2010-improved integral sliding mode control methods pmsm

International Journal of InnovativeComputing, Information and Control ICIC International c2011 ISSN 1349-4198Volume 7, Number 4, April 2011 pp. 1971{1982

IMPROVED INTEGRAL SLIDING MODE CONTROL METHODSFOR SPEED CONTROL OF PMSM SYSTEM

Cunjian Xia, Xiaocui Wang, Shihua Li and Xisong Chen

School of AutomationKey Laboratory of Measurement and Control of CSE, Ministry of Education

Southeast UniversityNo. 2, Sipailou, Nanjing 210096, P. R. China

[email protected]

Received December 2009; revised April 2010

Abstract. To improve the disturbance rejection property of permanent magnet syn-chronous motor (PMSM) speed control system, the integral sliding mode control (ISMC)method is introduced in the control design of speed loop. However, the simulation andimplementation results show that it is dicult to balance the chattering and the anti-disturbance capacity. To this end, three kinds of improved ISMC control methods aredeveloped. First, ISMC using linear varying gain is developed. Using this method, theswitching gain of ISMC controller can be smaller while still ensuring that the speed statereaches its steady state and the steady state uctuations can thus be reduced. Moreover,the anti-disturbance capacity of the PMSM system can also be assured. Second, an in-tegral sliding mode control based on extended state observer (ESO) is developed. ESOcan estimate both of the states and the disturbances simultaneously. By using ESO, anestimate of the lumped disturbances is obtained, which is employed for the feedforwardcompensation design of the composite ISMC control law. In this case, the controller maytake a smaller value for the switching gain without sacricing disturbance rejection per-formance, which helps to reduce large chattering caused by high control gains. Third, anadaptive composite control method combining linear varying gain and ESO is developedto take advantages of both improved methods. These improved methods show advantagesin reducing the chattering while ensuring the dynamic and disturbance rejection perfor-mance. Both of simulation and experiment results are provided.Keywords: PMSM, Integral sliding mode control, Extended state observer, Linearvarying gain, Composite control, Speed-regulation

1. Introduction. Permanent magnet synchronous motor has gained widespread accep-tance in numerical control machine tools, robots, aviation and so on, due to its excellentfeatures such as high power density, torque-to-current ratio and eciency [1]. Linear con-trol schemes such as proportional-integral (PI) control scheme have been widely used inPMSM servo system because of simple implementation [2]. However, it is very dicult toachieve a satisfactory performance in the entire operating rage by only using linear controlmethods. The reason is that the PMSM servo system is a nonlinear system with unavoid-able and unmeasured disturbances as well as parameters variations [3, 4, 5]. Thus, variousmethods of nonlinear control methods have been developed for PMSM system, such asadaptive control [6, 7], robust control [8], sliding mode control [9], input-output lineariza-tion control [4], backstepping control [10], neural network control [5], fuzzy control [11]and nite-time control [12], etc.Sliding mode control (SMC) is a very useful nonlinear control method [13, 14, 15] and

it has been introduced in AC servo drive systems [16, 17] due to its good robustnessfor external disturbances and variations of system parameters, fast response and easy

1971

1972 C. XIA, X. WANG, S. LI AND X. CHEN

implementation. Under the framework of vector control and cascade structure, in thecontrol design for speed loop, usually a rst-order model is used to approximately describethe relationship between the reference quadrature axis current and the speed output. Toconstruct a common sliding surface, the sliding-mode speed controller needs both thespeed and the acceleration signals [16, 18]. However, due to noise and uncertainties ofparameters, acceleration signals are dicult to be measured or to be estimated accurately[19]. These degrades the closed loop performance of system. To this end, integral slidingmode control (ISMC) method is proposed [20] and applied in asynchronous motor [21].The acceleration information is not required anymore.In this paper, a standard ISMC method is developed for the speed control of PMSM

system. However, the simulation and implementation results of the standard ISMCmethod on PMSM system show that it is dicult to balance the chattering and theanti-disturbance capacity. The anti-disturbance performance of the system mainly de-pends on the switching gain. While it is tuned to a small value, the motor speed can notrecover to its reference value when the load disturbance is added. When the switchinggain is increased, the anti-disturbance capacity of closed loop system becomes better.However, in this case, the closed loop system produces a greater chattering.According to the SMC theory, if the switching control gain is selected to be bigger

