MRAC BASED DC SERVO MOTOR MOTION CONTROL

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International Journal of Advanced Research in Engineering and Technology
(IJARET)
Volume 7, Issue 2, March-April 2016, pp. 53–63, Article ID: IJARET_07_02_005
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___________________________________________________________________________
MRAC BASED DC SERVO MOTOR MOTION
CONTROL
Kalpesh B. Pathak
Ph.D. Scholar, Dept. of Instrumentation & Control, Nirma University,
Ahmedabad, Gujarat, India
Dipak M. Adhyaru
Professor & Section Head, Dept. of Instrumentation & Control,
Nirma University, Ahmedabad, India
ABSTRACT
Adaptive Control strategies helps to get desirable output for system with
partial unknown dynamics or systems having unknown and unmodeled load
variation. DC servo motors are useful to track rapid speed trajectory for
various applications, particularly with need of high starting torque and low
inertia. Model Reference Adaptive Control (MRAC) parameter data of results
with Lyapunov stability MRAC has been used to generate adaptation
parameter for DC motor speed controller. Based on the data of error and
adaptation parameter new ANFIS based controller has been created and
trained. ANFIS based MRAC controller determines parameter based on
present value of error for each iteration. Problem definition, adaptive
controller using model output as a reference, basic block diagram of overall
system and derivation of control law has been presented. Introduction part
discusses literature survey, development of the topic and importance of the
work.
Key words: ANFIS, Lyapunov Stability, MRAC Motion Control, Servo
Cite this Article: Kalpesh B. Pathak and Dipak M. Adhyaru, Mrac Based DC
Servo Motor Motion Control. International Journal of Advanced Research in
Engineering and Technology, 7(2), 2016, pp. 53–63.
http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=7&IType=2
1. INTRODUCTION
Control system should be able to help achieving desirable response for a given set of
specifications. More important aspect is stability of system with accuracy as per need
of the application. High starting torque and low inertia motors are essentials for
motion control applications. DC servo motors are useful for rapid changes in velocity

Kalpesh B. Pathak and Dipak M. Adhyaru
for various applications. Model of DC servo motor and related control strategies for
speed control have been discussed here. MRAC technique based on Lyapunov
stability has been used to generate adaptation parameter for controller. Based on the
data set of model output, plant output and adaptation parameter new ANFIS based
controller has been created and trained. ANFIS based MRAC controller has been to
control speed of the servo motor. Problem identification and definition, Lyapunov
stability based and ANFIS based adaptive controller using model output as a
reference, basic block diagram of overall system with controller and adaptive
mechanism, application and derivation of control law has been presented. This section
of the paper discusses literature survey, development of the topic and importance of
the work.
Fundamentals of adaptive control, Development of adaptive control techniques
and advanced trends with applications have been rigorously compiled and nicely
discussed in [1]. This book contributes in depth analysis for adaptive control, stability
considerations and emphasizes MRAC as an important control strategy. Present
challenges, strength and features of adaptive control, have been reviewed and
common and uncommon issues about applying MRAC to process with time delay are
discussed in [2].
Researchers have suggested various strategies to apply soft computing based
controller. The model of generalized servo systems has been discussed in [3]. A linear
and adaptive DC type servo drive control system on basis of an observer theory and
on the basis of a theory of passive adaptive control is proposed in [4] for better drive
performance for DC servo motor. In [5] the speed control method with robustness for
a DC servo motor has been proposed to deal with problems like variation in values of
parameter and disturbance torque. Direct method of Lyapunov helps restrain effect of
estimation error. With a quantitative as well as qualitative study of fuzzy controller
[6] presents method for motion control using FLC for a separately excited D.C motor
and emphasizes that the controllers with fuzzy logic are applied widely with simple
configurations and their analytical knowledge has greater scope of improvement.
A robust observer to estimate state and to estimate fault having decoupling of
unknown input has been designed and robust natured fault tolerant control for
discrete-time linear process has been proposed in [7]. Design and analysis of an
intelligent control to achieve position tracking with high-precision for manipulator of
n-link robot is addressed in [8]. A robust natured neural fuzzy system based network
control is proposed to the position control for joint of an n link robot system
manipulator actuated by dc servo motors for periodic motion and Lyapunov stability
has been discussed for said approach. Equivalency of quantized system is proved to
the original one, on the sliding manifold in case of ideal value of sliding, for bit
stream based strategy of feedback control in [9].

