VGPI controller for high performance speed tracking of induction motor ...

Proceedings of the 3rd International Conference on Systems and Control, Algiers, Algeria, October 29-31, 2013

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VGPI Controller for High Performance Speed Tracking of Induction Motor Drive A. Mechernene, L. Chrifi Alaoui, M. Zerikat, N. Benharir and Hadda Benderradji 

Abstract— This paper presents experimental study whose objective is to show the dynamic performance of a variable gain PI controller (VGPI). Indeed, the PI, although very popular and mainly used in industry, present overshoots in the tracking trajectory mode. This major disadvantage can be eliminated by maintaining the traditional PI structure and introducing the variable proportional and integrator gains. The proposed regulator is used as speed control organ in vector control to an induction motor. The practical implementation is done on a hardware experimental platform equipped with a dSpace-DSP 1104 with Matlab-Simulink-DSpace system and Control-Desk software plugged in a standard personnel computer. The various tests demonstrate the great ability of the controller to remove the overshoots and also a precise trajectory tracking.

I. INTRODUCTION The induction machine associated with a static converter is a variable speed drive system whose industrial use is increasing important. This interest was partly because of its characteristics: low cost, easy maintenance and mechanical robustness. The vector control theory is nowadays mature and is usually applied in controlled drives systems with induction machines where high dynamic speed or position control performances are required [1]. In the classical structure of vector control by rotor flux orientation, PI regulators are used for controlling the rotor speed, rotor flux and the two-phase stator currents. These organs are characterized by a simple design and easy tuning of its parameters, which justifies its use in many applications [2]. However, the PI controllers have problems to remove the overshoots in the tracking trajectory mode and load disturbance rejection at the same time. This problem is had to the fact that the controller parameters are constant, hence the idea of designing a variable gain regulator to resolve this tradeoff. A (VGPI) controller is a generalization of a classical PI controller where the proportional and integrator gains vary along a tuning curve [3]. Some authors have chosen to solve this problem with modern approaches such as intelligent controllers based on

Fuzzy Logic [4], [5] and Artificial Neural Networks [6], [7], or with non-linear approaches such as Sliding Mode [8], or Backstepping Control [9], ... But these solutions are complex and not appreciated by the industrials. In this work, a variable gain PI regulator is proposed to replace the conventional PI regulator for controlling the speed of an induction motor. In order to show the behavior and performance of the proposed controller, some experimental tests were performed in real time after implementing the control algorithm on a testing platform equipped with a hardware environment dSpace DSP-1104. The paper is organized as follows: the dynamical model of induction motor and the principle of direct field oriented control are presented in section 2. In Section 3, the structure of the VGPI controller and tuning of its parameters are described. In section 4, experimental results are presented and the obtained performance of the VGPI controllers PI and conventional fixed-gain are discussed and compared. Finally, in section 5, we give some comments and conclusions. II. INDUCTION MOTOR MODEL A. Dynamic model of Induction Motor in (d-q) reference frame The induction motor can be described by an equivalent two-phase mathematical model established in an arbitrary synchronously rotating reference frame (d-q) as [10]:

disd v K   .isd  s .isq  . rd  K .r . rq  sd dt Tr  .Ls disq dt

 s .isd   .isq  K .r . rd 

d rd Lm 1  .isd  . rd  s  r  . rq dt Tr Tr d rq dt

A. Mechernene is with Electrical and Electronic Department, University Abou-Bekr Belkaïd, Tlemcen, Algeria, (corresponding author: e-mail: [email protected]). L. Chrifi-Alaoui is with Laboratory of Innovative Technology, University of Picardie Jules Verne, France, (e-mail: [email protected]). M. Zerikat and N. Benharir are with Electrical Engineering Department, ENP of Oran, Algeria. (e-mails: [email protected]; [email protected]). H. Benderradji, Electrical and Engineering Department, University Mohamed Boudiaf, M’sila, Algeria, (e-mail: [email protected]).

