Control Engineering Practice 19 (2011) 1377–1386
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Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac
High performance current control of a switched reluctance machine based on a gain-scheduling PI controller ¨ Hilairet , Claude Marchand Hala Hannoun, Mickael LGEP/SPEE Labs, CNRS UMR8507, SUPELEC, Univ Pierre et Marie Curie-P6, Univ Paris Sud-P11, 11, rue Joliot Curie, Plateau de Moulon, F91192 Gif sur Yvette Cedex, France
a r t i c l e i n f o
abstract
Article history: Received 11 June 2010 Accepted 17 July 2011 Available online 10 August 2011
Switched reluctance motor drives are under consideration in various applications requiring speed variation. This is certainly due to their mechanical robustness and low manufacturing cost. However, the non-linear characteristics of the flux and the torque, and the high acoustic noise complicate significantly the controller design. In order to take into account the phenomenon of magnetic saturation and its dependence on the rotor position and the current, a PI controller with variable gains is proposed. This controller compensates the inductance variation and maintains the dynamics of the closed-loop system constant. Simulations and experimental results of the standard PI controller and the gain-scheduling one are discussed. It shows the advantages of the gain adaptation compared to the fixed gains. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Switched reluctance machine Speed control Instantaneous torque control Current control Gain scheduling
1. Introduction The switched reluctance machine (SRM) had attracted many researchers over the last decade. This is certainly due to its numerous advantages such as simple and robust construction, high-speed and high-temperature performances, low costs, and fault tolerance control capabilities. The performance of SRMs has been enhanced greatly due to advances in power electronics and computer science. Nowadays, SRMs are under consideration in various applications requiring high performances such as in electric vehicle propulsion (Kalan, Lovatt, & Prout, 2002; Krishnamurthy et al., 2006; Rekik et al., 2008; Schofield, Long, Howe, & McClelland, 2009), automotive starter-generators (Fahimi, Emadi, & Sepe, 2004; Faiz & Moayed-Zadeh, 2005), aerospace applications (Naayagi & Kamaraj, 2005; Radun, 1992), elevator (Lim, Krishnan, & Lobo, 2008) and PFC (Chang & Liaw, 2009). However, several disadvantages like acoustic noise generation, torque ripple, non-linear electromagnetic characteristics and the strong dependence on the rotor position are limiting its utilization compared to other types of machines. One of the main limitations of the SRM is the non-linear electromechanical behavior (dependence on the current and mechanical position) and the extreme magnetic saturation in order to achieve high torque density (Radun, 1995). Therefore, the design of an appropriate controller to achieve high performances must take into account this non-linearity.
Corresponding author.
E-mail address:
[email protected] (M. Hilairet). 0967-0661/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2011.07.011
Several publications concerning linear and non-linear controllers that achieve high dynamic control are available in the literature. Due to the fact that the SRM is a non-linear multivariable system, modern non-linear designs have been studied in order to achieve high dynamic performances. The feedback linearization (Ben Amor, Dessaint, & Akhrif, 1995; Ilic’Spong, Marino, Peresada, & Taylor, 1987) or the passivity-based method (Espinosa-Perez, Maya-Ortiz, Velasco-Villa, & Sira-Raminez, 2004) are good examples. However, experimental results show that these modern controllers are not robust against parameter variation, in particular the feedback linearization. Moreover, the position or speed controllers do not contain current inner loops in order to protect the machine and converter against current surges. This latter constraint is mandatory for an industrial application. Therefore, a classical structure of the controller is based on an instantaneous torque control composed of two loops: current inner loops and an outer speed loop (or position loop), as shown in Fig. 1. The most commonly used method for the inner loop is the hysteresis which is robust, easy to implement and does not require any model of the system. However this type of controller has the disadvantage of variable switching frequency that may cause a subsonic noise in SRM (Blaabjerg, Kjaer, Rasmussen, & Cossar, 1999). The alternative solution is a PWM fixed switching frequency operation with linear and non-linear controllers. In Bae and Krishna (1996), a hybrid controller has been proposed. This controller is a cascade combination of a PI current error amplifier with a PWM output and a hysteresis current controller. When the current error is within the hysteresis window, the PWM block is enabled. The hysteresis block becomes ineffective, thereby the output of the controller block comes only from the PWM part of the controller.