Mrac Based DC Servo Motor Motion Control
Figure 1 Block Diagram of Servo Motor Motion MRAC
MRAC based on Dynamic Back Propagation and Fuzzy Emulator for Converter
application has been discussed in [10]. Output of master system has been used to
choose model for reference and T-S fuzzy model has been used to present the chaotic
and discrete-time slave nature system in [11]. With the fuzzy state estimator, and by
combination of the adaptive control backstepping technique with the decentralized
system design in[12] an adaptive decentralized output feedback control fuzzy
approach has been developed. For suggested control approach semi-globally and
uniformly and ultimately bounded probable value has been assured.
In [13] the sum of the output of conventional MRAC provide I/O of the neural /
fuzzy controller. Supervisory loop with intelligence has been incorporated with the
conventional MRAC framework design by using an online neural and fuzzy network
structure in parallel with it. Modeling with control orientation, design, structures and
simulation work with various techniques and control law strategies, result analysis
details and advanced control algorithms have been discussed in book [14]. A gradient
scheme known as the MIT rule is given by
d e
e
dt




 

where, error me y y  , γ is
adaptation gain and θ is for adjustment mechanism. Fig. 1 shows basic block diagram
for proposed system. After MIT rule based MRAC [15] various modifications were
suggested by researchers. A summary and rigorous compilation of all methods,
control techniques and study of application has been carried out in [16].
ANFIS based Robot manipulator control has been proposed in [17].NN control
and ANFIS based results have been compared with and without disturbance.
Importance of soft computing technique based MRAC with past and recent
publication survey has been discussed in [18]. MRAC sections classified in survey
paper are based on applications, techniques and soft computing. Optimal criterion for
energy efficiency should be given higher importance in design [19]. Mechatronic
devices normally performs well but are intrinsically energy intensive. It affects overall
system sustainability so energy optimal motion is needed.
Adaptive and fuzzy based output tracking using backstepping control technique
has been performed in [20] and unknown nonlinear part has been identified using a
fuzzy logic system. Optimal observer design using soft computing has been applied
for HJB equation based algorithm in [21]. A neural adaptive controller for DC motor
tracking problem is discussed in [22]. Existing techniques have been integrated in
[23], such as the linearization technique for I/O, application of NN to linearize
equation of control law, the network estimation errors are compensated with the

effective sliding mode control scheme and Lyapunov approach has been used to
update the neural network parameters. The DC servo motor with fixed and variable
load has been used in [24] for the plant response and the Self tuning adaptive
controller with parameter estimation. Application of a direct Fractional order MRAC
to an Automatic Voltage Regulator has been discussed in [25]. Soft computing tool
genetic algorithm has been used for optimization. STCs are mostly with base of the
certainty equivalence and is only suboptimal. Adaptive dual control, the bicriterial
approach has been suggested to improve the quality [26].
Error addressed in this work is type 2 model presented in error models part of
[27]. The book contributes about adaptive systems from fundamentals to applications.
The architecture and procedure of learning with ANFIS have been presented in [28].
Information about each layer of ANFIS, training, evaluation and related regression
part is covered in [29, 30]. Use of such strategy to generate adaptation parameter and
prove system stability for the adapted controller parameter has been discussed here.
NN based MRAC has been compared with classical MRAC in [31]. With focus on
multivariable processes and systems, identification, control, design, analysis and
implementation of nonlinear and linear systems have been covered in [32]. Robust,
nonlinear and adaptive control has nicely been introduced and covered and many
generalized solutions for control have been derived with proof in [33]. The work is
useful to derive Lyapunov based MRAC as a base for ANFIS based MRAC.
In this paper now section II presents use of ANFIS for parameter adaptation.
Section III discusses motion control study for DC servo motor. It also presents
generalization of Lyapunov based MRAC, simulation work and results and
discussion. Sections IV gives conclusion for the work done.
2. ANFIS STRUCTURE FOR PARAMETER ADAPTATION
Adaptive neuro fuzzy type inference system is used to replace Lyapunov stability
based adaptive controller. Data set of plant output, model output and generated
adaptation parameter for the control using Lyapunov stability based MRAC has
been used to train data.The generalized bell function with assumed three parameters
α, β, and γ for error input is given by
1 2
1
( , , , )
1
f e
e