vsq K . rq  Tr  .Ls



Lm 1 .isq  s  r  . rd  . rq Tr Tr

, K,  and Tr are positive constants defined as:



Rs R .L2  r m2  .Ls  .Ls .Lr

 =1-

L2m Ls .Lr

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K

Lm  .Ls .Lr

Tr 

Lr Rr

(1)

(2) (3)

(4)

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In equations (1,2,3,4), the quantities isd, isq, rd, rq and vsd, vsq, denote: stator current, rotor flux and stator voltage, the d and q in the subscripts stand for the direct and quadrature axes respectively, s and r are subscripts stand for stator or rotor quantities; r is the rotor angular frequency, s is the synchronously angular speed, sl is the slip angular frequency and s is the angular position of the (d-q) reference frame.

Finally, torque is controlled through the isq current and the rotor flux by the isd current as in DC motor. Figure 1 shows the magnetic field orientation, where (-β) is the stationary reference frame.

The different pulsations are linked by the relation:

s  r  sl  p.  sl

(5)

 is mechanical angular speed, p the number of pole pairs. The electromagnetic torque can be written as:

3 p.L Tem  . m .  rd .isq  rq .isd  2 Lr

(6)

The rotor angular frequency can be expressed with the mechanical torque balance equation:

dr p B  . Tem  Tl   .r dt J J

(7)

Where Tl is the load torque, J and B are respectively the total moment inertia on the shaft and the friction coefficient. This dynamical model defines in reference frame (d-q) is used to implement the vector control algorithm. B. Direct Field Oriented Control for Induction Motor Vector control with flux orientation is the most popular control technique for three-phase AC motors [11]. The aim is to restore decoupling between flux and the electromagnetic torque similar to that of the DC machine. In the case of induction motor, the control is usually achieved in the reference frame (d-q) attached to the stator flux, rotor flux or air gap flux. Typically, vector control drive is performed in the reference frame attached to the rotor flux. Its principle is to orient the (d-q) reference frame according to the rotor flux, canceling the quadrature component rd to keep only the direct component [12]. To achieve this, the stator current is separated in two components producing the flux and torque using a coordinate system transformation to the (d-q) reference frame, whose direct-axis is entirely aligned along the rotor flux. So, the rotor field orientation conditions are expressed by the following equations:

 rq  0 ;

d rq dt

0

 r   rd

and

(8)

This implies a new expression for the electromagnetic torque:

3 p.L Tem  . m . rd .isq 2 Lr

(9)

 Lm .isd

The implementation of vector control requires the precise information on the amplitude and the position of the rotor flux. In direct field oriented-control scheme proposed, the rotor flux amplitude is determinate by a simple flux estimator defined as:

ˆ r 

Lm .isd 1  Tr .s

(11)

and the position is obtained by integrating the stator pulsation:

ˆs   ˆ s .dt

ˆ s  p. 

with

Lm .isq Tr .ˆ r

 

 

 

 

vsd  k pd . isd*  isd  kid . isd*  isd .dt    * * vsq  k pq . isq  isq  kiq . isq  isq .dt

(13)

kpd = kpq and kid = kiq are the proportional and integral gains. To separate the mutual actions of d and q axis, two new variables are introduced; their expressions are given by the following equations [10]:

esd   .Ls .ˆ s .isq  Lm  ˆ ˆ ˆ esq   L .s . r   .Ls .s .isd r 

(14)

The control voltages are then obtained by the relations: * vsd  vsd  esd

and

* vsq  vsq  esq

(15)

The rotor flux is controlled by a conventional PI controller defined as follows, and delivering at its output the direct current reference i*sd :



(10)

(12)

Two identical PI current regulators deliver output voltages.







isd*  k p .  * ˆ r  ki .  * ˆ r .dt

If rotor flux is maintained constant, then:

r

Fig 1. Current and flux vectors representation

where: kp, ki are the proportional and integral gains.