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Fig. 1. Block diagram of the speed controller.
The difficulty consists in choosing the optimal time transition between the two controllers. Generally, all of these contributions do not take into account the non-linear nature of the SRM, i.e. the magnetic saturation is neglected by assuming only the mechanical position dependence on the magnetic flux. In this paper, we address these issues by designing a gainscheduled PI current controller. Because the phase inductance varies according to both rotor position and stator current, a controller with adjustable gains would give better performances than a regular fixed gain PI controller (Ho, Panda, Lim, & Huang, 1998). Another important aspect of this paper is that in the proposed controller, the back-EMF that is considered as a source of disturbance is compensated. In fact, the back-EMF introduces additional current harmonics that could be interesting to attenuate. The paper is organized as follows: the next section introduces the electromagnetic data obtained from the finite element analysis (FEA) and the analytical modeling of the SRM. In Section 3, the gain-scheduling PI current controller design is presented in detail. Finally, simulation and experimental results are presented to verify the performance and viability of the proposed current controller in Section 4.
2. SRM modeling This study considers four phases, 8/6 SRM prototype as shown in Fig. 2 whose characteristics are listed in Table 4. The SRM inverter used is an asymmetrical half-bridge inverter. The current controller design is based on the machine magnetization characteristics that are usually obtained from experimental measurements or from numerical calculations such as finite element analysis (FEA). In this study, the flux linkage fði, yÞ is generated by a numerical tool called MRVSIM based on FEA (Besbes & Multon, 2004). This is represented in Fig. 3(a) over one electrical period and for phase currents going up to 100 A. Mutual effects are neglected in this study. The electromagnetic data is stored in look-up tables and is used in simulations through linear interpolations. The self inductance L can be deduced from the flux linkage as Lði, yÞ ¼ fði, yÞ=i. Fig. 3(b) shows the phase inductance variation versus rotor position for different current values. For current values less than 20 A, the inductance is independent of the current. The magnetic saturation effect appears when the current exceeds 20 A and the inductance becomes a function of both current and position.
Fig. 2. 3D view of the 8/6 SRM prototype.
To take into account the position and current dependence of the inductance in the control so as to improve the performance, the flux linkage is generally stored in a look-up table. However, this storage requires an excessively large amount of memory and is time consuming. Therefore an analytical modeling is adopted in this study for the calculation of the phase inductance based on the curves given in Hannoun, Hilairet, and Marchand (2007). The position dependency is represented by a limited number of Fourier series terms (P þ1) and the non-linear variation with current is expressed by N order polynomial functions. The estimated inductance b L is a function of electrical rotor position y and phase current i can be finally written as follows: b Lðy,iÞ ¼
P X p¼0
ap ðiÞcosðpyÞ
with ap ðiÞ ¼
N X
bpn in
ð1Þ
n¼0
The choice of N and P depends on two factors:
The relative error, between the finite element data and the analytical expression, that decreases with N and P.
The computational time needed by the processor to compute one operating point b Lðy,iÞ: it depends on the number of multiplication and addition operations, which is (Pþ1)(3Nþ2).
H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386
3.5
0.12
1379
x 10−3 Aligned position
Aligned position Rotor position θ
0.08
Phase inductance (H)
Flux−linkage (Wb)
0.1
0.06 0.04
Phase current i
2.5 2 1.5 1
i=100A
0.02 0
i=0 to 20 A
3
0.5
Unaligned position
0
20
40
60
80
0
100
Unaligned position
0
1
2
Phase current (A)
3
4
5
6
Rotor position (°)
Fig. 3. Flux-linkage characteristics based on FEA (a), phase inductance based on FEA (b).
1
2
3 4 Rotor position (rad)
5
6
0.01 Relative error
x 10−3 1A 10A 20A 30A 40A 50A 60A 70A 80A 90A
3
0
0.005 0
2.5 2 1.5 1 0.5
−0.005 −0.01
3.5
MRVSIM L(θ)
Incremental inductance (H)
Inductance (H)
x 10−4 14 12 10 8 6 4
0
1
2
3 4 Rotor position (rad)
5
6
0
0
1
2
3 4 Rotor position (°)
5
6
Fig. 4. Phase inductance and relative error for i¼ 80 A.
