Proceedings of the 2008 International Conference on Electrical Machines
Paper ID 767
Implementation of a Vector Control Scheme using dSPACE Material for Teaching Induction Motor Drive and Parameters Identification C. Versèle, O. Deblecker and J. Lobry Electrical Engineering Division - Faculté Polytechnique de Mons, Bd Dolez, 31 B-7000 Mons
[email protected],
[email protected],
[email protected] This contribution is organized as follows, the experimental system is presented in section II and the education considerations are discussed in details in section III.
Abstract-In this paper, we present a project in which the students must determine the parameters and set up a vector control structure of a voltage-fed inverter induction motor (IM) drive using a dSPACE platform and Matlab/Simulink environment. Thanks to this platform, students can focus on the control scheme without spending too much time with details concerning the implementation of the control algorithm on the board.
I.
II. EXPERIMENTAL SYSTEM There are three identical experimental systems in the laboratory. Each of them consists of three essential parts: (1) the power part, (2) the control part and (3) the transducers. Fig. 1 shows a synoptic scheme of these experimental platforms. A. Power part The power part consists of a voltage-fed inverter and two machines: one squirrel-type induction motor of rated power 5.5 kW and a dc-machine with a separately excited field winding of rated power 14.6 kW. These machines are mechanically coupled and the dc-machine is used as the load of the induction motor. B. Control part The control part is based on the DS1104 Controller Board by dSPACE plugged in a computer. Its development software operates under Matlab/Simulink environment [2] and is divided in two main components: Real Time Interface (RTI) which is the implementation software and ControlDesk which is the experimentation software. RTI is a Simulink toolbox which provides blocks to configure models [2]. These blocks allow the users to access to the dSPACE hardware. ControlDesk allows the users to control and monitor the real-time operation by using a lot of virtual instruments and building a control window. When using dSPACE, the several steps required to implement a control system on the DS1104 Controller Board are described below. The first step consists in modelling the control system with Simulink and configuring the I/O connections of the Connector Panel thanks to the RTI toolbox. After that, the Real-Time Workshop (RTW) toolbox, using RTI, automatically generates the C-code for the board. Once the execution code has been generated, the dSPACE hardware can perform a real-time experiment which can be controlled from a PC with ControlDesk. ControlDesk could be used, i.e., to monitor the simulation progress, adjust parameters online, capture data (in a format compatible with Matlab) and communicate with the upper computer real-time easily [3]. Fig. 2 presents the connections between Matlab and dSPACE.
INTRODUCTION
Thanks to their robustness, low cost, performances and simplicity of design, IM have the favour of the manufacturers for many applications where variable speed is required. Unfortunately, the speed or torque control of these motors is difficult because of their nonlinear and complex structure. In the past decades, new control strategies for IM drives, such as vector or field-oriented control, have appeared. The principle of vector control is to control independently the two Park components of the motor current, responsible for producing the torque and flux respectively. In that way, the IM drive operates like a separately excited dc motor drive (where the torque and the flux are controlled by two independent orthogonal variables: the armature and field currents, respectively). In this paper, we present a project in which the students must set up a structure of vector control of a voltage-fed inverter IM drive using a dSPACE platform and Matlab/Simulink environment. During this project1, they firstly determine the induction motor parameters using a procedure which is based on the implemented vector control scheme. The accuracy of these measurements is very important because a wrong value of some machine parameters can heavily affect the drive performances [1]. Then, they tune the proportional (P) and integral (I) gains of the several feedback control loops present in the vector control structure. Finally, they perform some experiments in speed regulation and pursuit.
1 This project was awarded by ‘Le prix GREPES 2007’. This prize aims to reward a master thesis in power electronics distinguished by the originality of the method and results. GREPES (www.grepes.be) is an association of academics and industry for the promotion of power electronics in space, army, railways, etc.