than the upper bound of disturbances, the disturbances can be well rejected. However,for practical applications, the bound of disturbances is dicult to obtain which oftenresults in an inadequate selection of switching gain. Usually, an overlarge switching gaincauses a large chattering. To this end, three improved ISMC methods are proposed toimprove the performance of servo system. The main idea is to nd some ways to reducethe conservativeness of selecting switching control gain.First, an improved ISMC method based on linear varying gain is used. The switching

gain linearly varies at dierent stages. It takes a larger value when the states are far awayfrom the sliding surface (e.g., at the starting stage), so the dynamic response time of statecan be ensured. When the state approaches the sliding surface including its steady state,the switching gain takes a smaller value which helps to reduce the steady state chatteringof system. Meanwhile, the anti-disturbance capacity can still be assured.Second, an improved method employs a disturbance estimation technique to have an

adequate estimate for the lumped disturbances of PMSM system. Then, after distur-bance compensation based on ESO, the switching gain only need to be taken biggerthan the bound of the disturbance compensation error, which is usually much smaller.Thus, an ISMC method based on extended state observer (ESO), named ISMC+ESOmethod, is developed. An ESO in the feedback path provides estimates of both thespeed and the lumped disturbances. The estimate of the lumped disturbances is em-ployed for feedforward compensation design of the control law. In [9], a total slidingmode controller is proposed for the position control problem of PMSM system, where arecurrent-fuzzy-neural-network is adopted as a bound observer to facilitate adaptive con-trol gain adjustment. Compared with that technique, the ESO technique is very simplefor implementation.Third, to further enhance the performance, an adaptive ISMC method based on ESO,

named adaptive ISMC+ESO method, is developed. The eectiveness of the proposedthree improved schemes is veried and compared by simulation and experiment results.

INTEGRAL SLIDING MODE CONTROL METHODS FOR PMSM SYSTEM 1973

Figure 1. The diagram of PMSM system

2. The Mathematical Model of PMSM. The model of surface mounted PMSM isexpressed in d q coordinates as follows [27]:0@ _id_iq

_!

1A =0B@

RsLd

np! 0

np! RsLq np fLq

03np f2J

BJ

1CA 0@ idiq

!

1A+0@ udLduq

Lq

TLJ

1A (1)where Rs the stator resistance, ud, uq the d- and q- axes stator voltages, id, iq the d- andq- axes stator currents, Ld, Lq the d- and q- axes stator inductances Ld = Lq = L, npthe number of pole pairs, ! the rotor angular velocity, f the ux linkage, TL the loadtorque, B the viscous friction coecient, J the rotor inertia.The general structure of the PMSM servo system is shown in Figure 1. The overall

system consists of a PMSM with load, space vector pulse width modulation (SVPWM),voltage-source inverter (VSI), eld-orientation mechanism and three controllers. Thecontrollers employ a structure of cascade control loop including a speed loop and twocurrent loops. Here two PI controllers, which are used to stabilize the d q axes currenterrors of the vector controlled drive, are adopted in the two current loops respectively.As it can be seen from Figure 1, the rotor angular velocity ! can be obtained from theposition and speed sensor. The currents id and iq can be calculated from ia and ib (whichcan be obtained from measurements) by Clarke and Park transforms.

3. Control Strategy of PMSM Speed-Regulation System.

3.1. The standard integral sliding mode controller. The torque equation of PMSMsystem can be written as

_! =1:5np f iq B! TL

J=

3np f2J

iq + a(t) (2)

where a(t) =1:5np f

iq iq

B! TL =J is the lumped disturbances of system.Dene the speed error e = ! ! where ! is reference speed. Taking the derivative

of e and substituting (2) into it, yields:

_e = _! 3np f2J

iq a(t): (3)The sliding surface is designed as

s = e+3np f2J

m

Z t0

ed: (4)

And the speed controller can be designed as

iq = me+ f sgn(s) + (2J=(3np f )) _! (5)where m, f > 0, and sgn() is the standard signum function.


Figure 2. Speed response ofsystem under ISMC scheme

Figure 3. Speed response ofsystem with disturbance underISMC scheme

Assumption 3.1. The lumped disturbances of system a(t) satises 0 ja(t)j < l.Theorem 3.1. Assume that system (1) satises Assumption 3.1. Under the control law(5), the speed error of system (1) converges to zero if f > 2Jl

3np f.