Fig. 5. Incremental inductance variation.
A compromise between accuracy and suitability for computer aided design must be done and a reasonable choice seems to select N and P equal to 6 and 4, respectively. Fig. 4 shows a comparison between the inductance model and MRVSIM data for 80 A (saturated region). The maximum relative error is about 1%.
where u is the applied phase voltage, i the phase current, y the angular electrical position, o the angular electrical speed, R the phase winding resistance, E is the induced EMF and Linc ðy,iÞ is the incremental inductance that depends on the phase current and rotor position, as can be seen in Fig. 5. Eq. (2) indicates a non-linear model that depends on position, current and speed. The electrical time constant of a phase winding and the back-EMF vary strongly with current and rotor position. Therefore a controller that takes into consideration the variation of the SRM plant (back-EMF and inductance) should normally gives better performance.
3. Controller design 3.1. Electrical model The differential equation describing the dynamical behavior of one SRM phase is: @i u ¼ Ri þ Linc ðy,iÞ þ Eðy,i, oÞ @t
ð2Þ
It is clear from Eq. (2) that the design of the current controller could not be obtained by the regular linear control tools. Therefore, an exact linearization via a static state feedback control has been opted.
ð3Þ
Proposition. Consider one phase of the SRM represented by the model
with Linc ðy,iÞ ¼ Lðy,iÞ þi Eðy,i, oÞ ¼ io
@Lðy,iÞ @i
@Lðy,iÞ @y
3.2. Gain adaptation
_ ¼ uRi F ð4Þ
i ¼ hðF, yÞ
ð5Þ
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where the flux F is the state, i is the current, R the phase resistance and hðF, yÞ a non-linear function that represent the mapping between the flux, the position and the current. With the control law: u ¼ K 0p ðin iÞ þ
K 0i n ði iÞ þ Riþ Eðy,i, oÞ s
K 0i ðy,iÞ ¼ Linc ðy,iÞw2n K 0p ðy,iÞ ¼ 2xLinc ðy,iÞwn
ð6Þ
the closed-loop can be modeled by a second order system s2 þ 2xwn s þw2n , where x is the damping ratio and wn is the bandwidth. Proof. The proof proceeds in two steps, introducing first a static state feedback control u ¼ bðF,i, yÞm þ aðF,i, yÞ, where m is an external input. It is shown that the compensation aðF,i, yÞ equals to RhðF, yÞ þEðy,i, oÞ leads to _ ¼ bðF,i, yÞm F
b b y,i, oÞ ¼ io @Lðy,iÞ Eð @y
di ¼m dt
ð8Þ
Then, introducing a PI controller with a proportional gain Kp and an integral gain Ki leads to the second-order transfer function: K þ Kp s i ¼ 2 i in s þ Kp sþ Ki
ð9Þ
Equating the denominator with s2 þ 2xwn s þ w2n shows that Ki ¼ w2n Kp ¼ 2xwn
ð10Þ
From the definition of bðF,i, yÞ, aðF,i, yÞ and Eq. (10), one gets the control law: K u ¼ Linc ðy,iÞ Kp ðin iÞ þ i ðin iÞ þ Riþ Eðy,i, oÞ s K 0i n ði iÞ þ Riþ Eðy,i, oÞ s
ð11Þ
ð13Þ
Once the back-EMF term is calculated, it is added to the PI controller output to decouple its effect on the current loop as shown in Fig. 6. As shown in Fig. 5, the incremental inductance is highly nonlinear, i.e. it is a function of both position and current. This means that for a controller with fixed gains, the closed-loop transfer characteristics change over the electrical cycle. To show this variation, a simple case where the inductance varies only with the position, i.e. for current values less than 20 A is considered. For two different positions (y1 and y2 ), it is possible to write: Ki ¼ L1 w2n1 ¼ L2 w2n2 ¼ constant
ð14Þ
Kp ¼ 2x1 L1 wn1 ¼ 2x2 L2 wn2 ¼ constant0
ð15Þ
ð7Þ
and that the choice of bðF,i, yÞ equals to Linc ðy,iÞ gives the equation:
¼ K 0p ðin iÞ þ
