# Real-Time Analysis of a Modified State Observer for Sensorless Induction Motor Drive Used in Electric Vehicle Applications

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. General Configuration of Model Reference Adaptive Systems and System Modeling

_{ref}and X

_{adap}are outputs of respective models. The adaptation mechanism makes use of the classical Proportional-Integral theory to process the speed tuning signal. A Lyapunov function candidate is used for the speed derivation mechanism.

#### 2.1. Structure of Sliding Mode Luenberger State Observer

_{eq}(t) and u

_{sw}(t) represent the control, equivalent control and the switching vector. For stability, the switching vector is obtained [17,26]:

#### 2.1.1. Reference Model (Motor)

- $\mathrm{x}={\left[{\mathrm{i}}_{\mathrm{ds}}^{\mathrm{s}},{\mathrm{i}}_{\mathrm{qs}}^{\mathrm{s}},{\mathsf{\psi}}_{\mathrm{dr}}^{\mathrm{s}},{\mathsf{\psi}}_{\mathrm{qr}}^{\mathrm{s}}\right]}^{\mathrm{T}}$, $\mathrm{A}=\left[\begin{array}{cc}{\mathrm{A}}_{11}& {\mathrm{A}}_{12}\\ {\mathrm{A}}_{21}& {\mathrm{A}}_{22}\end{array}\right]$,
- $\mathrm{B}={\left[\frac{1}{{\mathsf{\sigma}\mathrm{L}}_{\mathrm{s}}}\mathrm{I}0\right]}^{\mathrm{T}}$, $\mathrm{C}=\left[\mathrm{I},0\right]$, $\mathrm{u}={\left[{\mathrm{v}}_{\mathrm{ds}}^{\mathrm{s}}{\mathrm{v}}_{\mathrm{qs}}^{\mathrm{s}}\right]}^{\mathrm{T}}$,
- $\mathrm{I}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, $\mathrm{J}=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$,
- ${\mathrm{A}}_{11}=-\left[\frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathsf{\sigma}\mathrm{L}}_{\mathrm{s}}}+\frac{1-\mathsf{\sigma}}{{\mathsf{\sigma}\mathrm{T}}_{\mathrm{r}}}\right]\mathrm{I}={\mathrm{a}}_{\mathrm{r}11}\mathrm{I},{\mathrm{A}}_{12}=\frac{{\mathrm{L}}_{\mathrm{m}}}{{\mathsf{\sigma}\mathrm{L}}_{\mathrm{s}}{\mathrm{L}}_{\mathrm{r}}}\left[\frac{1}{{\mathrm{T}}_{\mathrm{r}}}\mathrm{I}-{\mathsf{\omega}}_{\mathrm{r}}\mathrm{J}\right]={\mathrm{a}}_{\mathrm{r}12}\mathrm{I}+{\mathrm{a}}_{\mathrm{i}12}\mathrm{J}$,
- ${\mathrm{A}}_{21}=\frac{{\mathrm{L}}_{\mathrm{m}}}{{\mathrm{T}}_{\mathrm{r}}}\mathrm{I}={\mathrm{a}}_{\mathrm{r}21}\mathrm{I}$,
- ${\mathrm{A}}_{22}=\frac{-1}{{\mathrm{T}}_{\mathrm{r}}}\mathrm{I}+{\mathsf{\omega}}_{\mathrm{r}}\mathrm{J}={\mathrm{a}}_{\mathrm{r}22}\mathrm{I}+{\mathrm{a}}_{\mathrm{i}22}\mathrm{J}$.

#### 2.1.2. Estimation of Disturbance Torque from the Mechanical Model

#### 2.1.3. SMLO 1—Observer with Conventional Disturbance Rejection Mechanism (Adaptive Model)

- $\widehat{\mathrm{A}}=\left[\begin{array}{cc}{\mathrm{A}}_{11}& {\widehat{\mathrm{A}}}_{12}\\ {\mathrm{A}}_{21}& {\widehat{\mathrm{A}}}_{22}\end{array}\right]$,
- ${\widehat{\mathrm{A}}}_{12}=\frac{{\mathrm{L}}_{\mathrm{m}}}{{\mathsf{\sigma}\mathrm{L}}_{\mathrm{s}}{\mathrm{L}}_{\mathrm{r}}}\left[\frac{1}{{\mathrm{T}}_{\mathrm{r}}}\mathrm{I}-{\widehat{\mathsf{\omega}}}_{\mathrm{r}}\mathrm{J}\right]={\mathrm{a}}_{\mathrm{r}12}\mathrm{I}+{\widehat{\mathrm{a}}}_{\mathrm{i}12}\mathrm{J}$,
- ${\widehat{\mathrm{A}}}_{22}=\frac{-1}{{\mathrm{T}}_{\mathrm{r}}}\mathrm{I}+{\widehat{\mathsf{\omega}}}_{\mathrm{r}}\mathrm{J}={\mathrm{a}}_{\mathrm{r}22}\mathrm{I}+{\widehat{\mathrm{a}}}_{\mathrm{i}22}\mathrm{J}$.