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The overall block diagram of the direct rotor field oriented control (DRFOC) proposed is illustrated in Figure 2.

k p

n   t   k  k pi  .    k pi   pf  Ts   k pf

  t n k .   ki   if  Ts   kif

if t  Ts

(18)

if t  Ts

if t  Ts

(19)

if t  Ts

Where kpi and kpf are the initial and final values of the proportional gain, and kif is the integrator gain final value; Ts and n are the saturation time and the polynomial degree.

Fig. 2. Block diagram of direct field oriented control scheme based induction motor drive

The field weakening block delivers the reference value of rotor flux. The space vector modulation transform the reference stator voltages to Pulse Width Modulation (PWM) signals to impose the flux and the electromagnetic torque desired via the three-phase inverter voltage. III. DESIGN OF VARIABLE GAIN SPEED PI CONTROLLER A. Structure of Variable Gain PI Controller A variable Gain PI (VG-PI) controller is a generalization of a classical PI controller [13]. Its gains are not constant, as in the case of a conventional PI, but vary in time along a polynomial curve and they attain their final values in the steady state [3]. This controller, which the parameters are continually adapted or tuned, can limit overshoot during startups with a rapid load disturbance rejection. Fig.3 shows the block diagram of the VG-PI controller.

B. VGPI controller parameters setting The parameters are obtained by the test-error method as follows [3], [13]: -

choose a value kif to obtain a rapid load disturbance rejection,

- choose the degree n and the saturation time Ts, - determine the values kpi and kpf to obtain the smallest overshoot. - To eliminate completely the overshoot increase Ts, if the excess is not eliminated increase the degree n. The tests performed with the motor described in the appendix, have permitted to obtain the following values for the proportional and integral gains:

1,8.t 3  0,5 k p   5

0,1.t 3 ki   0, 25

if t  1

(20)

if t  1

if t  1

(21)

if t  1

with kpf = 5 ;

kpi = 0,5 ; kif = 0,25

and

Ts = 2,5s

For the classical PI controller, the values of proportional and integral gains would be given by: kp = 5

and

ki = 0,25

IV. EXPERIMENTAL RESULTS The digital implementations have been conducted on the experimental testing platform of Laboratory of Innovative Technologies (LTI, University Jules Verne of Picardie).

Fig. 3. Block diagram of VGPI controller

The speed VGPI controller delivering at its output the electromagnetic torque reference:









* Tem  k p . *    ki . *   .dt

kp, ki are defined by the relations (18) and (19) [13].

(17)

The experimentation has been achieved with the MatlabSimulink-DSpace system based on the control board DSP TMS320F240, offering a four channel 16-bit (multiplexed) ADC and four 12-bit ADC units. A sampling period is set to 100μs and the insulated gate bipolar transistors (IGBTs) are working at a switching frequency of 10 kHz.

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Proceedings of the 3rd International Conference on The drive system developed includes an induction motor coupled to a magnetic powder brake simulating the mechanical load and it’ is essentially composed of: - a static power electronics converter composed of a diode rectifier, a three-phase voltage source and an IGBT inverter (1000V-30A), switching frequency: 10 kHz); - Hall type sensors for stator currents measurements; - an encoder for measuring the motor speed; - a dSpace DS 1104 dSP with control desk software plugged in a standard personnel computer host, to program the DSP and to display acquisition data. The DSP performs data acquisition, generates speed profiles, implements DRFOC algorithms and generates the PWM inverter commands. The figure 4 show the hardware configuration scheme.