978-1-4244-1736-0/08/$25.00 ©2008 IEEE
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Proceedings of the 2008 International Conference on Electrical Machines Semikron converter
Source
Thanks to the values of the different parameters, they can tune proportional (P) and integral (I) gains of the several feedback control loops present in the vector control structure. Finally they perform some experiments in speed regulation and pursuit. These different parts of the project are detailed below. A. Model of IM Using the dq-winding equivalent circuits of the IM, as shown in Fig. 3, the following basic equations of IM can be derived [7]:
Induction motor + dc-machine
C
R S
Vd
T
R
DC
IM
C
Power part Control part
Errors
IGBT's pulses
Signal conditioning CMOS 0/15 V
PC + DS1104 Controller Board
TTL 0/5 V
fc
Vd
ia Dig. I / O ADC 5
Shielded cable
ib
Ωr
Slave I / O PWM
CP1104
vsd = Rs isd +
ADC 6 ADC 7
INC1
dφsd dt
Connector Panel
Fig. 1. Synoptic scheme of the experimental platform
vsq = Rs isq +
C. Transducers Each experimental system contains several current and voltage LEM transducers as well as a speed sensor. Moreover, the measured currents must be filtered in order to avoid aliasing when they will be converted into digital signals. Therefore, an anti-aliasing filter is added to each current transducer. The cut off frequency of this filter is estimated at 500 Hz (an order of magnitude above the rated frequency of 50 Hz).
vrq = 0 = Rr irq +
The analysis of an inverter-fed IM is difficult because of the nonlinear behaviour of these two elements. Moreover vector control of IM drive requires a lot of theoretical knowledge in many fields such as power electronics, electrical machines, digital control design, digital signal processing, etc. Thanks to the experimental system and especially the dSPACE material, students can focus on the control scheme without spending too much time with details concerning the implementation of the control algorithm on the board. The project which is proposed to the students is divided into several steps. First, they have some lectures about the Park model and vector control of IM. In a second step, they must implement the vector control algorithm in the Matlab/Simulink environment. After concluding off-line simulations using the blocks of the Simulink SimPowerSystems toolbox, the validated control strategy is transferred to the digital control board. In the next step, they determine the IM parameters by a procedure founded on the vector control scheme (discussed in details in [5]-[6]).
Simulink Model
RTI
Matlab
(1)
+ ω1φsd
(2)
dφrd dt dφrq dt
− ( ω1 − PΩ r ) φrq
(3)
+ ( ω1 − PΩ r ) φrd
(4)
φsd = Ls isd + Mird
(5)
φsq = Ls isq + Mirq
(6)
φrd = Lr ird + Misd
(7)
φrq = Lr irq + Misq
(8)
where: ¾
¾
vsd and vsq (respectively vrd and vrq) are the stator (respectively the rotor) voltages in the dq-axis; isd and isq (respectively ird and irq) are the stator (respectively the rotor) currents in the dq-axis; φsd and φsq (respectively φrd and φrq ) are the stator
¾
(respectively the rotor) fluxes in the dq-axis; ω1 is the angular speed of the dq-axis in the stator
¾
reference frame and ω1 − PΩ r is the angular speed of the
ControlDesk dSPACE hardware
RTW
dt
vrd = 0 = Rr ird +
III. EDUCATION CONSIDERATIONS
of the control system
dφ sq
− ω1φsq
¾
dq-axis in the rotor reference frame; Ω r is the rotor mechanical speed;
¾ ¾ ¾
Rs and Rr are respectively the stator and rotor resistances; Ls and Lr are respectively the stator and rotor inductances; M is the magnetizing inductance.
The electromagnetic torque expressed in terms of the dq-axes variables is:
dSPACE
Ce = P
C compiler
Fig. 2. Connections between Matlab and dSPACE [4]
M Lr
(φ
i − φrq isd )
rd sq
where P is the number of poles pairs.