To overcome this issue, in this study the back-EMF is analytically computed using Eq. (1) as:
)
wn1 wn2
2 ¼
L2 L1
and
x2 wn2 ¼ ¼ x1 wn1
sffiffiffiffiffi L1 L2
ð16Þ
Therefore, if the damping ratio is fixed to 1 and the bandwidth to 10,000 rad/s at the unaligned position (y ¼ 01) where the inductance is equal to 0.38 mH, the dynamics will vary with the position according to Eq. (16). The variation of the dynamics with three different positions [the unaligned position (y ¼ 01), an intermediate position (y ¼ 901) and the aligned position (y ¼ 1801)] is summarized in Table 1. It shows a slower system and fluctuation increase while the inductance increases. The Bode diagram of the closed-loop system corresponding to those three operating points, when no adaptation is used, can be seen in Fig. 7. As it can be seen in this figure, the magnitude of the closed-loop system varies widely according to the operating point and thus the resulting bandwidth and the phase margin. The benefit of the gain adaptation is that controller parameters vary with current and position so that the dynamics remain constant when the inductance varies. In Rahman and Schulz (2002), a linear gain adaptation has been adopted. Nominal PI gains are set for maximum current in the unaligned position. Two adaptation coefficients are introduced to adjust the PI gains with respect to the reference current and the rotor position, respectively, in a linear way. This method has the advantage of being simple. The variations of the bandwidth and the phase margin are limited but still exist.
where K 0i ¼ Linc ðy,iÞw2n K 0p ¼ 2xLinc ðy,iÞwn
&
ð12Þ
3.3. Discussion Compensation of the back-EMF term is essential in order to achieve high-performance current control. The back-EMF could be seen as a disturbance to be eliminated from the current loop. In Bae and Krishna (1996), the back-EMF term has been decoupled using a linear model of the inductance versus rotor position. However, for a highly saturated machine it is necessary to include the saturation effects due to current in the back-EMF compensation. In Rahman and Schulz (2002), saturation has been taken into consideration and the back-EMF term was computed as E ¼ oð@fðy,iÞ=@yÞ, where @fðy,iÞ=@y is stored in a two dimensional look-up table. However, the look-up table approach requires memory and valuable processing time.
Fig. 6. Bloc diagram of the current control loop.
Table 1 Loop dynamics variation for the fixed PI controller.
y (deg)
L (mH)
x
wn (rad/s)
0 90 180
0.38 1.35 3.22
1 0.5305 0.3435
10,000 5305 3435
H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386
Bode Diagram
Magnitude (dB)
10 0
1381
cosð3yÞ ¼ cosðyÞð14 sinðyÞ2 Þ
ð18Þ
cosð4yÞ ¼ 18 sinðyÞ2 þ 8 sinðyÞ4
ð19Þ
cosð5yÞ ¼ cosðyÞð112 sinðyÞ2 þ16 sinðyÞ4 Þ
ð20Þ
−10 −20 −30 −40
θ1=0° θ2=90° θ3=180°
Therefore, the computation of the gains scheduling needs 30 multiplications, 26 additions and no division, which is not excessive.
−50
Phase (deg)
0 −45 −90 −135 103
105
104
106
Frequency (rad/sec) Fig. 7. Bode diagram of the closed-loop system. Fig. 9. Discretize gain-scheduling PI controller.
Table 3 Dynamics variation with the classical PI controller. Fig. 8. Gain adaptation algorithm.
Table 2 Number of operations to compute the gain scheduling.
b, g, g2 , g4 Trigonometric function Gains ap(i) Lðy,iÞ Total
x
wn (rad/s)
tr (ms)
DHOL (dB)
DFOL (deg)
0.17 0.38 1.8 3.22
2.27 1.61 0.7 0.5234
3254 2300 1000 747
4 3.9 3 7.1
2.3 8.5 22.8 27.85
39 63.5 63 53
Number of multiplications
Number of divisions
12 8
10 6
0 0
Table 4 Prototype characteristics.