WeAB.5 Fig. 6 shows the response of the proposed system drive equipped with the VGPI controller at no load with a step change in reference speed at 0 rad/s to 140 rad/s. The speed and currents responses confirm a very a good precision and the elimination useful of the overshoot Fig. 7 illustrates the response of VGPI controller with a trapezoidal change in reference speed at 0 rad/s to 140 rad/s and application of a load torque 7 N.m at t = 4,1 s. This result shows clearly very satisfactory in tracking response. In Fig. 8, the same test is performed with the PI controller; one can note the presence of the overshoot and the same performance like the VGPI regulator. Figures 9 and 10 illustrate the responses of VGPI and PI controller under a trapezoidal change between 0 rad/s to 50 rad/s in reference speed, then another speed variation to 100 rad/s without load. At start, the controller VGPI follow perfectly their reference after suppress overshoot. However, during the second change, the saturation time is finished and the controller parameters have reached their final values, we can observe a small excess, as in the case of PI regulator. Rotor speed  [rad/s] 160 140 120 100 80 60

Magnetic powder brake

40 20 0 0

Fig. 4. Scheme of the hardware configuration

The reference flux is kept constant at the value 0,6 Wb and the flux and current stator controller parameters are set at: kp = 0,3 ;

ki = 10 ;

kpd = kpq = 0,5 ; kid = kiq = 4,5

The experimental tests are performed for the induction motor whose parameters are given in Appendix, with a photo of the experimental setup. Figure 5 shows a photograph of the experimental setup.

2,5

1

2

3

4

5

6

7

Direct and quadrature stator currents is [A]

2 1,5 1.36 1 0,5 0 0

1

2

3

4

5

6

7

5

6

7

Stator current [A]

3 2 1 0 -1 -2 -3 0

1

2

3

4

time [s] Fig. 5. Photograph of the experimental setup (LTI, University Jules Verne of Picardie)

Fig. 6. Response of VGPI controller at no load with a step change in reference speed (0 to 140 rad/s)

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*

160 140

140



120



120

100

100

80

80

60

60

40

40

20

20

0 0

*

160

0 1

2

3

4

5

6

7

0

Direct and quadrature stator currents [A]

1

2

3

4

5

6

Direct and quadrature stator currents [A] 4

4

isq

isq 3

3

2

2

isd

1.36

isd

1.36 1

1

0 0

7

0

1

2

3

4

5

6

7

0

1

2

time [s]

3

4

5

6

7

time [s]

Fig. 7. Response of VGPI controller at load torque change and with a trapezoidal change in reference speed (0 to 140 rad/s)

Rotor speed [rad/s] 120



*

100



80

Rotor speed [rad/s]

120

*

100

Fig. 8. Response of PI controller at load torque change and with a trapezoidal change in reference speed (0 to 140 rad/s)



80

60

60

40

40

20

20 0

0 0

2

4

6

8

10

Direct and quadrature stator currents [A]

2

2

isd

1,5 1.36

0

2

4

6

8

Direct and quadrature stator currents [A]

isd

1.5 1.36

1

10

1

isq

0,5

isq

0.5

0

0

0

2

4

6

8

10

0

2

time [s]

4

6

8

10

time [s]

Fig. 9. Response of VGPI controller at no load and with a trapezoidal change in reference speed (0 to 50 rad/s then to 140 rad/s)

Fig. 10. Response of PI controller at no load and with a trapezoidal change in reference speed (0 to 50 rad/s then to 140 rad/s)

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Proceedings of the 3rd International Conference on V. CONCLUSION In this paper, a VGPI regulator has been designed and used as speed controller, instead the classic PI regulator with fixed gains, in a direct rotor field oriented control scheme for induction motor. The algorithm of this variable speed drive system has been implanted on a testing platform equipped with a hardware environment dSpace DSP-1104. Some experimental tests were performed in different operating conditions to show the behavior of the regulator and its great faculty to eliminate the overshoots in the tracking trajectory mode. The results show, for the various profiles prescribed, a fast and precise tracking without speed overshoot. During the steady state, the load disturbance rejection of the load torque is the same for both regulators. In conclusion, this experimental study demonstrates that the overshoot difficulty and load disturbance rejection problem can be solved simultaneously using a variable gain regulator, it is a simple evolution of the conventional PI. APPENDIX

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[6] [7] [8] [9]

[10] [11] [12] [13]

Induction Motor Parameters 1,5 kW; 3 phases; 220/380 V; 3,7/6,5 A; 50 Hz-1420 rpm; Rs = 4,85 ; Rr = 3,805 ; Ls = 0,274 H; Lr = 0,274 H; Lm = 0,258 H; J = 0,031 kg.m2; B = 0,00334 kg.m.s-1.