_{2}” are chosen in such a way that the eigenvalues of the observer are shifted more negative as compared to the eigenvalues of the motor. They also directly affect the dynamics and damping of the observer. “k

_{1}” is dependent on the motor parameters.

#### 2.1.4. SMLO 2—Observer with Modified Disturbance Rejection Mechanism (Adaptive Model)

#### 2.1.5. Adaptive Mechanism

#### 2.2. Stability Analysis of Both the Observers by Means of Pole Placement

#### 2.3. Structure of Current Regulated Vector Controller

_{c}is the speed error, kp and ki are the proportional and integral gains for tuning the speed error, and Ts is the sampling time. For operation in the motoring and flux weakening region, the rotor flux is constant for the former and as a function of the speed for the latter:

## 3. The Concept of Real-Time Simulation

## 4. Real-Time Simulation Results: Analysis and Discussion

#### 4.1. Performance at Flux Weakening

#### 4.2. Performance at Step Speed Command

#### 4.3. Performance at Low Speeds

#### 4.4. Effect of Parameter Detuning on the Dynamic Performance

#### 4.5. Switching Surface and Convergence of the Stator Current Error

#### 4.6. Pole Placement Plot of the Modified nd Conventional Disturbance Observers

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

i_{ds}^{s}, i_{qs}^{s}, i_{dr}^{r}, i_{qr}^{r} | Direct and quadrature axes stator and rotor current components in stationary and rotating frame |

v_{ds}^{s}, v_{qs}^{s} | Direct and quadrature stator voltages in stationary frame |

T_{r}, R_{s}, R_{r} | Rotor time constant, stator and rotor resistance |

σ, L_{r}, L_{m}, L_{s} | Leakage reactance, rotor, magnetizing and stator self inductance |

L_{ls}, L_{lr} | Stator and rotor leakage inductances |

${\mathsf{\omega}}_{\mathrm{r}},{\widehat{\mathsf{\omega}}}_{\mathrm{r}},{\mathsf{\omega}}^{*},{\mathsf{\omega}}_{\mathrm{bsync}}$ | Actual, estimated, reference and base synchronous speed |

ψ_{ds}^{s}, ψ_{qs}^{s}, ψ_{dr}^{s}, ψ_{qr}^{s} | Direct and quadrature axes stator and rotor flux linkages in stationary frame |

${\widehat{\mathsf{\phi}}}_{\mathrm{d}},{\widehat{\mathsf{\phi}}}_{\mathrm{q}}$ | Direct and quadrature axes estimated rotor flux linkages |

${\mathsf{\theta}}_{\mathrm{f}},{\mathsf{\theta}}_{\mathrm{sl}},{\mathsf{\theta}}_{\mathrm{r}}$, ${\mathrm{T}}_{\mathrm{e}}^{*}$ | Field, slip and rotor angles and Torque reference |

${{\mathrm{i}}_{\mathrm{ds}}}^{*},{\mathrm{i}}_{\mathrm{qs}}^{*}$ | Direct and quadrature axes stator currents in synchronously rotating frame |

${\mathrm{i}}_{\mathrm{as}}^{*},{\mathrm{i}}_{\mathrm{bs}}^{*},{\mathrm{i}}_{\mathrm{cs}}^{*}$ | Three-phase reference currents |

## Appendix A

_{s}= 0.087 Ω, R

_{r}= 0.228 Ω, L

_{ls}= L

_{lr}= 0.8 mH, L

_{m}= 34.7 mH, Inertia, J = 1.662 kgm

^{2}, friction factor = 0.1.