2
(9)
Proceedings of the 2008 International Conference on Electrical Machines
+
+
−
+
lr
Rr ird
isd
vsd
+
−
ls
Rs
a flux observer. Its task is to provide estimates of the rotor flux or of the rotor magnetizing current (in module and phase) using the measured currents (transformed in the dq-axis) and speed. Once a flux estimate is available, the torque can easily be computed using (10). The flux observer implemented in the Matlab/Simulink/dSPACE environment is shown in Fig. 4. As can be seen in this figure, the phase μ of the rotor magnetizing current is obtained by integrating ω1. C. Voltage fed IM and decoupling compensation In this project, the IM is fed by a Voltage Supply Inverter (VSI) and a Space Vector Pulse-Width-Modulation (SV-PWM) is used to produce the instantaneous generation of the commanded stator voltages. The required voltages (vsd and vsq) that the VSI must supply to the IM, in order to make the stator currents (isd and isq) equal to their reference values, are expressed as follows:
(ω1 − PΩ r ) φsq
ω1φsq
vrd
M
−
−
(ω1 − PΩ r ) φsd
ω1φsd −
−
+
+
ls
Rs
+
Rr
irq
isq
vsq
+
lr
M
−
Fig. 3. dq-winding equivalent circuits
⎡ ⎢⎣
vsd = Rs isd + Ts ⎜ σ
(13)
−
⎡ ⎛ disq ⎞⎤ vsq = Rs ⎢isq + Ts ⎜ σ + (1 − σ ) ω1imr + σω1isd ⎟ ⎥ ⎣ ⎝ dt ⎠⎦
(14)
B. Vector Control The objective of vector control of IM is to allow an IM to be controlled just like a separately excited dc motor drive (where the torque and the flux are controlled by two independent orthogonal variables: the armature and field currents, respectively). This is achieved by a proper choice of the dq-axis. We consider a direct vector control strategy in which the dq-axis rotates along with the rotor flux (which is maintained at its rated value). The d-axis is aligning with the direction of the rotor flux. Therefore, the q-component of the rotor flux is null and the expression of the electromagnetic torque becomes: Ce = P
M
where Ts is the stator time constant and σ is the leakage factor of the IM. In the d-axis (respectively q-axis) voltage equation, only the first two terms of the right side are due to the d-axis (respectively q-axis) current isd (respectively isq). The other terms, due to imr and isq (respectively imr and isd), can be considered as disturbances [7]. Therefore, we can rewrite (13) and (14) as:
Lr
'
disd ⎤ dt ⎥⎦
disq ⎤ ⎡ ' vsq = Rs ⎢ isq + σ Ts dt ⎥⎦ ⎣
(10)
(11)
The rotor magnetizing current can be expressed in terms of d-axis stator current using (3), (7) and (11):
imr + Tr
dimr dt
= isd
(15)
(16)
Note that, in order to take into account the terms considered as disturbances, a “decoupling compensator” block is incorporated in the vector control scheme (see Fig. 5).
where imr is the rotor magnetizing current defined by:
φrd = Mimr
⎡ ⎢⎣
vsd = Rs isd + σ Ts
2
imr isq
⎛ disd + 1 − σ dimr − σω i ⎞⎤ ( ) 1 sq ⎟ dt ⎝ dt ⎠⎦⎥
vrq
(12)
where Tr is the rotor time constant. Using (10) and (12), we conclude that the d-axis stator current is control to maintain the flux at its rated value while the q-axis stator current is controlled to achieve the desired electromagnetic torque. Therefore, the IM can be controlled just like a separately excited dc motor drive because the d- and q- axis are orthogonal. Note that direct vector control of IM require to know, at each time, the module and phase of the rotor flux. Therefore, we use
Fig. 4. Flux observer implemented in Matlab/Simulink/dSPACE environment
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Proceedings of the 2008 International Conference on Electrical Machines we can conclude that all the IM parameters are properly determined. Moreover, the procedure based on the vector control structure permits to determine the mechanical parameters of the IM coupled with the dc-machine. Three parameters need to be determined: ¾ J – the total inertia; ¾ Tm – the mechanical time constant; ¾ B – the total damping factor. All the results are reported in Table II. F. PI tuning From the values of the parameters determined above, the students must calculate the proportional (KP) and integral (KI) gains of the four PI controllers present in the vector control structure. The gains of the PI controllers of the two inner current loops can be determined from (15) and (16). The gains of the PI controllers of the flux control loop and the speed control loop are, respectively, determined from (12) and the speed equation [6]:
D. Vector control scheme The vector control scheme is shown in Fig. 5 with the reference values indicated by ‘*’. This control scheme matches to a direct vector control strategy in which the rotor flux is assigned to a reference value (its rated value as mentioned *
above). The d-axis reference current, isd , controls the rotor flux (through the rotor magnetizing current) whereas the q-axis *
