SYNTHESIS AND.STABILITY ANALYSIS OF
Transcript of SYNTHESIS AND.STABILITY ANALYSIS OF
![Page 1: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/1.jpg)
.. •
--.
SYNTHESIS AND.STABILITY ANALYSIS OF
SELF-TUNING CONTROLLERS .
I
j
BY
-. ~-
@- LIU LI .
A Thesis . \.
•
Submitted to th~School of Graduate Studies
in Partial Fulfillment of the......R.e-s...ttireme·nts
for the Degree
~ Doctor of Philosophy
r
. McMaster University~
July 1987'
![Page 2: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/2.jpg)
•
... "
---.,
r
SYNTHESIS AND STABILITY ANALYSIS OF
~SELF-TUNING CONTROLLERS
-,
(I
\"\
-
![Page 3: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/3.jpg)
..
•
..-.
I
TO
my parents •
Lu and Si-cong
![Page 4: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/4.jpg)
DOCTOR OF PHILOSOPHY (1987) McMASTER UNIVERSITY
(Electrical Engineering)
Professor of Electrical and Computer Engineering
Synthe.9is and Stability Analysis of Self-tuning Controllers
-0
Liu. Li B.Sc. (China Univers i t'y of Science- & Technology)..M.Sc. (Beijing University of Iton & Steel Technology)
Hamilton. Ontario
233xv~.
B.Sc. Eng. (Banaras)
.f
Naresh K. Sinha
Ph.D. (Manchester)
..
NUMBER OF PAGES:
TITLE:
',,- -'
![Page 5: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/5.jpg)
ABSTRACT
The. problem of self-tuning reference signal tracking 1s
)considered for systems represented by autoregressive moving average
,(ARMA) as well as state-space models. By self-tuning control, it ls'
meant to be a combination of recursive parameter estimation and control
algorithm. A new strategy of controller design is proposed, which is
pole/~ero placement in the 'error transfer function' (ETF) in contrast
with the usual closed-loop pole-placement. Sufficient conditions for
arbitrary simultaneous assignment of !TF poles and zeros are derived.
For ARMA models, a recursive extended least squares type algorithm with
a general nonlinear criterion function, which can be defined by the
user, is suggested and the strong consistency of the algorlt~ is
proved. Reference signal model identification is introduced for the
first time into the context of adaptive control, which provides great
flexibility to track any unkno~-!xternal reference trajectory. The
global convergence of the adaptive ETF pole/zero placement is
theoretically established for deterministic. systems. New stQchastic
optimal control algorithms are derived for the case where the control
objective is reference signal tracking. The noyelty of the proposed
algori~hm9 is that the performance indices are determined by the
prespecified locations of ETF poles as well as zeros. State-space
approach to self-tuning control has been studied also. The recursive
v
![Page 6: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/6.jpg)
rI.
j
prediction error ~ethod is used for joint state and parameter estimation.
of state-space innovation~~odel. Adaptive reference signal tracking(
control laws are derived for sY8te~ output as well as an i~easurable
. physical state.
To demonstrate practical applications, the derived self-tuning\
.;
algorith~s were applied to surface accuracy co~ in turning and end
~ill~ng process. The results of simulations indicate considerable./
. ..
improvements in geometric accuracy of finished workpieces over
conventional numerical control in the~sence of significant tool /
workpiece deflection.~
vi
-
![Page 7: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/7.jpg)
I
ACKNOWLEDGEMENTS
•
1 wish to express my sincere gratitude to Professor N.K. Sinha
for his expert guidance and constant encouragement. I also thank..
Professor K.M. Wong and Professor M.A. Dokainish, members of my Ph.D.
super·visory committee for their continuing 'interest an~ support..
I am very grateful to Dr. S:C. Puthenpura and Dr •. F.K. Omani for', .