## References

- Anitha, P.; Badrul, H.C. Sensorless control of inverter-fed induction motor drives. Electr. Power Syst. Res.
**2007**, 77, 619–629. [Google Scholar] - Yang, Z.; Yue, Q.; Ye, Y. Induction Motor Speed Control Based on Model Reference. Procedia Eng.
**2012**, 29, 2376–2381. [Google Scholar] - Abd El-Halim, A.F.; Abdulla, M.M.; El-Arabawy, I.F. Simulation Aides in Comparison between Different Methodology of Field Oriented Control of Induction Motor Based on Flux and Speed Estimation. In Proceedings of the 22nd International Conference on Computer Theory and Applications, Alexandria, Egypt, 13–15 October 2012. [Google Scholar]
- Sun, D.; Lin, W.; Diao, L.; Liu, Z. Speed Sensorless Induction Motor Drive Based on EKF and Γ-1 Model. In Proceedings of the IEEE International Conference on Computer Distributed Control and Intelligent Environmental Monitoring, Changsha, China, 19–20 February 2011. [Google Scholar]
- Alonge, F.; D’Ippolito, F.; Sferlazza, A. Sensorless Control of Induction-Motor Drive Based on Robust Kalman Filter and Adaptive Speed Estimation. IEEE Trans. Ind. Electron.
**2014**, 61, 1444–1453. [Google Scholar] [CrossRef] - Rezgui, S.E.; Benalla, H. MRAS sensorless based control of IM combining sliding-mode, SVPWM, and Luenberger observer. In Proceedings of the International Conference on Computer as a Tool, Lisbon, Portugal, 27–29 April 2011. [Google Scholar]
- Zheng, Y.; Loparo, K.A. Adaptive Flux Observer for Induction Motors. In Proceedings of the American Control Conference, Philadelphia, PA, USA, 24–26 June 1998. [Google Scholar]
- Ticlea, A.; Besancon, G. Observer Scheme for State and Parameter Estimation in Asynchronous Motors with Application to Speed Control. Eur. J. Control
**2006**, 12, 400–412. [Google Scholar] [CrossRef] - Mikail, R.; Rahman, K.M. Sensorless Adaptive Rotor Parameter Estimation Method for Three Phase Induction Motor. In Proceedings of the IEEE 5th International Conference on Electrical and Computer Engineering, Dhaka, Bangladesh, 25–27 December 2008. [Google Scholar]
- Levi, E.; Wang, M. Impact of Parameter Variations on Speed Estimation in Sensorless Rotor Flux Oriented Induction Machines. In Proceedings of the IEEE Power Electronics and Variable Speed Drives, London, UK, 21–23 September 1998. [Google Scholar]
- Gadoue, S.M.; Giaouris, D.; Finch, J.W. Performance Evaluation of a Sensorless Induction Motor Drive at Very Low and Zero Speed Using a MRAS Speed Observer. In Proceedings of the IEEE 2008 Region 10 Colloquium and the Third International Conference on Industrial and Information Systems, Kharagpur, India, 8–10 December 2008. [Google Scholar]
- Rashed, M.; Stronach, A.F. A stable back-EMF MRAS-based sensorless low-speed induction motor drive insensitive to stator resistance variation. IEE Proc. Electr. Power Appl.
**2004**, 151, 685–693. [Google Scholar] [CrossRef] - Beguenane, B.; Ouhrouche, M.A.; Trzynadlowski, A.M. A new scheme for sensorless induction motor control drives operating in low speed region. Math. Comput. Simul.
**2006**, 71, 109–120. [Google Scholar] [CrossRef] - Lascu, C.; Boldea, I.; Blaabjerg, F. A Class of Speed-Sensorless Sliding-Mode Observers for High-Performance Induction Motor Drives. IEEE Trans. Ind. Electron.
**2009**, 56, 3394–3403. [Google Scholar] [CrossRef] - Gadoue, S.M.; Giaouris, D.; Finch, J.W. MRAS Sensorless Vector Control of an Induction Motor Using New Sliding-Mode and Fuzzy-Logic Adaptation Mechanisms. IEEE Trans. Energy Convers.
**2010**, 25, 394–402. [Google Scholar] [CrossRef] - Zhang, X. Sensorless Induction Motor Drive Using Indirect Vector Controller and Sliding-Mode Observer for Electric Vehicles. IEEE Trans. Veh. Technol.
**2013**, 62, 3010–3018. [Google Scholar] [CrossRef] - Krishna, S.M.; Daya, J.L.F. A modified disturbance rejection mechanism in sliding mode state observer for sensorless induction motor drive. Arab. J. Sci. Eng.
**2016**, 41, 3571–3586. [Google Scholar] [CrossRef] - Nayeem Hasan, S.M.; Husain, I. A Luenberger-Sliding Mode Observer for Online Parameter Estimation and Adaptation in High-Performance Induction Motor Drives. IEEE Trans. Ind. Appl.
**2009**, 45, 772–781. [Google Scholar] [CrossRef] - Albu, M.; Horga, V.; Ratoi, M. Disturbance torque observers for the induction motor drives. J. Electr. Eng.
**2006**, 6, 1–6. [Google Scholar] - Krzeminski, Z. Observer of induction motor speed based on exact disturbance model. In Proceedings of the IEEE 13th International Power Electronics and Motion Control Conference, Poznan, Poland, 1–3 September 2008. [Google Scholar]
- Krzeminski, Z. A new speed observer for control system of induction motor. In Proceedings of the IEEE International Conference on Power Electronics and Drive Systems, Hong Kong, China, 27–29 July 1999. [Google Scholar]
