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CONTROL AND STABILITY ANALYSIS FOR THE
Vdd-HOPPING MECHANISM Authors Carolina Albea,
Carlos Canudas de Wit Francisco
Gordillo Control and Stability Analysis for
the Vdd-Hopping Mechanism.
NeCS meeting October 2009
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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MOTIVATION
STABILITY OF THE CLOSED-LOOP SYSTEM
(1)S. Miermot et al. LECTURE NOTES IN COMPUTER
SCIENCE
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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SYSTEM
Vdd-Hopping System
System control model
where and
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SYSTEM
DC-DC converter circuit
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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DESIGN OF CONTROL LAWS
ROBUST CONTROL
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DESIGN OF CONTROL LAWS
ROBUST CONTROL
WITH STEP REFERENCE SIGNAL
BEWARE!!!!! This current peak can damage the
physic system
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DESIGN OF CONTROL LAWS
MANAGING CURRENT PEAKS
Maximal current peaks constraint
considering vc is continuous
This constraint can be introduced
Thus, the controller will be
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DESIGN OF CONTROL LAWS
ROBUST CONTROL WITH CURRENT PEAK CONSTRAINTS
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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STABILITY ANALYSIS OF THE CONTROLLER WITHOUT
CURRENT PEAKS CONSTRAINTS
Theorem 1 System
with the
controller
is locally asymptotically stable for all
initial condition , if and are
positives.
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STABILITY ANALYSIS OF THE CONTROLLER WITHOUT
CURRENT PEAKS CONSTRAINTS
Candidate Lyapunov function
The stability is established by LaSalles
invariant principle, since the maximum invariant
set with is the single point
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STABILITY ANALYSIS OF THE CONTROLLER WITH
CURRENT PEAKS CONSTRAINTS
Theorem 2 System
with the
controller
is locally asymptotically stable
for all initial condition , if and
are positives.
Proof
Remark The equilibriums of the system are in
Region I.
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STABILITY ANALYSIS OF THE CONTROLLER WITH
CURRENT PEAKS CONSTRAINTS
Lemma 2 System
with controller

saturated in the upper or lower current peak
limits for all initial condition converges
to the non-saturation region in a finite time, if
.

REGION II
Property In Region II the system
fulfills being
Proof
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STABILITY ANALYSIS OF THE CONTROLLER WITH
CURRENT PEAKS CONSTRAINTS
Candidate Lyapunov function Derivating and
substituting the second derivative error
equation
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STABILITY ANALYSIS OF THE CONTROLLER WITH
CURRENT PEAKS CONSTRAINTS
REGION III Proof
similar to REGION II
Proof
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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DISCRETIZATION
CONTROL WITH CURRENT PEAK CONSTRAINTS
Control patent pending under the name
ENergy-AwaRe Control (ENARC)
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COMPARISON
PREVIOUS CONTROL LAW S. Miermot et al. LNCS
ENARC
97
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OUTLOOK

• MOTIVATION
• SYSTEM
• DESIGN OF CONTROL LAWS
• STABILITY ANALYSIS
• DISCRETIZATION AND COMPARISON
• CONCLUSIONS

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CONCLUSIONS

• A control law is proposed for the Vdd-Hopping
  mechanism in order to
• Dissipated energy is reduced
• Current peaks are limited
• Transient time are reduced
• and robust control.
• Closed-loop system stability is analyzed in
  continuous time.
• A discretization of this controller is done.
• A comparison with a controller presented in S.
  Miermot et al. LNCS is done.

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THANK YOU!!! Control and Stability
Analysis for the Vdd-Hopping Mechanism.
NeCS meeting October 2009