Internal Model Control for
Assisting Unit of Wheeled
Walking Frames
報 告 者: 蔡 耀 德
授課老師: 曾 慶 耀
出
處: 2004 IEEE
大綱
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1.INTRODUCTION
2.IMPLEMENTATION FOR SPEED
CONTROL ASSISTING UNIT OF
WHEELED WALKING FRAME
3.CONTROL SYSTEM DESIGN FOR
ASSISTING UNIT
4.MODELING AND CONTROL DESIGN
5.CONCLUSION
1.INTRODUCTION

In the aging society of recent years, the expectation for the
wheeled walking frames increases. Wheeled walking frames
are supporting equipments, to he used by elderly people or
handicapped in rehabilitation.

The control application to speed control of wheeled walking
frames technology would he challenging by using the GIMC
design structure with LQ control
2.IMPLEMENTATION FOR SPEED
CONTROL ASSISTING UNIT OF
WHEELED WALKING FRAME
3.CONTROL SYSTEM DESIGN FOR
ASSISTING UNIT
3.1 Problem Formulation
Consider the linear time invariant system with disturbance as follows

 x  Ax  Bu  D 


 y  Cx
where
xR
n
is the state vector,
u  R is the input vect
m
yR
m
is the output vec
or,   R is the disturbanc
q
tor
e vector
The closed-loop system  is obtained as follows
f

The internal model of the closed-loop system
described as follows
is
3.2 Limiting Properties of LQ Control and Observer
By choosing
we obtain the
the weighing
limiting
matrix
feedback
R  I and Q  (1/  ) I as   0,
2
gain defined
as F  -B M 
T

The closed-loop system with the limiting feedback gain has
disturbance decoupling property like Lemma 1
[Lemma 1]
The closed-loop system (1) with Fe, can arrive at a disturbance
decoupled system, that is, the following statement holds
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Now shown by using the limiting property of the LQR
[Lemma 2]
Suppose that the minimum phase system (A, B,C) has a block diagonal
interactor matrix as follows:
By choosing the optimal feedback law with the limiting feedback
The closed-loop system can arrive at a decoupled system such that
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Finally we show the limiting property of observers
[Lemma 3]
For the system (A,D,C) , the state observer is described as
follows:
3.3 Property of Two-Degree-of-Freedom Servo
System using Stabilizing Controller

Propose the generalized IMC with servo compensation shown
in Fig . The proposed method is based on a two-degree-offreedom servo system using an observer-based Stabilizing
Controller.

The error equation is obtained by
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The augmented system is given
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We clarify the limiting properties of the augmented system
[Property 1]
Suppose the system (A, B. C) is minimum phase. If the system has a block diagonal
interactor matrix, then the transfer function from reference input r to output y is
arrived at
as   0 .Thus the closed loop system is arrived at the approximate decoupled
system
[proof]
By choosing
[Remark]
H  C ( sI  A  BF  )
1
and from Lemma 2
Not able to obtain for the following augmented system
However, if the input signal is limited to step input, then the closed loop
system with LQ control achieves a static decoupled system.
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Next, we obtain the disturbance decoupling property for the augmented
system . In this case, the disturbance is not limited to the step disturbance
[Property 2]
Suppose the system ( A , B,C) is minimum phase. The closed loop system can
immediately arrive at disturbance decoupled system by multiplicative of the
disturbance decoupling property of the IMC design structure and the disturbance
decoupling property of LQ control
[proof]
The transfer
function
from Lemma 1
H y (s) from  to y is described
as follows
from Lemma 3
[Property 3]
if we parameteri zed Q(s)as an approximat
then the
output
signal of Q(s) can be estimated
loop system maintains
[proof]
e inverse system Q(s)  - { C ( SI - A - L  C ) B } ,
servo property.
-1
unknown
disturbanc
-1
e  as   0 . The closed
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Finally, we show
numerical examples to
confirm the proposed
properties. confirm
validity of the disturbance
decoupling control in
Property 2 and the
disturbance estimation in
Property 3, respectively.
4.MODELING AND CONTROL DESIGN
The sampling
are obtained
time of the control system is 0.02[s]. Thecontrol
design parameter
under conditions
R  I ,   0 . 0 3 1 6 ,   0.0071,   0 . 08
The limiting
feedback
F  ( 31.62
9.01 )
L   ( 11.57
66.89 )
gain F , and the observer gain L  , are calculated
T
as follows
:
5.CONCLUSION

It proposed the generalized internal model control
with servo compensation based on LQ control,
and the experimental results showed that the
generalized IMC with servo compensation is
effective on speed control of the assisting unit for
the wheeled walking frame.
THE END
Thanks for your patient !!!