~stimulating and helpful discussions. I also express my ap2.t.§.ciation to
\Professor M.A. Elbestawi o~ the mechanica~engineeringdepartment for
~.
his valuable suggesti~ns on the application of adaptive control to
turning and end milling processes. '.-.
'1 WQU\d like to thank all my past and present control g~up
\ '"colleagues for participating in several of my presentations. and
~ubsequent discussions. I would also take this opportunity to thank my
/' friends for ~eir encour3gement~throughout this work.
-'
(
.-
vii
..,
![Page 8: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/8.jpg)
.'
• ;c>-.~
• 1:"---:
'"
.,-/ TABLE OF CONTENTS./
PAGE
\
(.". ~ .
I
\
ABSTRACT
ACKNOWLEDGEMENTS
LIST OF FIGURES
CHAPTER 1: INTRODUCTION
\
v
vii
xiii
1
\ 1.1
1.2
./Background
Contributions and Qr~anizations of the Thesis
1
5
CHAPTER 2: -SELF-TUNING C9NT~Ll..£RS FOR NONINVERTI8LE SYSTEMS: 9
AN OVERVIE'Il
2.1
2.2
"Introduction to this chapter
"-A Generalized Controller Structure
9
9
-
2.3 The Approaches by Generalization of Minimum Variance
Control Algotithm
2.4 Pole Placement'
2.S The Alternative Approaches\
2.6 Concluding Remarks
CHAPTER 3: STRONG CONS.ISTENCY OF A TYPE OF RECURSIVE
IDENTIFICATIQN SCHEMES WITH GENERAL NONLINEAR
CRITERION FUNCTION
3.1 Introduction to This Chapter..-
3.2 A Type o~Recursive Identification Scheme~~th General
viii
10
12
15
17
18
18
![Page 9: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/9.jpg)
· .·Nonlinear Cri~erion Functions.,'
3.'3' Concluding Remarks
23
27
CHAPTER 5: OPTIMAL ADAPTIVE TRACKING FOR STOCHASTIC SYSTEM
t, CHAPTER 4: ADAPTIVE ERROR'TRANSFER FUNCTION POLE/ZERO PLACEMENT
AND ADAPTIVE ~RACKING FOR DETERMINISTIC SYSTEMS
4.9 Simulated Examples
4.7 Summary of Algorithm
29
29 -'l
30
32
34
36
3~
39
41
41
42
4~·
46
59
70#
71
71
71
71
72
, .r.
4.6.1 Protess parameter estimation
4.6.2 Reference Signal Parameter Estimation
Cont~oller Design
4.5.2 Control Str~egy 2
Pa~ameter ~imation·I
,4.5,1 Control Strategy 1
5.2.2 Review: minimum variance regulation
5.2.1 Background
5.2 Minimum Variance Output Tracking
4.10 Concluding Remarks
5.1 Introduction to This Chapter
4.8 Stability and Convergence Analysis
4.6
4.5
4.4 The Concept of ETF Zero Placement
4.3 Schematic Diagram of Adaptive Control System
4.2 Problem Formulation.
4.1 Introduction to This Chapter
~.--
\
ix
![Page 10: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/10.jpg)
--
5.2.3 Minimum variance tracking
.5.2.4 On-line' self-tuning implem~~tatidn
75
78
,
0.
5.3 Quadratic-optimal ~lf-tuning Control with ETF.c'
Pole/Zero Placement
5.3.1 Background
5.3.2 Performance criterion
5.3.3 Optimal control law with fixed parameters,
5.3.4 Arbitrary ETF pole/zero placement
5.3.5 On-line self-tuning implementation
,...
