sliding mode control system

8/13/2019 Sliding Mode Control System

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Presenting by

Sreerag.K.S

S2 IDC

Roll No: 17

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Guided byMrs. Radhika.R

Asst. ProfessorRIT, Pampady


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Nonlinear Speed Control of PMSM

PMSM

SMCESMDO2/25

Contents


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Introduction PMSMs are widely used in low and mid power applications.

Increase in the need of PMSM drives evoked the requirement

of new and better control strategies.

PMSM has strong nonlinear characteristics.

In order to control PMSM a better suited control strategy like

SMC is required.

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PMSM

Characterized by the permanent magnets on rotor which

produces the air gap magnetic field.

No copper loss on the rotor.

High efficiency.

Simple and requires less maintenance.

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Exploded View of PMSM

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Operation of PMSM

Alternating magnets of the opposite magnetizationdirection produce radially directed flux density across theair gap.

This flux then reacts with currents in windings placed inslots on the inner surface of the stator to produce torque.

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Modeling of PMSM

Vq=

Vd=

Tem=

Te-TL=

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qaip5.1

ddrar

q

qqs iLwwdt

diLiR +++

qqrd

dds iL wdt

diiR L+

B

dt

d

p

J+


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Sliding Mode Control Efficient controllers for complex nonlinear plants operating under

uncertainties.

Decouples the overall system motion into independent partial

components of lower dimensions.

Control actions are discontinuous state functions, implemented byconverters with On-Off as the only admissible operation mode.

This control ensures the completion of control action in finite time.

Applicable to wide range of problems in robotics, electric drives,process control etc.

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SMC Design Design involves two steps

Choosing the sliding mode surface Designing the control input such that the system trajectory is forced

towards the sliding mode surface.

The state variable trajectory of the controlled system will have twophases Reaching Phase Sliding Phase

Reaching law ensures that trajectory of the system is driven towardsthe sliding surface.

Due to certain imperfections that are inherent to the design therewill be chattering phenomenon in the sliding phase

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Example

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System withoutdisturbance

System withdisturbance

System with disturbance under SMC


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Proposed Technique

The reaching law is modified to

If |s| increases, eq(x1,s) converges to k/

If |s| decreases, eq(x1,s) k|x1|/(1+|x1|)

The system state gradually reaches zero under thecontrol law for the system.

Implies eq(x1,s) vary between k/& zero.

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])||/11([),(

)sgn().,(

||1

1

1

sex

ksxeq

ssxeqs

++=

=


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Comparison

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SMC Speed Controller

Reaching law is given by

where , s is the sliding variable.

Speed Control algorithms should keep track of the actualspeed accurately.

Speed tracking error is

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])||/11([),(

)sgn().,(

||1

1

1

sex

ksxeq

ssxeqs

++=

=

10,0,0 k

==

==

ref

ref

es

es ;


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Contd.. From the machine equations

The reaching law becomes

Therefore the control law will be

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JBccc

Jpaaa

trcia

n

an

nqn

/

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)(

2

=+=

=+=

+=

)sgn().,1()( ssxeqiatrcs qnnref =+=

)}sgn()],([{ 11*

ssxeqlcai nrefnq +++=


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The System

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Simulation Result

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Contd..

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ESMDO ESMDO or Extended State Sliding Mode Disturbance

Observer.

Estimates the disturbances r(t) on line.

According to , r(t) can be considered asextended states of the system and

ESMDO can be constructed with the dynamics

Error equation is given by

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)(trcia nqn +=

)()( tdtr =

)sgn(,

)(

sugur

utrcia

smosmo

smonqn

==

++=

)(

)()()(

2

1

tdgue

utrtrce

smo

smon

=

++=


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Choice of Parametersshould be selected such that reaching condition must

be satisfied, for that < -m|e2-cne1|, m>1.

Observer with this value for can reach the sliding

mode in finite time and stay on it. Then

For the e2to converge to zero, g should be greater thanzero.

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[ ]+==++

=

==

dtetdCee

tdgee

ue

ee

gtgt

smo

)(

0)(

0

2

22

2

11


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Simulation Results

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Conclusion

Simulation results indicate that the proposed reaching lawcan reduce the chattering level of SMC system comparedwith the equal reaching law.

Response time of the system is also decreased.

With ESMDO the existence of lumped disturbances can beobserved and fed back to the SMC.

The composite operation of SMC and ESMDO ensures lesschattering and less effect of disturbance on theperformance of the system.

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References [1] Nonlinear Speed Control for PMSM System Using Sliding-Mode Control

and Disturbance Compensation Techniques Xiaoguang Zhang, Lizhi Sun,Senior Member, IEEE, Ke Zhao, and Li Sun, Member, IEEE

[2] W. Gao and J. C. Hung, Variable structure control of nonlinear systems:A new approach, IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 4555, Feb.1993.

[3]A Control Engineers Guide to Sliding Mode Control K. David Young,Senior Member, IEEE,Vadim I. Utkin, Senior Member, IEEE, and Umit Ozguner,Member, IEEE

[4]Control systems, Robotics and Automation Vol XIII- Sliding ModeControl- Vladimr Utkin

[5]www.wikipedia.org

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THANK YOU

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