   


 


(01)
In layer 2 nodes are fixed with its output as the product of all their entry inputs. As
normalization is important, in next layer normalization takes place. After calculation
of consequent evaluation interference in layer 4, the overall output after layer 5 is
ˆ i i i
i i
w f
w



 (02)

Figure 2 ANFIS Structure for Controller Adaptation Parameter
Fig. 2 shows ANFIS structure with details for each layer. For training purpose the
least squares method as well as the backpropagation gradient descent method has been
used in combination. The difference between FIS output and training data output has
been considered as error at each epoch for least square estimation. After generation
and training part final fuzzy inference system calculates for adaptation ˆ .
3. DC SERVOMOTOR MOTION CONTROL
Servo systems drive and control position and time derivatives of position. Armature
closed loop control is applied if size of servo motor is large and high torque is
required.
3.1. About System and Model
The considered system can be expressed as follows.
a
a a a b a
di
L R i k e
dt
  
(03)
a
d
j f k i
dt


 
(04)
Figure 3 DC servomotor
Fig. 3 shows working of DC servomotor. Based on resistance, inductance and
back emf system produces resultant speed for a provided value of armature voltage.
Two proportionality constants for back emf and torque have been used.
Control problem is to follow desirable reference trajectory speed. Control input
here is armature voltage input to the system. Even though original system parameter
changes, the system output should follow the model output.

3.2. Parameter Adaptation and Control Law
Model output represented as
m m m m my A y B u   (05)
and plant
my A y bu   where mu u (06)
So
( )m m me A e b B u    (07)
To update adaptation parameter we consider both e and e
Let fe e 
Let a Lyapunov function
2 21 1
( , ) ( ) ( )
2 2
f f mV e e b B
b
 

   
(08)
Derivative term of Lyapunov function
1
( )f f mV e e b B 

   
(09)
1
( ( ) ) 2( )m m m mV e A e b B u b B   

     
(10)
2 1
( )( )m m mV A e b B u e   

    
(11)
Taking mu e   gives negative semi definite value for the remaining derivative
part of Lyapunov function. So adaptation parameter has been chosen accordingly for
stable system.
In DC servomotor motion control, derived  can be written as
( )p me      (12)
Similarly, proof can be extended for higher order systems.
Consider following system dynamics to generalize the derivation
( ( ))x Ax B u f x    (13)
where n
x R , m
u R , n n
A R 
 system matrix and 1 2( , .... ) m m
mis diag R   
 
unknown matrices and sgn( i ) is known for i=1,2..m, n m
B R 
 is known and constant
matrix, Uncertain function ( ) ( )T m
f x x R    with matrix of unknown constant
parameters n m
R 
 ,
n basis functions with known value is 1 2 1( ) ( ( ), ( ).... ( ), ( ))T
n nx x x x x    

Stable Reference Model
m m m m mx A x B u  (14)
m
mu R n n
mA R 
 n m
mB R 
 . The goal is to have zero error, means
lim ( ) ( ) 0m
t
x t x t

