APARNA S.

M.Tech Control System

Roll No. 04

DESIGN OF ITERATIVE SLIDING MODE OBSERVER FOR SENSORLESS PMSM

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OVERVIEW

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Introduction Objective Modeling Of PMSM Conventional SMO ISMO System Configuration Experimental Results Conclusion References

INTRODUCTION

DC Motors Commutation using brushes Electronic switching AC Motors

AC Motors

Induction Motor Permanent Magnet Synchronous Motor

(IM) (PMSM) PMSM Advantages Disadvantages

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INTRODUCTION (contd…)

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Precise Position And Velocity Control Encoders And Resolvers Rotor Inertia

Sensorless Control Algorithm

Estimate Position And Velocity Of The Rotor Without Sensors Sliding Mode Observer (SMO)

OBJECTIVE

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To apply the proposed control approach for the sensorless control of PMSM.

To analyze the system robustness with the proposed control.

MODELING OF PMSM

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Voltage Equations Of The Stator Voltage in three phases is transformed into Two Phase Synchronous

Coordinate System

(1) Fixed Coordinate System

(2)

Where, = − and =

MODELING OF PMSM (contd.)

Nomenclature and Stator voltages in the synchronous frame. and Stator currents in the synchronous frame. and Stator resistance and inductance respectively. Electrical angular velocity Back EMF constant of PMSM motor. and Stator voltages for d and q axes, respectively. and Stator currents in the fixed coordinate system. Position of the electrical rotor.

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MODELING OF PMSM (contd.)

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State Equations Of Stator Current: From (2),

= (3a)

= (3b)

CONVENTIONAL SMO

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CONVENTIONAL SMO (contd.)

Cutoff frequency for the low pass filter (LPF)

= + (4)

Where = 2f, is the reference speed of the rotor, f is the cutoff frequency for the filter, is the previous value of

Use of signum function results in discontinuous control signal Chattering results in fluctuations in steady state response The use of LPF for integration causes time delay To overcome these we use a sigmoid function as switching function

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ITERATIVE SMO

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ITERATIVE SMO (contd.)

State equations of the ISMO

= (5a)

= (5b)

Where is used for the estimated value of, k is the gain constant of the observer, and H represents the sigmoid function.

The sigmoid function is formulated as

= (6)

Where is a positive constant used to regulate the slope of the sigmoid function and = and = represent the current errors of the stator current.

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ITERATIVE SMO (contd.)

Stability Analysis

The sliding surface is defined as

=(7) The Lyapunov function is defined as

V = (8) Error equations (from (3)and (5))

= = - = ) (9a)

= = - = ) (9b)

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ITERATIVE SMO (contd...)

Stability Analysis (contd...) To satisfy the existence condition of the sliding mode,

= < 0

should be satisfied, which is represented as

)) + )) < 0 (10) The observer condition is obtained as

. (11) Observer gain,

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ITERATIVE SMO (contd.)

Position And Velocity Estimation Of The Rotor With the predetermined observer gain , the sliding mode may exist

on the sliding surface as follows:

. (12)

Therefore, to satisfy the inequality condition (10), the following conditions are obtained:

) = (13a)

) = (13b)

ITERATIVE SMO (contd...)

Position And Velocity Estimation Of The Rotor (contd…) The estimation of the back EMF in (13) can be used to estimate the

position and velocity of the rotor as follows:

(14a)

. (14b)

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ITERATIVE SMO (contd.)

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SYSTEM CONFIGURATION

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SYSTEM CONFIGURATION (contd.)

The experimental PMSM has the following specifications:

Power = 1 kW, max. torque = 9.36 N·m, max. velocity = 3000 rpm, number of poles = 8, Rs = 0.25Ω', and Ls = 1.3 mH. Also, the controller parameters are set as follows:

Control cycle for velocity = 1 ms, control cycle for current = 0.1 ms, and a = 0.05494.

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EXPERIMENTAL RESULTS

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EXPERIMENTAL RESULTS (contd.)

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EXPERIMENTAL RESULTS (contd.)

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Fig 9(b)

Fig 9(a)

EXPERIMENTAL RESULTS (contd.)

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Fig (9c)

Fig. 9 Performance comparison of conventional SMO and ISMO for 2000 rpm motor control.(a) and of SMO with signum function. (b) and of SMO with sigmoid function. (c) and of ISMO.

EXPERIMENTAL RESULTS (contd.)

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CONCLUSION

The proposed ISMO was robust and fast, so that the sensorless control system using this ISMO had a fast response and was robust against disturbances.

The performance of the sensorless control system was verified with different velocities (500 and 2000 rpm) to ensure its fast response characteristics

To demonstrate the robustness of the system, the velocity characteristics were checked experimentally under a certain unknown load condition.

In future works, the observer gains need to be adjusted automatically using intelligent algorithms such as fuzzy interferences.

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REFERENCES

1. H. Lee and J. Lee, “Design of iterative sliding mode observer for sensorless PMSM control,” in IEEE Transactions on Control Systems Technology., accepted May 2012.

2. F. Parasiliti, R. Petrella, and M. Tursini, “Sensorless speed control of a PM synchronous motor by sliding mode observer,” in Proceedings of IEEE International Symposium in Industrial Electronics, vol. 3, Jul. 1997, pp. 1106–1111.

3. S. Chi, Z. Zhang, and L. Xu, “Sliding-mode sensorless control of direct-drive PM synchronous motors for washing machine applications,” IEEE Transactions on Industry Applications, vol. 45, no. 2, Mar.–Apr. 2009, pp. 582–590.

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REFERENCES

4. F. Genduso, R. Miceli, C. Rando, and G. R. Galluzzo, “Back EMF sensorless control algorithm for high-dynamic performance PMSM,” IEEE Transactions on Industrial Electronics, vol. 57, no. 6, Jun. 2010, pp. 2092–2100.

5. H. R. Kim, J. B. Son, and J. M. Lee, “A high-speed sliding-mode observer for the sensorless speed control of a PMSM,” IEEE Transactions on Industrial Electronics, vol. 58, no. 9, Sep. 2011, pp. 4069–4077.

6. Y. S. Han, J. S. Choi, and Y. S. Kim, “Sensorless PMSM drive with a sliding mode control based adaptive speed and stator resistance estimator,” IEEE Transactions on Magnetics, vol. 36, no. 5, Sep. 2000, pp. 3588–3591.

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