a novel motor drive design for incremental motion system...

A Novel Motor Drive Design for Incremental MotionSystem via Sliding-Mode Control Method

A Novel Motor Drive Design for Incremental MotionSystem via Sliding-Mode Control Method

T. C. Kuo

AbstractINTRODUCTIONFIELD-ORIENTED PMSMINCREMENTAL MOTION CONTROL OF PMSMA. Velocity Control ModeB. Position Control ModeC. Velocity Control ModeD. Position Control ModeSIMULATION RESULTSEXPERIMENTAL SETUP AND RESULTSA. Experimental System SetupB. Experimental ResultsCONCLUSIONREFERENCES

Outline

AbstractThis paper proposes a particular motor position control drive design via a novel sliding-mode controller.

The newly designed controller is especially suitable for the motor incremental motion control which is specified by a trapezoidal velocity profile.

The novel sliding-mode controller is designed in accordance with the trapezoidal velocity profile to guarantee the desired performance.

A motor control system associated PC-based incremental motion controller with permanent-magnet synchronous motor is built to verify the control effect.

The validity of the novel incremental motion controller with sliding-mode control method is demonstrated by simulation and experimental results.

INTRODUCTIONThe control of motors used in high-performance servo drives requires the prescribed torque accuracy, velocity, and/or position for all operating conditions being achieved.

To obtain the desired performance, a precise system model is needed.

It is difficult to construct because of the inherent nonlinearity of friction and dead zone, the parameter variations due to temperature, the uncertain external disturbances, and so on.

PI-type control methods are not robust enough to accommodate the variations of external disturbances, parameters, and perturbations during operation

INTRODUCTIONVariable-structure control (VSC) or sliding-mode control (SMC) has been known as a very effective way to control a system because it possesses many advantages.

such as insensitivity to parameter variations, external disturbance rejection, and fast dynamic responses.

VSC has been widely used in the position and velocity control of dc and ac motor drives.

The system dynamics of a VSC system can be divided into two phases: the reaching one and the sliding one.

The robustness of a VSC system resides in its sliding phase, rather the reaching phase.

INTRODUCTIONThis paper proposes a multisegment sliding-mode- control-method-based motion control drive design in accordance with a trapezoidal velocity profile.

It also shows that the reaching phase existing in the conventional VSC does not exist in the designed multisegment sliding-mode controller.

The robustness of the controlled system can be assured from start to finish.

FIELD-ORIENTED PMSM

, the d, q-axes stator voltages., the d, q-axes stator currents., the d, q-axes inductance., the d, q-axes stator flux linkages., the stator resistance and inverter frequency.

the equivalent d-axes magentizing current.the d-axis mutual inductance.

.fdmdddd ILiL +=λ

dqsqsqdq iLwiRidtdLv −+=

qqsdsddd iLwiRidtdLv −+= (1)

(2)

qqq iL=λ (3)

(4)

dv qv

di qi

dL

dλ qλqL

sR sw

fdI

mdL

FIELD-ORIENTED PMSM

the pole number of the motor.the rotor velocity.the rotor angular displacement.the moment of inertia.the damping coefficient.the external load.

The inverter frequency is related to the rotor velocity as

[ ]qdqdqfdmde iiLLiILpT )(23

−+=

mm w

dtd

=θ

Lemmm

m TTwBdt

dwJ −=+ (7)

(6)

(5)

.ms ww ρ=LTmBmJmθ

mw

p

FIELD-ORIENTED PMSM

Since the magnetic flux generated from the permanent magnetic rotor is fixed in relation to the rotor shaft position.

The flux position in the coordinates can be determined by the shaft position sensor.

qd -

FIELD-ORIENTED PMSM

The PMSM used inthis drive system isa threephase four-pole 750-W 3.47-A 3000-r/min type.

Fig.1. (a) System configurationof fiele-oriented synchronous motor.

FIELD-ORIENTED PMSM

Fig.1. (b) Simplified control system block diagram.

vKT te =

mmp BsJ

SH+

=1)(

,/mN2.2 vKt ⋅=2s/mN0021.0 ⋅=mJ

m/sN0015.0 ⋅=mB

v

(8)

(9)

is the inverter torque command which is proportional to the –axis current, .q

INCREMENTAL MOTION CONTROL OF PMSM

The rotor dynamics and the torque equation of PMSM givenin (6)-(8) are rewritten as follows:

mm w

dtd

=θ

m

L

m

em

m

mm

JT

JTw

JB

dtdw

−+−=

.vKT te = (10)


The incremental motion control is to move an object at rest at time to a fixed desired position at time , and then stop it.