 
Assume control law with parameter estimation
ˆ ˆ ( )T T
xu k x x   (15)
Thus, ˆ ˆm n m n
xk and 
 Parameters need to be estimated for adaptation.
ˆ ˆ( ) ( ) ( )T T T
xx A B k x B x        (16)
Model representing desired dynamics is (2). When system dynamics follows
model dynamics, terms can be compared as ˆ ˆ( )T T
x m x xA B k A B k k      and
ˆ( ) 0T T
mB B    
Tracking error dynamics given by
ˆ ˆ( ) (( ) (( ) ( )) ) ( ( ) ( ))T T T
x m m m m m m me t A B k x B x A x B u A x A x x t x t              (17)
( ( ))T T
m xe A e B k x x        (18)
The Lyapunov function is
1 1
( , , , ) ( ) ( )T T T
x x x xV e k e Pe trace k k trace   
            (19)
Where 0, 0 0T T T
x xP P and          are symmetric positive definite
matrices.
P is the solution of T
m mPA A P Q   (20)
Choosing adaptive laws
ˆ sgn( )T
x xk xe PB  
ˆ ( ) sgn( )T
x e PB     (21)
T
V e Qe  becomes negative semidefinite. It indicates Lyapunov stability for the
system for applied adaptive MRAC law.
3.3. Simulation work results and discussion
Initially classical Lyapunov based MRAC is applied for the DC servo motor plant and
model, with variations in input voltage trajectory. Simulation Parameter values are
Armature resistance Ra=10 Ω; Inductance of armature La=300 H; kτ=20 newton-
m/amp; j=8 kg-m2
, f=30 (newton-m)/(rad/msec), kb=1.1 volts/(rad/msec)
Adaptation gain γ =0.7 has been used and control law is given by
* pu e
(22)

Figure 4 Output and Error plot for DC Servo System Reference Model Output
The response seems desirable in both Lyapunov based and ANFIS based MRAC
for system, butfor partly uncertain plant dynamics, Lyapunov based MRAC is not
able to approximate for uncertain part and gives average results. Use of ANFIS to
adapt and apply control effort helps for good results in such situations. Fig. 4 presents
the value of output and error plot for DC Servo System reference model output.
Model output varies based on variation in armature input voltage.
Figure 5 Adaptation Parameter Generated with ANFIS Trained using Data from Lyapunov
Based MRAC
Fig. 5 shows adaptation parameter generated with ANFIS and with Lyapunov
stability Based MRAC. It shows that approximate model tries to remove oscillations
and mostly approximates smooth value for new signal.
0 200 400 600 800 1000 1200
0
1
2
3
Output y and ym with ANFIS and Lyapunov rule
time, msec
Output,rad/msec
Model
ANFIS
Lyapunov
0 200 400 600 800 1000 1200
-0.4
-0.2
0
0.2
0.4
Error for MRAC with ANFIS and Lyapunov Rule
time, msec
Error,rad/msec
ANFIS
Lyapunov
0 200 400 600 800 1000 1200
0
0.5
1
1.5
2
Adaptation parameter  - Lyapunov based MRAC
time, msec

0 200 400 600 800 1000 1200
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Adaptation parameter  - ANFIS based MRAC
time, msec