A. Mechernene, M. Zerikat, M. Hachlef, “Fuzzy Speed Regulation for Induction Motor Associated with Field-Oriented Control”, International Journal on Sciences and Techniques of Automatic Control & Computer Engineering (IJ-STA), Vol. 2, No. 2, pp. 804817, Tunisia, December 2008. J. Žilková, J. Timko, P. Girovský, “Nonlinear System Control Using Neural Networks”, Acta Polytechnica Hungarica, Vol. 3, No. 4, pp. 85-94, 2006. P. Vas, “Artificial-Intelligence-Based Electrical Machines and DrivesApplication of Fuzzy, Neural, Fuzzy-Neural and Genetic Algorithm Based Techniques”, Oxford University Press, New York, 1999. R.J. Wai, “Adaptive sliding-mode control for induction servomotor drives”, IEE Proceeding. Electr. Power Appl., Vol. 147, No. 6, pp. 553-562, November 2000. O. Benzineb, H. Salhi, M. Tadjine, M.S. Boucherit , M. Benbouzid, “A PI/Backstepping Approach for Induction Motor Drives Robust Control”, International Review of Electrical Engineering (IREE), Vol. 5, No. 2, pp. 426-432, April 2010. N.P. Quang, J-A. Dittrich, “Vector control of three-phase AC machines, system development in the practice”, Springer Berlin, 2008. J. Bocker, S. Mathapati, “State of the Art of Induction Motor Control”, IEEE International Conference on Electric Machines & Drives, IEMDC '07, Vol. 2, pp. 1459-1464, 3-5 May 2007. F.Blaschke, “The principle of Field Orientation as applied to the new Transvektor Closed-Loop Control System for Rotating-Field Machines,” Siemens Review, XXXIX, n°5, pp. 217-220, 1972. A. Miloudi, E-A. A1 Radadi, A. Draou, Y. Miloud, “Simulation and Modelling of a Variable Gain PI Controller For Speed Control of a Direct Torque Neuro Fuzzy Controlled Induction Machine Drive”, Proceeding of PESC'04, Aachen, Germany, pp. 3493-3498, June 2025, 2004.

Nomenclature (.)d , (.)q in (d-q) reference frame (.)α , (.)β in (α-β) reference frame Rs , Rr stator and rotor resistances Ls , Lr stator and rotor inductances Lm mutual inductance Ts stator time constant Tr rotor time constant  total leakage coefficient p number of pole pairs J moment of inertia B coefficient of friction Te electromagnetic torque Tl load torque  flux linkage and s angle defining the position of rotor flux r electrical angular rotor speed s synchronously rotating angular speed  = r /p rotor mechanical angular speed REFERENCES [1] [2] [3]

[4]

P. Vas, “Sensorless Vector and Direct Torque Control”, Oxford University Press, New York, 1998. B.K. Bose. Modern Power Electronics and AC Drives. Prentice-Hall International Editions, 2001. A. Miloudi, E-A. A1 radadi, A. Draou, “A Variable Gain PI Controller Used for Speed Control of a Direct Torque Neuro-Fuzzy Controlled Induction Machine Drive”, Turkish Journal of Electrical Engineering, Vol. 15, No. 1, 2007. G. Mallesham, K.B. Venkata Ramana, “Improvement in Dynamic Response of Electrical Machines with PID and Fuzzy Logic Based Controllers”, Proceedings of the World Congress on Engineering and Computer Science 2007, WCECS 2007, San Francisco, USA, October 24-26, 2007.

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