6 4 30
6 4 26
0 0 0
Geometric parameters Number of rotor poles Number of stator poles Stator outer diameter Shaft diameter
6 8 143 mm 23 mm
Stator pole arc Rotor pole arc Airgap length
19.81 20.651 0.8 mm
Electrical parameters Number of phases Nominal power
4 1.2 kW
Nominal speed Nominal voltage
3000 rpm 24 V
In the proposed controller, gain adaptations ensure exactly the same dynamics when the position and the current vary. The gainscheduling controller assumes that a measurement of the shaft position as well as the current are available so that the inductance given by Eq. (1) can be computed. This value is then used to adjust the parameters of the PI controller, according to Eq. (12). The proportional and the integral gains vary with current and rotor position so that the bandwidth and the damping ratio remain constant. This procedure is summarized in Fig. 8. Table 2 shows the number of arithmetic operations required at each time sample by our algorithm. The complexity and the memory requirements are significantly increased. For the evaluation of the total number of arithmetic operations, the trigonometric functions required by the estimator are supposed to be computed by fifth degree polynomials, as done for example on DSPs. Therefore, each trigonometric functions uses 5 multiplications and 5 additions by applying Horner’s rule to rearrange polynomials in Horner form. This is useful for an effective implementation. However, in order to increase the reduction of the computational complexity, the main operations required for computing these coefficients are the evaluation of b ¼ cosðyÞ, g ¼ sinðyÞ, g2 , g4 . No other trigonometry functions are required, because: cosð2yÞ ¼ 12 sinðyÞ2
ð17Þ
10 Electromagnetic torque (N.m)
Computation of Number of additions and subtractions
Linc (mH)
Phase current i
5
0
−5
−10 0
1
2
3
4
Rotor position (rad) Fig. 10. Torque characteristics based on FEA.
5
6
Fig. 11. Block diagram of the SRM and controller.
40 35 30 25 20 15 10 5 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
25 20 15 10 5 0 1.95
Fig. 12. Simulation result of the current regulation using the GSPI controller.
1.5
x 10−3
1 0.5 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
12000 10000 8000 6000 4000 2000 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
6 5 4 3 2 1 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
Fig. 13. Gain-scheduling of the GSPI controller.
H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386
3.4. Dynamic’s choice The proposed controller has been implemented using a Dspace board, therefore it must be digitized first. This is achieved using the Euler transformation associated with an anti-windup followed by a zero-order holder, as shown in Fig. 9. In order to tune gains Kp and Ki, the desired closed-loop response time tr need to be define in agreement with the
1383
sampling time. In our case, a Dspace board has been used so that the sampling time has been fixed to 100 ms. Considering a response time tr equal to 10 times the sampling period (tr ¼1 ms), a reasonable choice of x and wn seems to be x and wn equal to 0.7 and 3000 rad/s, respectively. In order to compare the gain-scheduling with the regular PI controller, the dynamics of the latter must be settled. The choice is more delicate in this case because the inductance variation can
40 35 30 25 20 15 10 5 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
25 20 15 10 5 0 1.95
Fig. 14. Simulation result of the current regulation using the regular PI controller.
1.5
x 10−3
1 0.5 0 1.95
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
1.955
1.96
1.965
1.97
1.975
1.98
1.985
1.99
1.995
2
2000 1500 1000 500 0 1.95 3 2 1 0 1.95
Fig. 15. Phase inductance variation and fixed gains with the regular PI controller.
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degrade the stability margin. The adopted dynamics must ensure the system stability whatever the inductance value is. The critical value is the minimal one, i.e. 0.17 mH. Table 3 summarizes the dynamics variation of the closed-loop, the gain and phase margins for different inductance values (minimal, maximal, intermediate). Theses values are computed according to Eq. (16) together with an initial tuning. From theses values, we conclude that the system is stable for every inductance
PIGV PIGF
4
3.5
3
2.5
2 1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995
2
Fig. 16. Simulation result of a torque comparison.
value, therefore a reasonable choice for the regular PI controller would be equal to x ¼ 0:7 and wn ¼1000 rad/s at the mean value of the inductance (1.8 mH). This is the adopted choice in this study.