Proof: Choosing Lyapunov function V = 12s2, and taking the derivative of it along

system (3), yields:

_V = s _s = s

_e+

3np f2J

me

: (6)

Substituting (3) into (6) yields:

_V = s _s = 3np f2J

s

iq +

2J

3np fa(t)me 2J

3np f_!: (7)


_V = s _s = 3np f2J

f jsj+ 2J

3np fa(t)s

: (8)

From Assumption 3.1, if f > 2Jl3np f

, one obtains

_V 3np f2J

jsjf 2J

3np fl

< 0 (s 6= 0) (9)

So the control law (5) makes (4) converge to zero in nite time. When the speed

error reaches its sliding surface, i.e., s = e +3np f2J

mR t0ed = 0, which implies that

_e = (3np f=(2J))me. Thus, the speed error will converge to zero. The theorem isproved.

3.2. Simulation results and experiment results. Here, the parameters of the PMSMare: the resistance of stator Rs = 0:8, the inductances of d and q axes Ld = Lq =2:9 103H, the ux of rotor f = 0:2wb, the rotor inertia J = 6:5 104kg m2, theviscous friction coecient B = 1:28 104n m s, the number of poles np = 4.3.2.1. Simulation results. The speed regulation system of the PMSM is simulated byMATLAB. The parameters of the integral sliding mode controller are m = 0:8; f = 10.The reference speed is 1000rpm, and the load torque TL = 4Nm is added at t = 1s.The speed response of the PMSM speed-regulation system is shown in Figure 2. Figure2 shows that when the ISMC scheme is used, a speed response with no overshoot isobtained. Figure 3 shows the anti-disturbance property of system when a load disturbance


Figure 4. Speed response of system under ISMC method

Figure 5. Speed response ofsystem with disturbance underISMC method with a smallergain

Figure 6. Speed response ofsystem with disturbance underISMC method with a largergain

is added. It shows that the speed response of the system used ISMC scheme has an obviouschattering and the anti-disturbance capacity is not satisfactory.

3.2.2. Experiment results. As for the experimental test setup, the whole speed controlalgorithms is implemented by the program of the DSP TMS320F2808 with a clock fre-quency of 100MHZ. The PMSM is driven by a three-phase PWM inverter with an IPMwith a switching frequency of 10kHz. The phase currents are measured by the Hall-eectdevices and are converted through two 12-bit A/D converters. An incremental positionencoder of 2500 lines is used to measure the rotor speed and absolute rotor position. Theparameters of the ISMC are m = 1200, f = 18. The reference speed is 1000rpm.The speed response of the closed loop system under ISMC scheme is shown in Figure 4.

The speed responses under dierent switching gains are shown in Figures 5 and 6 whena step load disturbance of TL = 2Nm is added. The anti-disturbance performance of thesystem mainly depends on the switching gain f and m, here m is selected to be m = 1200.When f is tuned to a small value, e.g., f = 18, the motor speed can not recover to itsreference value when the load disturbance is added and the performance of disturbancerejection is worse, as shown in Figure 5. Usually, it is expected that when the switchinggain is increased, the anti-disturbance capacity of closed loop system may become better.As shown in Figure 6, when f is tuned to a larger value, e.g., f = 80, the speed responsecan recover to its reference value. However, in this case, the system produces a greaterchattering. Through parameters tuning of control gain f for many times, we nd that it isvery dicult to have a good balance between disturbance rejection and chattering underthe standard ISMC method. In fact, this phenomena of the ISMC method has alreadybeen mentioned in [28] for synchronous reluctance motor drive system.


4. The Integral Sliding Mode Controller with Linear Varying Gain.

4.1. Design of controller. The torque equation of PMSM system is written as (2). Andthe sliding surface is designed as (4). The speed controller can be designed as:

iq = me+ f^ sgn(s) +2J

3np f_! (10)

where the state feedback gain m > 0 and f^ is the linear varying switching gain. Here,

f^ = c1 +jsjc2

and c1, c2 can be changed.

Theorem 4.1. Assume that system (1) satises Assumption 3.1. Under the control law(10), the speed error of system (1) converges to zero if c1 >

2Jl3np f

.