5.3.6 Simulated examples
5.4 Concluding Rem;rks
CHAPTE~ 6: APPLICATION: ADAPTIVE CONTROL FOR GEOMETRIC
TRACKING IN TURNING
6.1 Overview of This Chapter
6.2 ~ntrodyction to Geometric Adaptive Control in
Turning
-6.3 The Machining System
0.4 Simulation
6.5 Concluding Remarks
CHAPTER 7: STATE SPACE SELF-TUNING CONTROL
7.1 Introduction to This Chapter
7.2 Problem Formulation
7.3 Joint State and Parameter Estimation of State
_0,.
x
100
100
100
104
110
130
131
131
134
![Page 11: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/11.jpg)
.,Inoovation~ Model
7.4' State Feedback Control Law with ETF Pole/Zero
P13cement
7.4.1 Controller configuration.
7.4.2 Pole placement
7.4.3 Output tracking
7.~~-State tracking
7.5 On-line Imple~entation Procedure
7.6 ·-Simulated Examples
7.7 Concluding-Remarks
CHAPTER 8: APPLICATION: SgRFACE ACCURACY CONTROL IN MILLING
USING ADAPTIVE STATE TRACKING
8.1 Overview of This Chapter
8.2 Introduction to Surface Accuracy Control in End--4Il
Milling Process
}
136
140
141
143
~44
147
148
165
167
167
168
8.3 Workpiece Surface Errors in Flexible End Milling 171
--8.4 ·The Slate-space Model for End Milling Process--,8.5 Simulation ~_j
8.6 Concluding Remarks
CHAPTER 9: CONCLUSIONS AND RECOMMENDATIONS
9.1 Conclusions
9.2 Suggestions for Further Research
176
181
186
198
198
201
APPENDIX I MATRIX rNVERSION LEMMA AND SOME COROLLARIES
xi
.-
203
![Page 12: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/12.jpg)
APPENDIX II PROOF OF THEOREM 3.1
APPENDIX III MARTINGALE CONVERGENCE THEOREM
-APPENDIX IV LINEAR DIOPHANTINE EQUATION IN POLYNOMIALS
REFERENCES
,
xi i
f
207
215 ....
216
220
![Page 13: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/13.jpg)
LIST OF FIGURES
FIGURE PAGE
2.1
4.1
4.2
~he augmented system suggested Kumar and Moore
~chematic diagram of adaptive control system
Block diagram_of the controller configuration (4.5.1)~
11
33
36
4.3 System response by using control law (4.5.1) with
ETF ze~o placement
4.4 System ~esponse by using control law (4.5.1) without
ETF zero placement
4.5a Adaptive contro~ by using control law (4.5.6) with
ETF pole/zero placement
4.5b Control action of controller (4.5.6) with ETF pole/
zero placement
4.5c Process parameter estimation of self-tuning control
with ETF pole/zero placement
4.5d Reference signal parameter estimation of 8elf-tuni~g
control with ETFAPole/zero placement
5.1 Deterministic quadratic-optimal control with and
without ETF pole/zero placement
5.2 Self-tuning quadratic-optimal control with and
without pole/zero placement
5.3 Parameter estimation of self-tuning quadratic-
xiii
63
63
65
66
67
68
93
94
![Page 14: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/14.jpg)
Conttol signal of self-tuning quad~atfc-optimal5.4
.S.5-c
•
optimal control with and without pole/zero placeme~
.~
cont~ol with and without EtF pole/zero placement
Triangular wave reference input. Self-tuning
95
96
~.6
quadratic-optimal control with ETF pole/ze~o placement 98
Triangular wave reference input. Self-tuning
quadratic-optimal control with pole-placement only
6.1 Notation of axes for the machine tool 105
6.2 R~lationship between the cutting process and machine
tool structure 106
Control action of the adaptive system in X axis 121
Response of the adaptive control system in X axis 120
6.3
6.4a
6.4b
6.4c
(). 6.5a
b.Sb
b.Sc
6.6
6.7
Continuous-time model of turning process in X-axis
Desired finally finished shape
Surfq.i:e generated by the given position coaunand
Surface generated by using the proposed adaptive
control system
Reference signal in X direction
Response. 0 f the·NC system in X axis
Geometric genera~ed with & without adaptive tracking• ':'>
(sectional view)
108
112
116
117
118
119
122
6.8 Geometric generated with & without adaptive tracking
xiv
![Page 15: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/15.jpg)
,
'('
-..