- Vieira, R.P.; Gabbi, T.S.; Grundling, H.A. Sensorless decoupled IM current control by sliding mode control and disturbance observer. In Proceedings of the IEEE 40th Annual Conference, Dallas, TX, USA, 30 October–1 November 2014. [Google Scholar]
- Comanescu, M. Design and analysis of a sensorless sliding mode flux observer for induction motor drives. In Proceedings of the IEEE International Electric Machines and Drives Conference, Niagara Falls, ON, Canada, 15–18 May 2011. [Google Scholar]
- Krishna, S.M.; Daya, J.L.F. MRAS speed estimator with fuzzy and PI stator resistance adaptation for sesnorless induction motor drives using RT-Lab. Perspect. Sci.
**2016**, 8, 121–126. [Google Scholar] [CrossRef] - Krishna, S.M.; Daya, J.L.F. Adaptive Speed Observer with Disturbance Torque Compensation for Sensorless Induction Motor Drives using RT-Lab. Turk. J. Electr. Eng. Comput. Sci.
**2016**, 24, 3792–3806. [Google Scholar] [CrossRef] - Mikkili, S.; Prattipati, J.; Panda, A.K. Review of real-time simulator and the steps involved for implementation of a model from matlab/simulink to real-time. J. Inst. Eng. India Ser. B.
**2014**, 96, 179–196. [Google Scholar] [CrossRef] - Daya, J.L.F.; Sanjeevikumar, P.; Blaabjerg, F.; Wheeler, P.; Ojo, O.; Ertas, A.H. Analysis of Wavelet Controller for Robustness in Electronic Differential of Electric Vehicles—An Investigation and Numerical Developments. J. Electr. Power Compon. Syst.
**2016**, 44, 763–773. [Google Scholar] [CrossRef] - Sanjeevikumar, P.; Daya, J.L.F.; Blaabjerg, F.; Wheeler, P.; Oleschuk, V.; Ertas, A.H.; Mir-Nasiri, N. Wavelet-Fuzzy Speed Indirect Field Oriented Controller for Three-Phase AC Motor Drive-Investigation and Implementation. Int. J. Eng. Sci. Technol.
**2016**, 19, 1099–1107. [Google Scholar] - Daya, J.L.F.; Subbiah, V.; Iqbal, A.; Sanjeevikumar, P. A Novel Wavelet-Fuzzy based indirect field oriented control of Induction Motor Drives. J. Power Elect.
**2013**, 13, 656–668. [Google Scholar] [CrossRef] - Saponara, S.; Fanucci, L.; Bernardo, F.; Falciani, A. Predictive Diagnosis of High-Power Transformer Faults by Networking Vibration Measuring Nodes With Integrated Signal Processing. IEEE. Trans. Instrum. Meas.
**2016**, 65, 1749–1760. [Google Scholar] [CrossRef] - Costantino, N.; Serventi, R.; Tinfena, F.; D’Abramo, P.; Chassard, P.; Tisserand, P.; Saponara, S.; Fanucci, L. Design and Test of an HV-CMOS Intelligent Power Switch With Integrated Protections and Self-Diagnostic for Harsh Automotive Applications. IEEE. Trans. Ind. Electron.
**2011**, 58, 2715–2727. [Google Scholar] [CrossRef] - Saponara, S.; Petri, E.; Fanucci, L.; Terreni, P. Sensor Modeling, Low-Complexity Fusion Algorithms, and Mixed-Signal IC Prototyping for Gas Measures in Low-Emission Vehicles. IEEE. Trans. Instrum. Meas.
**2011**, 60, 372–384. [Google Scholar] [CrossRef] - Sanjeevikumar, P.; Daya, J.L.F.; Wheeler, P.; Blaabjerg, F.; Viliam, F.; Ojo, O. Wavelet Transform with Fuzzy Tuning Based Indirect Field Oriented Speed Control of Three-Phase Induction Motor Drive. Proceedings of 18th IEEE International Conference on Electrical Drives and Power Electronics, Tatranska Lomnica, Slovakia, 21–23 September 2015. [Google Scholar]
- Daya, J.L.F.; Subbiah, V.; Sanjeevikumar, P. Robust Speed Control of an Induction Motor Drive using Wavelet-Fuzzy based Self-tuning Multiresolution Controller. Int. J. Comput. Intell. Syst.
**2013**, 6, 724–738. [Google Scholar] [CrossRef] - Sanjeevikumar, P.; Daya, J.L.F.; Blaabjerg, F.; Mir-Nasiri, N.; Ertas, A.H. Numerical Implementation of Wavelet and Fuzzy Transform IFOC for Three-Phase Induction Motor. Int. J. Eng. Sci. Technol.
**2016**, 19, 96–100. [Google Scholar] - Daya, J.L.F.; Sanjeevikumar, P.; Blaabjerg, F.; Wheeler, P.; Ojo, O. Implementation of Wavelet Based Robust Differential Control for Electric Vehicle Application. IEEE Trans. Power Electron.
**2015**, 30, 6510–6513. [Google Scholar] [CrossRef]