The control process is subjected to the desired velocity and acceleration.

Therefore, the incremental motion control is performed under velocity control in obedience to a desired velocity profile, whereas stopping is done by position control mode.

dθ dt0t


One first has to select a velocity profile which rapidly changes the load position in discrete step.

The velocity profile should satisfy the motion constraints of the system.

The velocity and acceleration limitations are generally taken into consideration for the determination of velocity profile.

To satisfy the velocity and acceleration limitations, a trapezoidal velocity profile is usually used.

The object here is to design a multisegment sliding mode controller according to the trapezoidal velocity profile


Fig.2. Trapezoidal velocity profile for incremental motion control.


With a specified rotor position , which is assumed to be a constant within the control process, one first defines the position error and its derivative as

Combining (11) with (6) and (7), one obtains

Note that (12) and (13) hold because the specified position is a constant.

dθ

m

dm

wxx=

−=

2

1 θθ (11)

(12)

(13)

dθ

21 xx =&

m

L

m

e

m

m

JT

JTx

JBx −+−= 22&


According to the error dynamical equations (12) and (13), a multisegment SMC is proposed to drive the motor from initial position

to the specified position according to the trapezoidal velocity profile given in Fig. 2.

The multisegment SMC is composed of two modes, the velocitycontrol mode and the position control mode.

The velocity control mode is used to drive the rotor to the desired position and the position control mode is used to hold the rotor at thedesired position

dθ0θ

A. Velocity Control Mode

1) Acceleration segment

: is the initial position error.

To check the motor acceleration on

Thus, the motor dynamics on the acceleration segment (14) have the desired constantacceleration .

1s

02

110

22

111 =−−= xxxs

dα(14)

dxxx −= 010

01 =s

d1α

21 xx =&

dtdw

x md == 12 α&

0122

11

1 =−= xxxdtds

d

&&α

A. Velocity Control Mode

2) Run segment

3)Deceleration segment 3s

022 =−= dwxs

2s

02

1 22

313 =+= xxs

dα (16)

(15)

03 =s

dtdw

x md =−= 32 α&

02 =sdm wxw == 2

B. Position Control Mode

In the position control mode, the following position control segment is proposed:

where is a positive constant.

Lemma [6]–[8]: If a switching surface of the controlled system satisfies the following sliding condition:

Where and are parameters to be designed in accordance with the corresponding sliding segment, and has been defined in (8).

01424 =+= xcxs (17)

4c

)(ts

0<ss& (18)

vKT te =

)( 221 xhhKt += (19)

2h1h

tK

C.Velocity Control Mode

First, the acceleration segment is considered. The parameters and in (19) will be designed to satisfy the sliding condition of theacceleration segment

where , and is the sign function.

1h 2h

011 <ss & (20)

)1( 221

1111 xxxsssd

&&α

−=

.)(11 22121

21 ⎥⎦

⎤⎢⎣

⎡+−−+= Lttm

md

TxhKhKxBJ

xsα

(21)

)sgn()sgn( 12111 dxsh αα=

)sgn()sgn( 1112 dsh αβ=

(22)

(23)

tmtLmd KBKTJ /,/)( 111 >+> βαα )sgn(⋅

C.Velocity Control Mode

where and

where and

033 <ss &

)sgn( 221 sh α−=

)sgn( 2222 xsh β−=

tL KT /2 >α

022 <ss &

)sgn()sgn( 32331 dxsh αα−=

( ) )sgn(sgn 3332 dsh αβ−=

tmdL KJT /( 33 αα −> ./3 tm KB>β

./2 tm KB>β

(23)

(24)

(25)

(27)

(26)

(28)

D.Position Control Mode

Where

and

044 <ss & (29)

02211 vxhxhv ++=

)sgn( 1441 xsh α−=

)sgn( 2442 xsh β−=

).sgn( 400 sTv −=

,/)(,0 444 tmm KcJB −>> βα ./0 tL KTT >

(30)

(31)

(32)

Position Control Mode

Fig. 3. Multisegment SMC-based incremental motion control for PMSM system

Fig. 4. Simulated results of multisegment sliding-modemotion control.

(a) Velocity responses.

(b) Position responses.

(c) Control output.

SIMULATION RESULTS

Fig. 5. Trajectories of four switching functions of multisegment sliding-mode controller.