6.9a
(sectional view)
Effect of the sinusoidal di;turbance
124
126
6.9b Rejection of. the sinusoidai disturbance by using
adaptive controller 127
6.10 Parameter estimation of turning process 128
7.1 Nonadaptive control with & without ETF zero placement
~losed-Ioop pole location: zl=O.8191. z2=O.6700
7.2 Nonadaptive dead beat control with.& without
152
ETF zero placement\
153
error transfer function zero placement
7.3 Overdamped system with & without state trac~ing
~
I.'
-7.4 Underdamped system with & without stat;~rac~ing
error transfer function zero placement
154
155
7.5
7.6
7.7
8.1
8.2
Dead beat control system with & without state
~t~acking error transfer function zero placement 156
Adaptive state tracking for square ~ave reference 158
Adaptive state tracking for triangular wave reference 160
End milling with helical teeth 172
Cutting force in end milling 173
8.3 Typical surface error in end milling of rigid
workpiece
8.4 Typical surf~ce error in end milling of fl~xible
Lv17~
![Page 16: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/16.jpg)
8.5
8.6
8.7
8.8'
8,9
workpiece
End milling machining system
Position output of HC system
Position output of adaptive control system
Actual tool position ( X- and Y- component
Control action in X- and Y- axis
175
177
187
188
189
191
(
8.10 Estimated F and G matrices and Kalman gain in X
and Y- axis
xvi
193
![Page 17: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/17.jpg)
CHAPTER 1
INTRODUCTION
1.1 BacKground
One of the most challenging fields of modern control theory is
adaptive con~rol. It has received a lot of attention since the early
19505.
The tasK of a control engineer is to produce a desired response
from a variety of systems. The complete knowledge of the systems to bec
controlled is almost essential to fulfill this task. However, the real
life situation wO'\ild never be ideal, hence produces several hurdles:-
1. The input-output relationship of a system often presents a certain
kind of "nonlinearity". It is found that linear feedback system can
work well in one operating condition, but the performance Can be
degraded when operating point (set point) is change~.
2. Some physical systems are too complex to analyze. The only
information available could be the input-output.data.
3. The aging of systems. changes in operating environments or the
nature of system itself can give rise to time varying phenomena. Hence
the controller design based on linear time-invariant system theory could
become inadequate.
-1-
![Page 18: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/18.jpg)
)-2-
Because of these reasons, it is desirable that the-@ontrol
system should -adapt-. itself to circumstances.
The first adaptive system reported was a model rbference
adaptive control scheme for aircraft by Whitaker et al. at MIT (1958).
From then on. there has been considerable interest on model reference
adaptive systems (MRAS) for deterministic continuous time systems as
well as discrete time systems. (See for examples. Parks. 1966; Monopoli,
1974; 'Landau. 1974, 1979; Narendra and Valavani, 1979. 1980). The
specification of MRAS is given in terms of a reference model which telis
how the system output ideally should respond to the 'command signal. The
approaches to MRAS can be categorized into: (1) parametric optimization,
and (2) the use of Lyapunov function and Popov's hyperstability theory.
In the early 1970s, Peterka (1970) and Astrom and Wittenmark
(1973) suggested the use of a self-tuning regulator to reduce the effect
of the stochastic disturbance for plants with unkno~~arameters. The
self-tu~ing regulator was originally proposed by ~alman (1958), who
built a special-purpose computer to implement the regulator. Starting
with the work of 'Astrom and Wittenmark, in the last fifteen years this
branch of adaptive control - self-tuning control has attracted
considerable attention and evolved rapidly. This type of adaptive
control system assumes that the plant has known structure but unknown
and is characterized as a combination of recursive parameter
~•,I\ parameters
~mationmethods and control algorithms. Thus. the· two substantial
steps are executed sequentially in each control cycle. The controller
{/
~
![Page 19: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/19.jpg)
law computation.