Proof: Choosing Lyapunov function V = 12s2, and taking the derivative of it along

system (3), yields (6). Substituting (3) into (6) yields:

_V = s _s = 3np f2J

s

iq +

2J

3np fa(t)me 2J

3np f_!: (11)


_V = s _s = 3np f2J

c1jsj+ jsj

2

c2+

2J

3np fa(t)s

: (12)

From Assumption 3.1, one obtains

_V 3np f2J

c1 2J

3np fl

jsj+ jsj

2

c2

: (13)

If c1 >2J

3np fl, _V = s _s 0. So the control law (10) can make the sliding surface (4)

converge to zero in nite time. When the speed error reaches its sliding surface, i.e.,

_e = 3np f2J

me, it converges to zero. The theorem is proved.

4.2. Simulation and experiment results.

4.2.1. Simulation results. The parameters of the integral sliding mode controller are m =0:8, f = 10 and the parameters of the integral sliding mode controller with linear varyinggain are m = 0:65, c1 = 5, c2 = 40. The reference speed is 1000rpm, and the loadtorque TL = 4Nm is added at t = 1s. The speed responses of system are shown inFigure 7. Figure 7 shows that the rising time of the ISMC method is almost the same asthat of ISMC method with linear varying gain. Figure 8 is the anti-disturbance capacitycomparison of the system used two dierent controllers. And the result shows that thespeed response of ISMC with linear varying gain has less chattering when the system isat its steady state and has better anti-disturbance capacity when the same disturbanceload is added.

4.2.2. Experiment results. The parameters of the ISMC are m = 1200, f = 18 and theparameters of the ISMC with linear varying gain are m = 850, c1 = 18, c2 = 100. Thereference speed is 1000rpm. The step responses of the ISMC and ISMC with linear varyinggain are shown in Figure 9. It shows that the rising time of the ISMC with linear varyinggain is a little longer than the rising time of the ISMC and its overshoot is a little bigger.From Figure 10, when load disturbance is added, the speed can return to the referencespeed in short time and the maximum speed uctuations of the closed loop system underISMC with linear varying gain control method is only about 30rpm, much smaller thanthat of standard ISMC method. As the switching gain is smaller than that of standard


Figure 7. Speed responses ofsystem under ISMC and ISMCwith linear varying gain

Figure 8. Speed responses ofsystem with disturbance underISMC and ISMC with linearvarying gain

Figure 9. Speed responses ofsystem under ISMC and ISMCwith linear varying gain

Figure 10. Speed responsesof system with disturbance un-der the ISMC with linear vary-ing gain

ISMC method, so the steady uctuations of the servo system is also reduced. And theanti-disturbance capacity and the performance of the system are improved.

5. ESO-based Composite Control Strategy.

5.1. Design of controller. Here, a kind of disturbance observer techniques is employedto have an adequate estimate for the lumped disturbances of PMSM system. This tech-nique is extended state observer [22, 23, 24]. A control frame based on ESO, called activedisturbance rejection control (ADRC) is also developed. This method has also been ap-plied in many areas, such as robotic systems [25], machining processes [26], PMSM systems[2, 6], and so on. The ESO regards the internal and external disturbances of the systemas the lumped disturbances, and the lumped disturbances can be considered as a newextended state. ESO can observe and estimate the state and the lumped disturbances ofsystem respectively. The estimate of the lumped disturbances is employed to compensatethe disturbances through a feedforward design in the control law.A linear ESO can be constructed as follows [29]:

_z1 = z2 2p(z1 !) + 3np f2J

iq; _z2 = p2(z1 !) (14)where z1 is an estimate of speed !, z2 is an estimate of the lumped disturbances, and p(p > 0) is the desired double-pole of ESO. The sliding surface is designed as (4). And the


Figure 11. Speed responsesof system under ISMC andISMC+ESO methods

Figure 12. Speed responsesof system with disturbance un-der ISMC and ISMC+ESOmethods

control law can be designed as:

iq = me+ f sgn(s)2J

3np fz2 +

2J

3np f_! (15)

where the state feedback gain m > 0 and f is the switching gain, 2J3np f

z2 is the feedfor-

ward component of the control law.Here, a(t) represents disturbances of the system, z2 is the estimate of a(t) from ESO.

Assumption 5.1. Assume that a(t) z2 is bounded, which satises 0 ja(t) z2j < l0.Theorem 5.1. Assume that system (1) satises Assumption 5.1. For PMSM speed-regulation system (1), if the switching gain f > 2Jl

03np f

, the speed error of system (2)

converges to zero under the control law (15).