current, isq , controls the electromagnetic torque developed by the motor. The dq-axis reference currents are generated by a flux and a speed control loops, respectively. The dq-axis '
'
voltages, vsd and vsq , are generated from the given dq-axis reference currents and using (15) and (16). To obtain these command signals, we employ two PI controllers (in two inner current loops) and we assume that the compensation is perfect. The terms considered as disturbances are then added to the dq-axis voltages in the “decoupling compensator” block. Therefore, the dq-axis reference voltages vsd and vsq are obtained. Finally, these reference voltages are converted into the reference phase voltages va, vb and vc and supplied by the VSI using the SV-PWM technique. E. Determination of IM parameters As it is well known, vector control of IM imposes an accurate determination of machine parameters. Five parameters need to be determined: ¾ Rs, Rr – the stator and rotor resistances; ¾ ls, lr – the stator and rotor leakage inductances; ¾ Lm – the magnetizing inductance. These parameters are determined both by a procedure founded on the vector control scheme (discussed in details in [5]-[6]) and by a conventional method (no-load and blocked rotor tests). The method based on the vector control scheme is divided into eight steps. Initially, the name plate machine parameters are stored into the computer’s memory. Precisely, the method needs to know the rated stator voltage and current, the rated frequency and the number of poles pairs of the IM. In a second step, the stator resistance is determined by a test at dc level. Next, the stator transient time constant is measured. Thanks to the stator resistance and transient time constant, the two inner current loops can be tuned. In the fifth step, the rotor time constant is determined. Next, the magnetizing inductance is measured. Note that in this sixth step the value of the rotor time constant is also verified because it is the most important parameter to obtain an accurate rotor flux estimation. Thanks to the value of the rotor time constant, the flux controller can be tuned in the seventh step. Finally, the mechanical parameters of the IM coupled with the dc-machine (see below) are determined and the speed controller can be tuned. The method based on the vector control structure has the major advantage that it can be automated. Therefore, this procedure can evaluate the motor parameters at each start-up of the experimental platform. All the results are reported in Table I. As can be seen, very small differences are obtained between the two methods, whatever the parameters. Therefore,
Ce = J
d Ωr dt
+ BΩ r
~
(17)
= Vd
IM
~
=
ia Vd
μ
(a, b, c ) → (d , q)
SV − PWM va
vb
isd
vc
imr φlr ω1 Ce μ
vsq'
vsd'
q − axis current controller
d − axis current controller
−
− +
* sd
i
Flux controller imr
Observers
vsq = vsq' + esq
Decoupling Compensator
ω1
* imr
+
isq
* sq
i
Ce* → isq*
Ce*
−
Speed controller
+
* imr
−
*
* φ r → imr
+ *
φ r
Ωr
Ω*r
Fig. 5. Direct vector control scheme
4
μ
isq
( d , q ) → ( a, b, c ) vsd = vsd' + esd
isd
ib
Ωr
Proceedings of the 2008 International Conference on Electrical Machines TABLE III PROPORTIONAL (KP) AND INTEGRAL (KI) GAINS OF PI CONTROLLERS
TABLE I INDUCTION MOTOR PARAMETERS
Parameters
Rs Rr ls lr Lm
Conventional method 0,805 Ω 0,5679 Ω 0,004 H 0,004 H 0,1601 H
Method based on the vector control structure 1,2625 Ω 0,415 Ω 0,0039 H 0,0039 H 0,1640 H
Inner current loops Flux control loop Speed control loop
KP 9,46 48,6 0,89
KI 1630,68 120 0,42
TABLE II MECHANICAL PARAMETERS
Parameters J Tm B
Values 0,0731 kg.m² 2,1 s 0.00348 kg.m²/s
The gains of the several PI controllers are shown in Table III. We obtained these values by imposing a five percents time response of 2.5 ms for the inner current loops, 25 ms for the flux control loop and 250 ms for the speed control loop. G. Implemented control strategy After concluding off-line simulations using the blocks of the Simulink SimPowerSystems toolbox, the validated control strategy is transferred to the digital control board. Fig. 6 and 7, respectively, show the control algorithm implemented with Simulink and the control window of the ControlDesk software which controls the dSPACE hardware. H. Experimental results After the algorithm implementation, students must carry out several tests to evaluate the vector control behavior in speed regulation and pursuit. For these tests, the switching frequency of the VSI is set at 9 kHz. First, a speed regulation test is carried on at no-load by supplying a speed reference of 1200 rpm (the load generator remained coupled to the shaft). In Fig. 8, we can see an excellent and fast response to the 1200 rpm step. We can conclude that the rotor magnetizing current and the dq-axis stator currents are properly regulated. This figure also presents the stator voltage, stator current and the torque developed by the IM.
