DOB Presentation by Shim
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Transcript of DOB Presentation by Shim
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7/29/2019 DOB Presentation by Shim
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ANALYSIS AND SYNTHESIS OF DISTURBANCE OBSERVERAS AN ADD-ON ROBUST CONTROLLER
Hyungbo Shim
(School of Electrical Engineering, Seoul National University, Korea)
in collaboration with Juhoon Back, Nam Hoon Jo, and Youngjun Joo
under the support from Hyundai Heavy Industries, Co., LTD.
Oct. 15, 2010, at UCSB
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Overview2
disturbance observer (DOB)
dates back to the Japanese article (K. Ohnishi, 1987)
has been of much interest in control application community, butdid not draw much attention in control theory community
41 pub. record in IEEE Trans. Indus. Elec. (2003-2007)
8 in IEEE Trans. Contr. Sys. Tech. (2003-2007)
3 in IEEE Trans. Automat. Contr. (2003-2007) original idea is intuitively simple, but less analyzed rigorously
This talk is about
developing theoretical framework for DOB approach, and
appreciation of it as a robust control tool presentation of robust stability condition and robust nominal
performance recovery
discussion about various aspects of DOB, and extension to
nonlinear systems
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Overviewproblem statement
Inner-loop dynamic controller:
The same input-output behavior!
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Overviewproblem statement
not only just the same steady-state behavior,but also the same transient behavior(with the same IC between the nominal and the real)
important feature required by industrywhere settling time, overshoot, etc., should be uniformamong many product units
a sharp contrast to other robust or adaptive redesign approach
which possibly changes the transient behavior
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The same input-output behavior!
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Linear DOB: Intuition5
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Linear DOB: Intuition6
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Linear DOB: Intuitive justification7
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More Issues to be Solved8
The argument so far does not present real power and limitations.
robust stability is still of question
what about transient performance recovery?
unanswered observations from practice:
It does not work for non-minimum phase plant.
High bandwidth of Q(s) destabilizes the closed-loop.
It cannot handle large parameter variation. Higher order Q(s) leads to instability.
can we extend the DOB-based controller for uncertain
nonlinear plants?
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Our Starting Point9
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Normal form realization of Q(s)10
Byrnes-Isidori
Normal Form
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Representation of P (nonlinear plant)11
Byrnes-Isidori
Normal Form
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Representation of nominal plant Pn (with Q)12
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Summary: Problem Statement13
State-space realization of DOB structure
?
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* (too brief) Review of Tikhonovs Theorem14
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Robust stability of DOB structure with small
= Robust stability of Boundary-Layer subsystem
+ Robust stability of Quasi-Steady-State subsystem
Closed-loop system in the Standard Singular Perturbation Form15
With coordinate change given by
the overall closed-loop system is expressed by
outer-loopcontroller C
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Quasi-Steady-State Subsystem16
It is the same as the disturbance-free nominal closed-loop! z-dynamics becomes unobservable.
z-dynamics should be ISS (minimum phase in linear case).
implies (so Q-filter with the plant inverse acts
as a state observer!)
QSS subsystem:
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Boundary-Layer Subsystem17
Robust stability condition:
Q-filter should be stable.
No matter how large the uncertainty is, once bounded,there are s so that two polynomials are Hurwitz! proof
Semi-global result for boundedness of
S 18
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Summary:
Robust Stability
Robust stability of the closed-loop with DOB isguaranteed if, on a compact set of the state-space,
1. zero dynamics of uncertain plant is ISS,2. outer-loop controller stabilizes the nominal plant,
3. coefficients of Q-filter are chosen for the RS condition,
4. is sufficiently small.
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Robust Steady-State Performance19
Nominal closed-loop
(slow) transient steady-state
Real closed-loop
(fast) transient (slow) transient steady-state
nominal plant
outer-loop controller C
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Robust (slow) Transient Performance20
I. Tikhonovs theorem guarantees that
if
II. However, (0) and (0) become unbounded as ! 0.
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Peaking phenomenon reflected in coordinate change21
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Robust (slow) Transient Performance
I. Tikhonovs theorem guarantees that
if
II. However, (0) and (0) become unbounded as ! 0.
Lesson: Due to peaking phenomenon, it is not true that
conventional DOB recovers (slow) transient performance.
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Saturating the Peaking Components
Peaking components that affect slow dynamics:
Replace with
and
[Esfandiari & Khalil, 1992]
S bili L i BL S b24
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Stability Loss in BL Subsystemand its recovery by a dead-zone function
BL -dynamics becomes
and loses GES.
Add a dead-zone function:
to recover GES.
S bili A l i f BL S b25
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Stability Analysis of BL Subsystemwith saturation & deadzone
A l f T kh Th26
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Application of Tikhonovs Theoremfor the second interval
Summary 27
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Summary:
Robust Transient Performance Recovery
thanks to saturation & dead-zone functions.
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Proposed Nonlinear DOB Structure [Back/S, AUT, 08]
M S29
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Example: Point Mass Satellite [Back/S, TAC, 09]
l M S ll30
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Example: Point Mass Satellite
Nominal: Real: with DOB (solid=nominal)
Real: w/o DOB:
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Robust Stability Condition for Linear DOB
Shim & Jo, AUT, 2009
back to linear
presents simple linear robust stability conditionworking on frequency domain
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Problem Formulation
Standing Assumption:where is a collection of
Ass: C(s) is designed
for Pn(s).
Problem: Design of
Q(s) for robust stability
Ch h Q( )33
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Characteristic equation with Q(s)
Q(s) =( s)l + bl1( s)
l1 + + b1( s) + a0
( s)l+r + al+r1( s)l+r
1 +
+ a1( s) + a0=:
NQ(s; )
DQ(s; ); > 0
R b S b l f h O ll S34
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Robust Stability of the Overall System
Observation 1:
Observation 2:
[S/Jo, AUT, 09]
D i f Q( ) h35
a0
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Design of Q(s): when
How to choose Q(s):
Q(s) =a0
( s)r + ar1( s)r1 + + a0
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Discussion: Answers to the raised questions
1. It does not work for non-minimum phase plant. Correct, for small .
2. Small destabilizes the closed-loop.
No, if Q(s) satisfies RS condition. It may be the effect of initialpeakings but not a destabilization.
3. It cannot handle large parameter variation.
No in general. By following the design guidelines, any bounded
variation can be handled.
4. Higher order Q(s) leads to instability.
No in general. But, for higher order Q(s), the selection of
coefficients becomes more complicated.
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robust stability condition in action
Experiments
Taken from Yi, Chang, & Shen, IEEE/ASME Trans. Mechatronics, 2009
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St39
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Step responses
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Robust tracking control
Hyundai HS-165 (handling 165kg)
[Bang/S/Park/Seo, IEEE Trans. Industrial Elect., 2010]
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Robust tracking control
Experiment results
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Summary
theoretical study on DOB
robust stability condition
(new even for classical linear DOB) transient performance recovery
(thanks to saturation/dead-zone functions)
DOB = Inner-loop controller = Your first AID kit!
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THANK YOU
Any feedback or comments are welcome