Proof: Let Lyapunov function V = 12s2, and the derivative of it with respect to time

is (6). Substituting (3) into (6), yields (7). And substituting (15) into (7), yields:

_V = s _s = 3np f2J

f jsj+ 2J

3np f[a(t) z2]s

: (16)

From Assumption 5.1, one obtains

_V 3np f2J

f 2J

3np fl0jsj: (17)

If f > 2Jl0

3np f, _V = s _s < 0 (s 6= 0). The control law (15) makes the state of the speed error

of system (2) converge to s(x) = 0 in nite time. When the speed error reaches its slidingmode, i.e., s = 0, it will converge to zero. The theorem is proved.

5.2. Simulation and experiment results.

5.2.1. Simulation results. The parameters of the ISMC are m = 0:8, f = 10 and theparameters of the ISMC+ESO are m = 2, f = 0:1, p = 3000. The reference speedis 1000rpm, and the load torque TL = 4Nm is added at t = 1s. Speed responses areshown in Figure 11. Figure 11 shows that rise time of the ISMC+ESO is a little longer.Simulation results of anti-load disturbance of the two controllers are shown in Figure12. Figure 12 shows that speed response of the ISMC+ESO has a less chattering. Andwhen the same disturbance load is added, the maximum uctuation of the ISMC+ESOis smaller , so the PMSM speed-regulation system using the ISMC+ESO controller has abetter anti-disturbance capacity.


Figure 13. Speed responsesof system under ISMC andISMC+ESO methods

Figure 14. Speed responseof system with disturbance un-der ISMC+ESO method

Figure 15. The diagram of adaptive ISMC+ESO scheme for PMSM system

5.2.2. Experiment results. The parameters of the ISMC controller are m = 1200, f = 18and the parameters of the ISMC+ESO controller are m = 1050, f = 20, p = 500. Andthe reference speed is 1000rpm. Comparisons of speed responses under ISMC law (5) andISMC+ESO law (15) respectively are shown in Figure 13. The rising time of ISMC+ESOis a little longer and its overshoot is a little bigger. The speed responses of ISMC+ESOwith disturbance load is shown in Figure 14. It can be seen that the maximum speed

uctuation of the closed loop system under ISMC+ESO control method is only about25rpm, much smaller than that of standard ISMC method. Since the estimate of lumpeddisturbances is employed for feedforward compensation design of the control law, theperformance degradation caused by disturbances is suppressed, and the closed loop systemunder ISMC+ESO control method has a less chattering, and a better anti-disturbancecapacity.

6. Adaptive ESO-based Composite Control Strategy.

6.1. Design of controller. In this section, an adaptive ESO-based composite controlleris proposed. Here, the switching gain is changed with the variations of the speed error.As same as Section 5.1, ESO is used to estimate the lumped disturbances of PMSMsystem. Then, the estimate value of lumped disturbances is employed for feedforwardcompensation design of the control law. Here, the linear ESO is designed as (14), thesliding surface is designed as (4). And the speed controller can be designed as

iq = me+c3 +

jsjc4

sgn(s) 2J

3np fz2 +

2J

3np f_! (18)

where c3, c4 > 0 are constants, m is the feedback gain. The principle diagram of theadaptive ESO-based composite control (Adaptive ISMC+ESO) is shown in Figure 15.Note that the generalized plant in Figure 15 represents the two current loops whichinclude PMSM and other components the same as that of Figure 1.


Figure 16. Speed responseof system under ISMC+ESOand adaptive ISMC+ESOmethods

Figure 17. Speed responseof system with disturbance un-der ISMC+ESO and adaptiveISMC+ESO methods

Theorem 6.1. Assume that system (1) satises Assumption 5.1. For PMSM speed-regulation system (1), if switching gain c3 >

2Jl03np f

, the speed error of system (1) converges

to zero under the control law (18).

Proof: The proof process is a combination of that of Theorems 4.1 and 5.1, which isomitted here.

6.2. Simulation results and experimental results.

6.2.1. Simulation results. Here, the parameters of ISMC+ESO controller are m = 2,f = 0:1, p = 3000, and the parameters of adaptive ISMC+ESO controller are m = 2,c3 = 0:3, c4 = 80, p = 2000. The reference speed is 1000rpm, and the load torqueTL = 4Nm is added at t = 0:2s. Speed responses are shown in Figure 16. Figure 16shows that, compared with that of ISMC+ESO method, the rising time of the systemunder adaptive ISMC+ESO method is shorter although the overshoot is a little bigger.When the same load disturbance is added, as shown in Figure 17, the maximum uctuationof the system using adaptive ISMC+ESO method is decreased. It shows that the anti-disturbance capacity is further improved by using the adaptive ISMC+ESO method.