**Figure 3.**Basic configuration of parameter adaptive model reference adaptive system (MRAS) scheme with parallel disturbance torque estimation.

**Figure 6.**(

**a**) Estimated speed of conventional sliding mode luenberger observer (SMLO) 1; and (

**b**) zoomed version of (

**a**).

**Figure 10.**(

**a**) Estimated speed of Modified Sliding Mode Luenberger Observer (SMLO 2); and (

**b**) zoomed version of (

**a**).

**Figure 20.**Speed tuning signal for 50% incorrect setting of stator resistance (R

_{s}) and rotor time constant (T

_{r}) for (

**a**) SMLO 1, and (

**b**) SMLO 2.

**Figure 21.**Speed tuning signal for nominal setting of stator resistance (R

_{s}) and rotor time constant (T

_{r}) for (

**a**) SMLO 1; and (

**b**) SMLO 2.

**Figure 22.**Speed tuning signal for 150% incorrect setting of stator resistance (R

_{s}) and rotor time constant (T

_{r}) for (

**a**) SMLO 1; and (

**b**) SMLO 2.

**Figure 23.**SMLO 1 (

**a**) sliding surface; (

**b**) flux component of stator current; (

**c**) torque component of stator current; and (

**d**) stator current error.

**Figure 24.**SMLO 2 (

**a**) sliding surface; (

**b**) flux component of stator current; (

**c**) torque component of stator current; and (

**d**) stator current error.

Test Cases | SMLO 1 | SMLO 2 |
---|---|---|

Low flux weakening region | Maximum speed oscillation of around 70 rad/s (around 42% of the reference value). Speed oscillations do not die out. | Initial maximum speed oscillation of around 20 rad/s (around 12% of the reference value). Speed Oscillations gradually reduce with time. |

Step speed command | Very high overshoot and undershoot observed at the instance of fast deceleration. | Smoother tracking during fast acceleration and deceleration. |

Low speed operation | Does not track, becomes unstable and speed convergence goes out of bounds. | Tracks well, initial undershoot and overshoot, which results for a very small interval of time. |

Disturbance torque | Higher torque pulsations as a result of high stator current pulsation. | Comparatively lower torque pulsation resulting in better torque holding capability. |

Speed and Stator error convergence | Slower convergence, higher speed and stator current error | Faster convergence, resulting in smoother tracking |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Krishna S., M.; Daya J.L., F.; Padmanaban, S.; Mihet-Popa, L. Real-Time Analysis of a Modified State Observer for Sensorless Induction Motor Drive Used in Electric Vehicle Applications. *Energies* **2017**, *10*, 1077.
https://doi.org/10.3390/en10081077

**AMA Style**

Krishna S. M, Daya J.L. F, Padmanaban S, Mihet-Popa L. Real-Time Analysis of a Modified State Observer for Sensorless Induction Motor Drive Used in Electric Vehicle Applications. *Energies*. 2017; 10(8):1077.
https://doi.org/10.3390/en10081077

**Chicago/Turabian Style**

Krishna S., Mohan, Febin Daya J.L., Sanjeevikumar Padmanaban, and Lucian Mihet-Popa. 2017. "Real-Time Analysis of a Modified State Observer for Sensorless Induction Motor Drive Used in Electric Vehicle Applications" *Energies* 10, no. 8: 1077.
https://doi.org/10.3390/en10081077