Fig. 7. ControlDesk virtual control panel
Then, a speed pursuit test is performed at no-load. To do so, the speed reference varies from 1000 rpm to -1000 rpm as can be seen in Fig. 9. In this figure, we observe a good response to the speed profile. As in the previous test, we also note that the rotor magnetizing current and the dq-axis stator currents are properly regulated. Finally, a variation torque test is done. In this test, we supply a speed reference of 1200 rpm to the motor at no-load. When the reference speed is reached, a resistant torque is applied to the IM (with the dc-machine coupled with the IM).
Fig. 8. Speed regulation (speed ref. in red and measured in blue)
Fig. 6. Control algorithm implemented with Simulink
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Proceedings of the 2008 International Conference on Electrical Machines
Fig.9. Speed pursuit (speed ref. in red and measured in blue)
Fig.10. Torque variation (speed ref. in red and measured in blue)
In Fig. 10, we observe that the IM slows down to the speed of 1000 rpm. After that, the IM takes about five seconds to recover to the reference speed. Thanks to this test, we can conclude that the compensation is perfect. Indeed, the rotor magnetizing current remains properly regulated despite the torque variation.
REFERENCES [1] [2]
IV. CONCLUSION It is shown in this paper that the dSPACE material offers multiple advantages from the point of education, because it shows to the student many aspects concerning: ¾ modeling and simulation using the Matlab/Simulink/dSPACE environment; ¾ IM parameters identification and drives; ¾ some practical aspects concerning the SV-PWM and signal measurements. Therefore, the dSPACE platform and Matlab/Simulink environment give a powerful tool for the teaching of IM parameters identification and drives. Thanks to this experimental system the students can easily put into practice a lot of theoretical knowledge through a unique project.
[3]
[4]
[5] [6] [7]
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C. Attaianese, V. Nardi and G. Tomasso, “A self-commissioning Algorithm for VSI-Fed Induction Motors”, IEEE Transactions on Power Electronics, Vol. 17, No. 6, pp. 1017-1023, November 2002. R. Bojoi, F.Profumo, G. Griva, R. Teodorescu and F. Blaabjerg, “Advanced Research and Education in Electrical Drives by Using Digital Real-Time Hardware-in-the-Loop Simulation”, Proceedings of the 10th International Power Electronics and Motion Control Conference, EPEPEMC 2002, Dubrovnik, September 2002. G. Luo, W. Liu, K. Song and Z. Zeng, “dSPACE Based Permanent Magnet Motor HIL Simulation and Test Bench”, Proceedings of the IEEE International Conference on Industrial Technology, ICIT 2008, China, April 2008. K. Mäki, A. Partanen, T. Rauhala, S. Repo and P. Järventausta, “Realtime simulation environment for power system studies using RTDS and dSPACE simulators”, Proceedings of the 11th International Power Electronics and Applications, EPE 2005, Dresden, September 2005. A. M. Khambadkone and J. Holtz, “Vector-Controlled Induction Motor Drive with a Self-Commissioning Scheme”, IEEE Transaction on Industrial Electronics, Vol. 38, No. 5, pp322-327, October 1991. B. K. Bose, “Modern Power Electronics and AC Drives”, Book, Chapter 8, Prentice Hall, New Jersey, 2001. Mohan N., “Advanced Electric Drives: Analysis, Control and Modelling using Simulink”, Book, MNPERE, 2001.