-3~
ris said to possess the 'self-tunIng': property, if the: parameter
.estimates converge to appropriate values and the control soal Is
asymptotically achieved.
For minimum p~ase (inverse stable) systems, there are
similarities between MRAS and self-tuning-control. Hence unification of
MRAS and self-tuning control methods has been attempted by many authors
(Ljung and Landau, 1978; Egardt, 1979, 1980; Landau and Lozano, 1981; ",
Landau, 1979, 1982; Astrom, 1983) .. ~
Early design of self-tuning regulators and many MRAS algorithms
involve pole-zero cancellations, which restricts the plant to be inverse
stable. However, it is more a rule than an exception that a sampled
data ~ystem has unstable zeros (Astrom et al., 1984). In a certain
sense, the development of self-tuning control in the last decade may be
viewed as to find a solution to the control of inv~rse unstable ~ant.A variety of approaches are used t? span the spectrum of all existing
control algorithms, which would produce a stable result when combined
with some recursive schemes for parameter identification.
Since the 1970s, computer hardware and software development
entered a dramatic stage. It is reported that the world's fastest
.digital integrated circuit today runs at a clock rate of 18 billion
cycles per second. The low-priced microcomputer or microcomputer array,
with sufficient speed, reasonable memory size and software support,
provides an e{ficient tool for on-line system identification and control
Moreover. It haa been reell.ed thet tbe~la •
![Page 20: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/20.jpg)
,
-4-
necessity to build an expert system, with the aid of advanced computer
so~ware. which provides functions such as stability-supervision and
control algorithm selection for the practical implementation of
self-tuning control. Very recently, a few papers have appeared which
are concentrated on the design of such an expert system (eg. Trankle and
Markosian, 1985j Isermann and Lachmann, 1985; Astrom et ale 1986).
Where systems are essentially of stochastic nature, the
self-tuning controller is designed to regulate the effect of disturbance
on system output. For systems where both reference input changes and
disturbances occur, control objective specifications should be different
than original self-tuning regulators. One of the "important requirements
for this case is that the expectat~on of the tracking error, in the
steady state. should be zero for any arbit~ary external reference
signal. Most of the existing adaptive algorithms, however, does not
take care of this point. Furthermore, if a system description is given
in state variable form with some entries of the state variable matrices
known, and with a few entries depending on possibly fewer unknown
parameters, is it possible to seek a synthesis where the prior
knowledge of the system parameters could be uaed? In addition. it also
seems unclear how to obtain a solution to the tracking problem in an
adaptive manner for the case where a imDeasurable physical state of a
system is required to follow the external reference closely. The main
effort of the research reported in this thesis is to present a
systematic procedure for solving the above problems and investigate the
![Page 21: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/21.jpg)
![Page 22: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/22.jpg)
![Page 23: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/23.jpg)
![Page 24: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/24.jpg)
![Page 25: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/25.jpg)
![Page 26: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/26.jpg)
![Page 27: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/27.jpg)
![Page 28: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/28.jpg)
![Page 29: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/29.jpg)
![Page 30: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/30.jpg)
![Page 31: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/31.jpg)
![Page 32: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/32.jpg)
![Page 33: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/33.jpg)
![Page 34: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/34.jpg)
![Page 35: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/35.jpg)
![Page 36: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/36.jpg)
![Page 37: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/37.jpg)
![Page 38: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/38.jpg)
![Page 39: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/39.jpg)
![Page 40: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/40.jpg)
![Page 41: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/41.jpg)
![Page 42: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/42.jpg)
![Page 43: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/43.jpg)
![Page 44: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/44.jpg)
![Page 45: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/45.jpg)
![Page 46: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/46.jpg)
![Page 47: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/47.jpg)
![Page 48: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/48.jpg)
![Page 49: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/49.jpg)
![Page 50: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/50.jpg)
![Page 51: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/51.jpg)
![Page 52: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/52.jpg)
![Page 53: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/53.jpg)
![Page 54: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/54.jpg)
![Page 55: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/55.jpg)
![Page 56: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/56.jpg)
![Page 57: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/57.jpg)
![Page 58: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/58.jpg)
![Page 59: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/59.jpg)
![Page 60: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/60.jpg)
![Page 61: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/61.jpg)
![Page 62: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/62.jpg)
![Page 63: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/63.jpg)
![Page 64: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/64.jpg)
![Page 65: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/65.jpg)
![Page 66: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/66.jpg)
![Page 67: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/67.jpg)
![Page 68: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/68.jpg)
