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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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Questions