Figure 6 Lyapunov Function and its Time Derivative for ANFIS Based MRAC
Results shown in Fig. 6 are Lyapunov Function V for MRAC based on adaptation
parameter generated by ANFIS and its Time Derivative. Observation shows that
positive definite Lyapunov function and negative semidefinite derivative term proves
stability of proposed system.
6. CONCLUSION
In this paper MRAC using Lyapunov and ANFIS applied to control motion
parameters of DC servo motor. Results are compared for both strategies. It has been
observed that ANFIS based MRAC gives better results in terms of error convergence.
Introduction, Literature survey, system fundamentals, development of classical
MRAC, soft computing and ANFIS based MRAC has been included to understand the
importance of the work, problem definition and simulation work. Data of adjustment
parameter  has been saved after applying Lyapunov based rule and used to apply
ANFIS technique to generate ˆ . Lyapunov stability with suitable V and derivation of
V has been shown. Comparison with other new computing techniques and analysis
with case studies of higher order systems may give better vision on future scope,
importance and development of the topic.
ACKNOWLEDGEMENT
The present work is a part of PhD research work carried out at Nirma University.
REFERENCES
[1] Karl Johan Astrom, Adaptive Control, 2nd Ed., Pearson Education, 2001
[2] Brian D O Anderson, Arvin Dehghani “Challenges of adaptive control–past,
permanent and future”, Annual Reviews in Control, Volume: 32, Issue: 2,
Pages: 123-135, ISSN: 13675788, Elsevier, 2008
[3] Bo Zhao, Hongjie Hu "A new inverse controller for servo‐system based on
neural network model reference adaptive control", COMPEL - The
0 200 400 600 800 1000 1200
216.45
216.46
216.47
216.48
V
time, msec
V
0 200 400 600 800 1000 1200
-0.8
-0.6
-0.4
-0.2
0
Vdot
time, msec
Vdot

international journal for computation and mathematics in electrical and
electronic engineering, Vol. 28,2009
[4] K. Ohishi; K. Ohnishi; K. Miyachi "Adaptive DC servo drive control taking
force disturbance suppression into account" IEEE Transactions on Industry
Applications Volume: 24, Issue: 1,1988
[5] T. Senjyu, H. Kamifurutono, K. Uezato “Robust speed control of DC servo
motor based on Lyapunov's direct method” 25th Annual IEEE Conference,
Power Electronics Specialists Conference, PESC '94, 1994
[6] Dipraj, Pandey “Speed Control of D. C. Servo Motor By Fuzzy Controller”
International Journal of Scientific & Technology Research Volume 1, Issue 8,
September 2012
[7] M. Buciakowski; M. Witczak; J. Korbicz “Adaptive fault tolerant control:
Application to a DC servo motor” 20th International Conference on
Methods and Models in Automation and Robotics (MMAR), 2015
[8] R. J. Wai, P. C. Chen “Robust Neural-Fuzzy-Network Control for Robot
Manipulator Including Actuator Dynamics” IEEE Transactions on Industrial
Electronics ,Volume:53 , Issue: 4, 2006
[9] D. J. Almakhles, A. K. Swain, N. D. Patel "Stability and Performance
Analysis of Bit-Stream-Based Feedback Control Systems" IEEE Transactions
on Industrial Electronics, Volume:62, Issue: 7, 2015
[10] S. G. Kadwane, A. Kumar, B. M. Karan “Dynamic Back Propagation based
MRAC with Fuzzy Emulator for DCDC Converter”, Elektronika ir
Elektrotechnika, ISSN 1392 – 1215, No. 1(73), 2007
[11] Won-Ki Lee, Chang-Ho Hyun, Heejin Lee, Euntai Kim, Mignon Park
"Model reference adaptive synchronization of T–S fuzzy discrete chaotic
systems using output tracking control" Chaos, Solitons and Fractals 34 1590–
1598, Elsevier, 2007
[12] Yue Li, Yongming Li, Shaocheng Tong “Adaptive fuzzy decentralized output
feedback control for stochastic nonlinear large-scale systems”
Neurocomputing, Volume 83, Pages 38-46, Elsevier,2012
[13] Dr.A.Muruganandham, Dr. R.Prakash “a novel model reference intelligent
adaptive control using neural network and fuzzy logic controller” Journal of
Theoretical and Applied Information Technology,Vol. 62 No.1, 2014
[14] B. Wayne Bequette, Process control Modeling Design and Simulation, PHI,
2004
[15] P.V. Osburn, H.P. Whitaker and A. Kezer, “New developments in the design
of adaptive control systems” Institute of Aeronautical sciences, 1961
[16] I.D.Landau, “A survey of model reference adaptive techniques theory and
applications” Automatica, Vol. 10, pp. 353-379, 1974
[17] Adhyaru, D.M, Jimit Patel, Rishi Gianchandani "Adaptive Neuro-Fuzzy
Inference system based control of Robotic Manipulators" International
Conference on Mechanical and Electrical Technology,IEEE lCMET, 2010
[18] Kalpesh B. Pathak, Dipak M. Adhyaru, “ Survey of Model Reference
Adaptive Control” IEEE International Conference NUiCONE, 2012
[19] Giovanni Berselli, Federico Balugani, Marcello Pellicciari, Michele Gadaleta
“Energy-optimal motions for Servo-Systems: A comparison of spline
interpolants and performance indexes using a CAD-based approach”
Robotics and Computer-Integrated Manufacturing, Volume 40, 2016