![Page 69: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/69.jpg)
![Page 70: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/70.jpg)
![Page 71: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/71.jpg)
![Page 72: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/72.jpg)
![Page 73: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/73.jpg)
![Page 74: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/74.jpg)
![Page 75: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/75.jpg)
![Page 76: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/76.jpg)
![Page 77: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/77.jpg)
![Page 78: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/78.jpg)
![Page 79: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/79.jpg)
![Page 80: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/80.jpg)
![Page 81: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/81.jpg)
![Page 82: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/82.jpg)
![Page 83: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/83.jpg)
![Page 84: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/84.jpg)
![Page 85: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/85.jpg)
![Page 86: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/86.jpg)
![Page 87: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/87.jpg)
![Page 88: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/88.jpg)
![Page 89: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/89.jpg)
![Page 90: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/90.jpg)
![Page 91: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/91.jpg)
![Page 92: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/92.jpg)
![Page 93: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/93.jpg)
![Page 94: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/94.jpg)
![Page 95: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/95.jpg)
![Page 96: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/96.jpg)
![Page 97: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/97.jpg)
![Page 98: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/98.jpg)
![Page 99: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/99.jpg)
![Page 100: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/100.jpg)
![Page 101: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/101.jpg)
![Page 102: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/102.jpg)
![Page 103: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/103.jpg)
![Page 104: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/104.jpg)
![Page 105: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/105.jpg)
![Page 106: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/106.jpg)
![Page 107: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/107.jpg)
![Page 108: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/108.jpg)
![Page 109: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/109.jpg)
![Page 110: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/110.jpg)
![Page 111: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/111.jpg)
![Page 112: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/112.jpg)
![Page 113: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/113.jpg)
![Page 114: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/114.jpg)
![Page 115: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/115.jpg)
![Page 116: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/116.jpg)
![Page 117: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/117.jpg)
![Page 118: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/118.jpg)
![Page 119: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/119.jpg)
![Page 120: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/120.jpg)
![Page 121: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/121.jpg)
![Page 122: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/122.jpg)
![Page 123: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/123.jpg)
![Page 124: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/124.jpg)
![Page 125: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/125.jpg)
![Page 126: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/126.jpg)
![Page 127: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/127.jpg)
![Page 128: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/128.jpg)
![Page 129: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/129.jpg)
![Page 130: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/130.jpg)
![Page 131: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/131.jpg)
![Page 132: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/132.jpg)
![Page 133: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/133.jpg)
![Page 134: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/134.jpg)
![Page 135: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/135.jpg)
![Page 136: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/136.jpg)
![Page 137: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/137.jpg)
![Page 138: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/138.jpg)
![Page 139: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/139.jpg)
![Page 140: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/140.jpg)
![Page 141: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/141.jpg)
![Page 142: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/142.jpg)
![Page 143: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/143.jpg)
![Page 144: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/144.jpg)
![Page 145: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/145.jpg)
![Page 146: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/146.jpg)
![Page 147: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/147.jpg)
![Page 148: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/148.jpg)
![Page 149: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/149.jpg)
![Page 150: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/150.jpg)
![Page 151: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/151.jpg)
![Page 152: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/152.jpg)
![Page 153: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/153.jpg)
![Page 154: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/154.jpg)
![Page 155: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/155.jpg)
![Page 156: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/156.jpg)
![Page 157: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/157.jpg)
![Page 158: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/158.jpg)
![Page 159: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/159.jpg)