6.2.2. Experimental results. The parameters of ISMC+ESO controller are m = 1050,f = 20, p = 500, and the parameters of adaptive ISMC+ESO controller are m = 1020,c1 = 10, c2 = 100, p = 480. The reference speed is 1000rpm. From Figure 18, comparedwith that of ISMC+ESO method, we can see that, the system under adaptive ISMC+ESOmethod has shorter rising time and settling time although its overshoot is a little bigger.Figure 19 shows that when the same load disturbance is added, the maximum uctuationof speed under the ISMC+ESO and the adaptive ISMC+ESO methods are 25rpm and17rpm respectively. So the system using adaptive ISMC+ESO method has a better anti-disturbance capacity.

7. Conclusion. In this paper, ISMC technique has been studied for the speed control ofPMSM system. Since the standard ISMC method is dicult to balance the chattering andthe anti-disturbance capacity, three kinds of improved ISMC control methods have beendeveloped from dierent considerations. An improved method based on linear varyinggain and an improved method based on extended state observer have been developed,respectively. To further improve system performance and take advantages of the bothimproved methods, an adaptive ISMC method based on combination of linear varying


Figure 18. Speed responseof system under ISMC+ESOand adaptive ISMC+ESOmethods

Figure 19. Speed responseof system with disturbance un-der ISMC+ESO and adaptiveISMC+ESO methods

gain and extended state observer has been developed. Simulation and experimental resultshave shown that the three improved methods can reduce the steady state chattering whileensuring the system performance.

Acknowledgement. This work was supported by Natural Science Foundation of JiangsuProvince (BK2008295) and National 863 Project (2009AA04Z140,2009AA01Z314).

REFERENCES

[1] P. Pillay and R. Krishnan, Control characteristics and speed controller design for a high performancepermanent magnet synchronous motor drive, IEEE Trans. on Power Electronics, vol.5, no.2, pp.151-159, 1990.

[2] Y. X. Su, C. H. Zheng and B. Y. Duan, Automatic disturbances rejection controller for precisemotion control of permanent-magnet synchronous motors, IEEE Trans. on Industrial Electronics,vol.52, no.3, pp.814-823, 2005.

[3] K. H. Kim and M. J. Youn, A nonlinear speed control for a PMSM using a simple disturbanceestimation technique, IEEE Trans. on Industrial Electronics, vol.49, no.3, pp.524-535, 2002.

[4] B. Grcar, P. Cafuta, M. Znidaric and F. Gausch, Nonlinear control of synchronous servo drive, IEEETrans. on Control Systems and Technology, vol.4, no.2, pp.177-184, 1996.

[5] G. J. Wang, C. T. Fong and K. J. Chang, Neural-network-based self-tuning PI controller for precisemotion control of PMAC motors, IEEE Trans. on Industrial Electronics, vol.48, no.2, pp.408-415,2001.

[6] S. H. Li and Z. G. Liu, Adaptive speed control for permanent magnet synchronous motor systemwith variations of load inertia, IEEE Trans. on Industrial Electronics, vol.56, no.8, pp.3050-3059,2009.

[7] H. C. Cho, K. S. Lee and M. S. Fadali, Adaptive control of PMSM systems with chaotic nature usingLyapunov stability based feedback linearization, International Journal of Innovative Computing,Information and Control, vol.5, no.2, pp.479-488, 2009.

[8] T. L. Hsien, Y. Y. Sun and M. C. Tai, H1 control for a sensorless permanent-magnet synchronousdrive, IEE Proc. of Electric Power Applications, vol.144, no.3, pp.173-181, 1997.

[9] R. J. Wai, Total sliding-mode controller for PM synchronous servo motor drive using recurrent fuzzyneural network, IEEE Trans. on Industrial Electronics, vol.8, no.5, pp.926-944, 2001.

[10] M. Vilathgamuwa, M. A. Rahman, K. Tseng and M. N. Uddin, Nonlinear control of interior perma-nent magnet synchronous motor, IEEE Trans. on Industry Applications, vol.39, no.2, pp.408-415,2003.

