optimal control: (a) variations of the control inputs u1 and u2 (blue lines) (b) variation of the tracking error variables ei, i = 1,…,6 associated with the state variables xi, i = 1,…,6. MGIM, magnetically geared induction motor.

Figure 5.

Tracking of setpoint 2 by the MGIM with the use of non-linear optimal control: (a) convergence of state variables x1 to x3 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering (b) convergence of state variables x4 to x6 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering. MGIM, magnetically geared induction motor.
Tracking of setpoint 2 by the MGIM with the use of non-linear optimal control: (a) convergence of state variables x1 to x3 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering (b) convergence of state variables x4 to x6 (blue lines) to the associated setpoints (red lines) and estimated values provided by Kalman Filtering. MGIM, magnetically geared induction motor.

Figure 6.

Tracking of setpoint 2 by the MGIM with the use of non-linear optimal control: (a) variations of the control inputs u1 and u2 (blue lines) (b) variation of the tracking error variables ei, i = 1,…,6 associated with the state variables xi, i = 1,…,6. MGIM, magnetically geared induction motor.
Tracking of setpoint 2 by the MGIM with the use of non-linear optimal control: (a) variations of the control inputs u1 and u2 (blue lines) (b) variation of the tracking error variables ei, i = 1,…,6 associated with the state variables xi, i = 1,…,6. MGIM, magnetically geared induction motor.

Tracking RMSE for the MGIM in the disturbance-free case

RMSEx1RMSEx2RMSEx3RMSEx4RMSEx5RMSEx6
Test10.00520.00260.00640.00370.00010.0002
Test20.00410.00200.00640.00630.00020.0003

Tracking RMSE for the MGIM in the case of disturbances

Δa%RMSEx1RMSEx2RMSEx3RMSEx4RMSEx5RMSEx6
0%0.00520.00260.00640.00370.00010.0002
10%0.00570.00290.00640.00140.00010.0003
20%0.00620.00310.00640.00070.00010.0003
30%0.00660.00330.00640.00270.00020.0001
40%0.00690.00350.00650.00460.00020.0003
50%0.00730.00360.00650.00640.00020.0003
60%0.00750.00380.00650.00810.00020.0003

Parameters of the MGIM dynamic model_

ParameterDefinition
ωm, ωLAngular speed of the motor, load
Jm, JL, JgMoment of inertia of the rotor, load, gear
Te, TL, TgTorque of the rotor, load, gear
ϕAngle denoting the speed difference between rotor and load
GrTransmission ratio of the magnetic gear
Bm, BL, BgFriction coefficient at rotor, load and gear
po, pmNumber of ferromagnetic pole pieces and air gaps
nLSum of ferromagnetic pole pieces and air gaps
isd, isqd,q axis components of the IM stator currents
Rs, RrResistance of the IM’s stator, rotor
ψrd, ψrqd,q axis components of the IM rotor flux
Ls, LrInductance of the IM’s stator, rotor
MMutual inductance between IM’s stator and rotor
npNumber of poles of the IM’s stator
ρOrientation of the IM’s magnetic field
α, β, γ α=RrLr,β=MσLsLs,γ=M2RrσLsLr2+RsσLs \alpha = {{{R_r}} \over {{L_r}}},\beta = {M \over {\sigma {L_s}{L_s}}},\gamma = {{{M^2}{R_r}} \over {\sigma {L_s}{L_r}^2}} + {{{R_s}} \over {\sigma {L_s}}}
μ, σ μ=npMJ,σ=1−M2LsLr \mu = {{{n_p}M} \over J},\sigma = 1 - {{{M^2}} \over {{L_s}{L_r}}}
DOI: https://doi.org/10.2478/pead-2025-0009 | Journal eISSN: 2543-4292 | Journal ISSN: 2451-0262
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Language: English
Page range: 227 - 240
Submitted on: Feb 19, 2025
|
Accepted on: May 7, 2025
|
Published on: Aug 19, 2025
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
magnetically geared induction motors,
non-linear optimal control,
Taylor series expansion,
Lyapunov analysis,
differential flatness
Related subjects:
Computer sciences,
Artificial intelligence,
Engineering,
Electrical engineering,
Electronics

© 2025 G. Rigatos, P. Siano, M. Abbaszadeh, G. Cuccurullo, K. Ouahada, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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