![Page 160: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/160.jpg)
![Page 161: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/161.jpg)
![Page 162: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/162.jpg)
![Page 163: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/163.jpg)
![Page 164: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/164.jpg)
![Page 165: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/165.jpg)
![Page 166: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/166.jpg)
![Page 167: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/167.jpg)
![Page 168: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/168.jpg)
![Page 169: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/169.jpg)
![Page 170: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/170.jpg)
![Page 171: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/171.jpg)
![Page 172: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/172.jpg)
![Page 173: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/173.jpg)
![Page 174: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/174.jpg)
![Page 175: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/175.jpg)
![Page 176: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/176.jpg)
![Page 177: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/177.jpg)
![Page 178: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/178.jpg)
![Page 179: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/179.jpg)
![Page 180: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/180.jpg)
![Page 181: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/181.jpg)
![Page 182: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/182.jpg)
![Page 183: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/183.jpg)
![Page 184: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/184.jpg)
![Page 185: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/185.jpg)
![Page 186: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/186.jpg)
![Page 187: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/187.jpg)
![Page 188: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/188.jpg)
![Page 189: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/189.jpg)
![Page 190: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/190.jpg)
![Page 191: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/191.jpg)
![Page 192: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/192.jpg)
![Page 193: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/193.jpg)
![Page 194: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/194.jpg)
![Page 195: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/195.jpg)
![Page 196: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/196.jpg)
![Page 197: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/197.jpg)
![Page 198: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/198.jpg)
![Page 199: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/199.jpg)
![Page 200: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/200.jpg)
![Page 201: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/201.jpg)
![Page 202: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/202.jpg)
![Page 203: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/203.jpg)
![Page 204: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/204.jpg)
![Page 205: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/205.jpg)
![Page 206: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/206.jpg)
![Page 207: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/207.jpg)
![Page 208: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/208.jpg)
![Page 209: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/209.jpg)
![Page 210: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/210.jpg)
![Page 211: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/211.jpg)
![Page 212: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/212.jpg)
![Page 213: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/213.jpg)
![Page 214: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/214.jpg)
![Page 215: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/215.jpg)
![Page 216: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/216.jpg)
![Page 217: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/217.jpg)
![Page 218: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/218.jpg)
![Page 219: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/219.jpg)
![Page 220: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/220.jpg)
![Page 221: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/221.jpg)
![Page 222: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/222.jpg)
![Page 223: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/223.jpg)
![Page 224: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/224.jpg)
![Page 225: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/225.jpg)
![Page 226: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/226.jpg)
![Page 227: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/227.jpg)
![Page 228: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/228.jpg)
![Page 229: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/229.jpg)
![Page 230: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/230.jpg)
![Page 231: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/231.jpg)
![Page 232: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/232.jpg)
![Page 233: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/233.jpg)
![Page 234: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/234.jpg)
![Page 235: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/235.jpg)
![Page 236: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/236.jpg)
![Page 237: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/237.jpg)
![Page 238: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/238.jpg)
![Page 239: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/239.jpg)
![Page 240: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/240.jpg)
![Page 241: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/241.jpg)
![Page 242: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/242.jpg)
![Page 243: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/243.jpg)
![Page 244: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/244.jpg)
![Page 245: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/245.jpg)
![Page 246: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/246.jpg)
![Page 247: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/247.jpg)
![Page 248: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/248.jpg)
![Page 249: SYNTHESIS AND.STABILITY ANALYSIS OF](https://reader034.fdocuments.us/reader034/viewer/2022051420/627e400afecb8f69154c736e/html5/thumbnails/249.jpg)