SIMULATION RESULTS

Fig. 6. Simulated results of conventional sliding-mode motion control.



(c) Control output.

SIMULATION RESULTS

Fig. 7. Simulated results withexternal load 2 N‧m.



(c) Control output.

SIMULATION RESULTS

Fig. 8. Simulated results with external load 2 N‧m and mm JJ 4=Δ

SIMULATION RESULTS

Experimental System Setup

Fig. 9. Pentium-800–based PMSM incremental motion control system.

Fig. 10. (a)Experimental results controlled by multisegment SMC controller.From top to bottom: velocityresponses, position responses, control output, and phase-A current.

Fig. 10. (b)Experimental trajectories of four segments controlled by multisegment SMC controller.

Fig. 11.Experimental results controlledby conventional SMC controller.From top to bottom: velocity responses, position responses, control output, and phase-A current.

Fig. 12. Experimental results with generator load. From top to bottom: velocity responses, position responses, and phase-A current.

CONCLUSION

A particular incremental motion control using novel VSC strategy for a PMSM is presented. It has been shown that the multisegment SMC has the ability to control the motor system with a constant acceleration and deceleration rate to match the trapezoidal velocity profile of the incremental motion.

Furthermore, the proposed system is robust to the external time-varying load.

Both simulations and experimental results confirm the validity.

REFERENCES

[1] K. Ohnishi, Y. Ueda, and K. Miyachi, “Model reference adaptive systemagainst rotor resistance variation in induction motor drive,” IEEE Trans.Ind. Electron., vol. 4, no. 3, pp. 217–223, Aug. 1986.

[2] F. J. Lin, R. F. Fung, and Y. C. Wang, “Sliding mode and fuzzy controlof toggle mechanism using PM synchronous servomotor drive,” Proc.IEE—Control Theory Appl., vol. 144, no. 5, pp. 393–402, 1997.

[3] T. H. Liu and M. T. Lin, “A fuzzy sliding mode controller design fora synchronous reluctance motor drive,” IEEE Trans. Aerosp Electron.Syst., vol. 32, no. 3, pp. 1065–1075, Jul. 1996.

[4] G. J. Wang, C. T. Fong, and K. J. Chang, “Neural-network-based selftuningPI controller for precise motion control of PMAC motors,” IEEETrans. Ind. Electron., vol. 48, no. 2, pp. 408–415, Apr. 2001.

[5] B. Grcar, P. Cafuta, M. Znidaric, and F. Gausch, “Nonlinear control ofsynchronous servo drive,” IEEE Trans. Contr. Syst. Technol., vol. 4, no.2, pp. 177–184, Mar. 1996.

REFERENCES

[6] K.-C. Hsu, “Variable structure control design for uncertain dynamic systemswith sector nonlinearity,” Automatica, vol. 34, no. 4, pp. 505–508, Apr. 1998.

[7] “Decentralized variable structure control for uncertain large-scale systemswith series nonlinearities,” Int. J. Control, vol. 68, no. 6, pp.1231–1240, 1997.

[8] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: A survey, ” IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2–22, Feb. 1993.

[9] F. J. Lin, “Real-time IP position controller design with torque feedforwardcontrol for PM synchronous motor,” IEEE Trans. Ind. Electron.,vol. 44, no. 3,pp. 398–407, Jun. 1997.

[10] F. J. Lin and S. L. Chiu, “Robust PM synchronous motor servo drive withvariable-structure model-output-following control,” Proc. IEE—Elect.Power Appl., vol. 144, no. 5, pp. 317–324, 1997.

REFERENCES

[11] M. Ghribi and H. Le-Huy, “Optimal control and variable structure combination using a permanent-magnet synchronous motor,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, 1994, pp. 408–415.

[12] K. K. Shyu and H. J. Shieh, “A new switching surface sliding-modespeed control for induction motor drive systems,” IEEE Trans. PowerElectron., vol. 11, no. 4, pp. 660–667, Jul. 1996.

[13]“Variable structure current control for induction motor drives by space voltage vector PWM,” IEEE Trans. Ind. Electron., vol. 42, no. 6,pp. 572–578, Dec. 1995.

[14] K. K. Shyu, C. K. Lai, and J. Y. Hung, “Totally invariant state feedbackcontroller for position control of synchronous reluctance motor,” IEEETrans. Ind. Electron, vol. 48, no. 3, pp. 615–624, Jun. 2001.

a novel motor drive design for incremental motion system...

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