[11] Y. S. Kung and M. H. Tsai, FPGA-based speed control IC for PMSM drive with adaptive fuzzycontrol, IEEE Trans. on Power Electronics, vol.22, no.6, pp.2476-2486, 2007.

[12] S. H. Li, H. X. Liu and S. H. Ding, A speed control for a PMSM using nite-time feedback controland disturbance compensation, Trans. on the Institute of Measurement and Control, vol.32, no.2,pp.170-187, 2010.


[13] M. Zhang, Z. Yu, H. Huan and Y. Zhou, The sliding mode variable structure control based oncomposite reaching law of active magnetic bearing, ICIC Express Letters, vol.2, no.1, pp.59-63,2008.

[14] W. Xiang and F. Chen, Sliding mode control strategies for the hyperchaotic MCK system, ICICExpress Letters, vol.3, no.3(A), pp.283-288, 2009.

[15] S. Li, Z. Wang and S. Fei, Finite-time control of a bioreactor system using terminal sliding mode,International Journal of Innovative Computing, Information and Control, vol.5, no.10(B), pp.3495-3504, 2009.

[16] E. Y. Y. Ho and P. C. Sen, Control dynamics of speed drive systems using sliding mode controllerswith integral compensation, IEEE Trans. on Industry Applications, vol.27, no.5, pp.883-892, 1991.

[17] C.-Y. Chen, Sliding mode controller design of induction motor based on space-vector pulsewidthmodulation method, International Journal of Innovative Computing, Information and Control, vol.5,no.10(B), pp.3603-3614, 2009.

[18] T. L. Chern and Y. C. Wu, Design of brushless DC position servo systems using integral variablestructure approach, IEE Proc. of Electric Power Applications, vol.140, no.1, pp.27-34, 1993.

[19] P. K. Nandam and P. C. Sen, Sliding mode speed control of a self-controlled synchronous motorbased on state estimation (observer) and digital dierentiation, Proc. of the 1990 InternationalPower Electronics Conference, Tokyo, Japan, pp.291-295, 1990.

[20] T. L. Chen and Y. C. Wu, Design of integral variable structure controller and application to elec-trohydraulic velocity servosystems, IEE Proc. of Control Theory and Applications, vol.138, no.5,pp.439-444, 1991.

[21] W. Q. Yang, X. Cai and J. G. Jiang, Sliding-mode variable structure speed control with integralaction for vector-controlled asynchronous motor, Journal of Shanghai Jiaotong University, vol.39,no.3, pp.426-432, 2005 (in Chinese).

[22] J. Q. Han, The extended state observer of a class of uncertain systems, Control and Decision, vol.10,no.1, pp.85-88, 1995 (in Chinese).

[23] J. Q. Han, Nonlinear design methods for control systems, Proc. of the 14th IFAC World Congress,Beijing, China, pp.521-526, 1999.

[24] Y. Huang and W. G. Zhang, Development of active disturbance rejection controller, Control Theoryand Applications, vol.19, no.4, pp.485-496, 2002 (in Chinese).

[25] J. B. Su, W. B. Qiu, H. Y. Ma and P. Y. Woo, Calibration-free robotic eye-hand coordination basedon an auto disturbance-rejection controller, IEEE Trans. on Robotics, vol.20, no.5, pp.899-907, 2004.

[26] D. Wu, K. Chen and X. Wang, Tracking control and active disturbance rejection with application tononcircular machining, International Journal of Machine Tools and Manufacture, vol.47, pp.2207-2217, 2007.

[27] P. C. Krause, Analysis of Electric Machinery, 2nd Edition, McGraw-Hill Company, NJ, 1995.[28] H. K. Chiang and C. H. Tseng, Integral variable structure controller with grey prediction for synchro-

nous reluctance motor drive, IEE Proc. of Control Theory and Application, vol.151, no.3, pp.349-358,2004.

[29] B. S. Sun and Z. Q. Gao, A DSP-based active disturbance rejection control design for a 1-kW H-bridge DC-DC power converter, IEEE Trans. on Industrial Electronics, vol.52, no.5, pp.1271-1277,2005.

2010-improved integral sliding mode control methods pmsm

Documents

backstepping control

control of cse

fuzzy control

asadaptive control

robust control

high control gains

neural network control

nitetime control