4. Simulation results Simulation tests have been carried out using MATLAB-Simulink software package. The non-linear characteristics of the SRM are modeled using the static data obtained by finite element analysis (see Figs. 3(a) and 10). Fig. 11 shows the SRM non-linear model and the controller. The controller contains two sample times: one for the current control (100 ms), and a second one for the speed control (1 ms). In our application, the power supply is regular half-bridge inverter with a DC-bus voltage equal to 24 V. The results consider a steady state of 500 rpm with a 3 N m load torque. Fig. 12 shows the four phases current regulation using the gain-scheduling PI controller (GSPI) and the four mean voltages obtained at the output of the controllers (one regulator per phase). The output of the speed controller is nearly equal to 30 A which corresponds to the saturated zone. The phase inductance variation is illustrated in Fig. 13 together with the resulting gain adaptation in order to maintain constant dynamics. For the same operating point (500 rpm, 3 N m), the results obtained using the regular PI controller are represented in Figs. 14 and 15. During the transient period, the voltage resulting from the GSPI controller is greater than the one given by the regular PI controller, therefore it boosts the phase current, resulting in a better and faster response than the regular PI controller. This fact is reflected on the produced torque shown in Fig. 16 where we can notice that torque ripple is decreased with GSPI.
45 40 35 30 25 20 15 ΔL = 0%
10
ΔL = +20%
5 0
ΔL = −20%
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6 x 10−3
25 20 15 10 5 0
6 x 10−3
Fig. 17. Robustness test of the GSPI controller.
H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386
The performance of the proposed controller is limited because of the DC source voltage limitation (24 V). For a given speed, the controller is able to produce better current response until the resulting phase voltage saturates. In that case, the two controllers become equivalent and a regular PI one would be enough. Inductance variation is introduced on the model in order to test the robustness of the new controller according to the phase inductance uncertainties. Fig. 17 represents the current response and the mean voltage at the controller output for a 720% inductance variation at 500 rpm. The current response is slightly affected by this parameter variation.
1385
40 35 30 25 20 15
5. Experimental results 10
The proposed controller has been implemented on a test bench shown in Fig. 18 using a DSPACE DS1103 board. Angular velocity and rotor position are detected by means of an incremental encoder mounted on the SRM rotor shaft (on the left of the test bench). Phase currents are measured using a hall effect current sensor and an electromagnetic particle brake is used in order to vary the load. Moreover, the test bench is equipped with a torque transducer in order to evaluate the mean torque and torque ripple. The tests performed in simulation have been repeated on the test bench. Fig. 19 shows the measured currents with both controllers. As noticed, the simulation and the experimental results agree excellently.
5 0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
40 35 30
6. Conclusion
25
An adaptive PI current controller has been developed for SR motor drives. The variable structure PI controller is self-tuning. Its design is based on a regular PI controller concept, except that its parameters are adjusted on-line as the current and the position change. In addition, a back-EMF compensation scheme has been implemented to reduce the bandwidth requirements placed upon the controller. This controller limits the loop bandwidth variations due to the radically changing plant gain seen by the controller, thus resulting in a well controlled system. The proposed gain-scheduling PI controller has been tested by simulation and validated on the experimental test bench. The results prove the interest of this type of regulation. However, the
20 15 10 5 0
Fig. 19. Experimental result of one phase current with GSPI controller (a) and regular PI controller (b).
improvement has been limited due to the DC voltage supply saturation of the specific application.
References
Fig. 18. Experimental test bench.
Bae, H. K., & Krishna, R. (1996). A study of current controllers and development of a novel current controller for high performance SRM drives. IEEE IAS annual meeting (pp. 68–75). Ben Amor, L., Dessaint, L. A., & Akhrif, O. (1995). Adaptive nonlinear torque control of a switched reluctance motor via flux observation. Mathematics and Computers in Simulation, 38, 345–358. Besbes, M., & Multon, B. (2004). MRVSIM Logiciel de simulation et d’aide a la conception de Machines a re´luctance variable a double saillance a alimentation e´lectronique. Deposit APP CNRS n.IDDN.FR.001.430010.000.S.C.2004.000.30645. Blaabjerg, F., Kjaer, P. C., Rasmussen, P. O., & Cossar, C. (1999). Improved digital current control methods in switched reluctance motor drives. IEEE Transactions on Power Electronics, 14(3), 563–572. Chang, H. C., & Liaw, C. M. (2009). Development of a compact switched-reluctance motor drive for EV propulsion with voltage-boosting and PFC charging capabilities. IEEE Transactions on Vehicular Technology, 58(7), 3198–3215.
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