[20] Yongming Li, Shaocheng Tong, Tieshan Li "Adaptive fuzzy backstepping
control design for a class of pure-feedback switched nonlinear systems"
Nonlinear Analysis: Hybrid Systems, Volume 16, pp 72–80, May 2015
[21] Dipak M.Adhyaru, “State Observer Design For Nonlinear Systems using
Neural Network Based HJB formulation”, Applied Soft Computing,
Vol.12(1), 2012
[22] Rui Bai “Neural network control-based adaptive design for a class of DC
motor systems with the full state constraints”, Neurocomputing Volume 168,
2015
[23] Jui-Hong Horng “Neural adaptive tracking control of a DC motor”
Information Sciences, Volume 118, Issues 1–4, 1999
[24] Mustafa A. Khamis “Design and Simulation of Self Tuning Controller for
DC Servo Motor” Diyala Journal of Engineering Sciences, Vol. 06, No. 04,
2013
[25] Norelys Aguila-Camacho, Manuel A. Duarte-Mermoud “Fractional adaptive
control for an automatic voltage regulator” ISA Transactions 52, 2013
[26] Vladimír Bobál, Petr Chalupa, Petr Dostál, Marek Kubalcík, “Self-tuning
Control of Non-linear Servomotor: Standard Versus Dual Approach “
WSEAS Transactions on Systems, 2013
[27] Narendra K.S. and Annaswamy A.M. “Stable adaptive systems” Dovers
publications, Mineola, New York, 2005
[28] Jyh shing Roger Jang “ANFIS: Adaptive Network Based Fuzzy Inference
System” IEEE transactions on systems, man and cybernetics, vol. 23, no. 3,
May/June 1993
[29] Adriano Oliveira Cruz “ANFIS: Adaptive Neuro-fuzzy inference systems”
IM, UFRJ, Mestrado NCE, October, 2013
[30] Melek Acar Boyacioglu, Derya Avci “An Adaptive Network-Based Fuzzy
Inference System for the prediction of stock market return” Expert Systems
with Applications 37 pp.7908–7912, 2010
[31] Kalpesh B. Pathak, Dipak M. Adhyaru, “Performance analysis of neural
network based MRAC” IEEE International Conference on Electrical,
Electronics, Signals, Communication and Optimization, EESCO, 2015
[32] S.E. Lyshevski, “Control Systems Theory with Engineering Applications”
Jaico Publication, 2006
[33] Rajiv Ranjan and Dr. Pankaj Rai, Fuzzy Logic Based Mrac for A Second
Order System. International Journal of Electrical Engineering and
Technology, 4(2), 2013, pp. 13–24.
[34] Rajiv Ranjan, Dr. Pankaj Rai, Performance Analysis of A Second Order
System Using MRAC. International Journal of Electrical Engineering and
Technology, 3(3), 2012, pp. 110–120.
[35] Eugene Lavretsky, Kevin A. Wise “Robust and Adaptive Control” Springer,
2013.

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