A New Approach to Model Reference Adaptive Control using Fuzzy Logic Controller for Nonlinear Systems by ijcsis

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									                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                       Vol. 9, No. 2, February 2011



 A New Approach to Model Reference Adaptive
Control using Fuzzy Logic Controller for Nonlinear
                     Systems
                          R.Prakash                                                                                R.Anita
    Department of Electrical and Electrnics Engineering,                     Department of Electrical and Electrnics Engineering,
           Muthayammal Engineering College,                                     Institute of Road and Transport Technology,
              Rasipuram, Tamilnadu, India.                                                 Erode, Tamilnadu, India.
            Email: prakashragu@yahoo.co.in                                              Email: anita_irtt@yahoo.co.in

Abstract— The aim of this paper is to design a fuzzy logic              Adaptive Network-Based Fuzzy Inference System (ANFIS)
controller- based model reference adaptive intelligent                  for speed and position estimation of permanent-magnet
controller. It consists of fuzzy logic controller along with a          synchronous generator presented in [17].An adaptive fuzzy
conventional Model Reference Adaptive Control (MRAC). The               output feedback control approach is proposed for Single-
idea is to control the plant by conventional model reference            Input-Single-Output (SISO) nonlinear systems without the
adaptive controller with a suitable single reference model, and         measurements of the states. It is discussed in [18]. Gadoue et
at the same time control the plant by fuzzy logic controller. In        al. presented a fuzzy logic adaptation mechanisms and it is
the conventional MRAC scheme, the controller is designed to             used in model reference adaptive speed-estimation schemes
realize plant output converges to reference model output based          that are based on rotor flux[19].An adaptive fuzzy-based
on the plant which is linear. This scheme is for controlling            dynamic feedback tracking controller will be developed for
linear plant effectively with unknown parameters. However,              a large class of strict-feedback nonlinear systems involving
using MRAC to control the nonlinear system at real time is              plant uncertainties and external disturbances and it is
difficult. In this paper, it is proposed to incorporate a fuzzy         discussed in [20].Chang-Chun Hua et al. [21] presented an
logic controller (FLC) in MRAC to overcome the problem. The
                                                                        adaptive fuzzy-logic system and it is investigated for a class
control input is given by the sum of the output of conventional
                                                                        of uncertain nonlinear time-delay systems via dynamic
MRAC and the output of fuzzy logic controller. The rules for
the fuzzy logic controller are obtained from the conventional PI
                                                                        output-feedback approach. A development of Adaptive
controller. The proposed fuzzy logic controller-based Model             Fuzzy Neural Network Control (AFNNC), including direct
Reference Adaptive controller can significantly improve the             and indirect frameworks for an n-link robot manipulator, to
system’s behavior and force the system to follow the reference          achieve high-precision position tracking is discussed in [22].
model and minimize the error between the model and plant                An-Min Zou et al. [23] proposed a controller for the robust
output.                                                                 backstepping control of a class of nonlinear pure-feedback
                                                                        systems using fuzzy logic. A set of fuzzy controllers is
   Keywords-Model Reference Adaptive Controller (MRAC),                 synthesized to stabilize the nonlinear multiple time-delay
Fuzzy Logic Controller (FLC), Proportional-Integral (PI)                large-scale system is presented in [24]
controller                                                                  In this paper a proposal of designing a fuzzy logic
                      I. INTRODUCTION                                   controller- based model reference adaptive intelligent
                                                                        controller is designed from a fuzzy logic controller in
    Model Reference Adaptive Control (MRAC) is one of                   parallel with a MRAC. From the designed PI controller,
the main schemes used in adaptive system. Recently MRAC                 fuzzy rules are generated and it is used to design a fuzzy
has received considerable attention, and many new                       logic controller. The fuzzy controller is connected in parallel
approaches have been applied to practical processes [1], [2].           with an MRAC and its output is added and then given to the
In the MRAC scheme, the controller is designed to realize               plant input. The fuzzy logic controller is used to compensate
plant output converges to reference model output based on               the nonlinearity of the plant and it is not taken into
the assumption that plant can be linearized. Therefore this             consideration in the conventional MRAC. The role of
scheme is effective for controlling linear plants with                  MRAC is to perform the model matching for the uncertain
unknown parameters. However, it may not assure for                      linearized system to a given reference model. Finally to
controlling nonlinear plants with unknown structure. It is              confirm the effectiveness of proposed method, it is
well known that fuzzy technique has been widely used in                 compared with the simulation results of the conventional
many physical and engineering systems, especially for                   MRAC.
systems with incomplete plant information [3]-[8]. In
addition to fuzzy logic, it has been widely applied to                                    II. STATEMENT OF THE PROBLEM
controller designs for nonlinear systems [9]-[13].A learning                To Consider a Single Input and Single Output (SISO),
approach of combining MRAC with the use of fuzzy                        Linear Time Invariant (LTI) plant with strictly proper
systems as reference models and controllers for control                 transfer function
dynamical systems can be found in [14]. A hybrid approach
by combing fuzzy controller and neural networks for                                y P (s)           Z   p   (s)                                      (1)
                                                                        G ( s)             K
learning-based control is proposed in [15]. A problem of                           u p (s)
                                                                                                 P
                                                                                                     R P (s)
Fuzzy-Approximation-Based adaptive control for a class of               where up is the plant input and yp is the plant output .Also,
nonlinear time-delay systems with unknown nonlinearities                the reference model is given by
and strict-feedback structure is discussed in [16]. An



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                                                                                                                     ISSN 1947-5500
                                                            (IJCSIS) International Journal of Computer Science and Information Security,
                                                            Vol. 9, No. 2, February 2011


                                                                (2)         ~
G m (s) 
            ym (s)
                    Km
                        Z m (s)                                              and the tracking error e is Strictly Positive Real (SPR),
             r (s)      Rm (s)
where r and ym are the model’s input and output. To define                  [1] and the adaptation rule for the controller gain θ is given
the output error as                                                             e1 sgn( K p / K m )                                (11)
 e  y p  ym                                          (3)                  where e1= yp-ym and  is a positive gain.
    Now the objective is to design the control input u such as                  The adaptive laws and control schemes developed are
that the output error e goes to zero asymptotically for                     based on a plant model that is free from disturbances, noise
arbitrary initial condition, where the reference signal r(t) is             and unmodelled dynamics. These schemes are to be
piecewise continuous and uniformly bounded.                                 implemented on actual plants that most likely to deviate
                                                                            from the plant models on which their design is based. An
                                                                            actual plant may be infinite in dimensions, nonlinear and its
                  III. STRUCTURE OF AN MRAC DESIGN                          measured input and output may be corrupted by noise and
A. Relative Degree n =1                                                     external disturbances. It is shown by using conventional
   As in Ref [1] the following input and output filters are                 MRAC that adaptive scheme is designed for a disturbance-
used,                                                                       free plant model and may go unstable in the presence of
                                                                            small disturbances.

 1  F1  gu p                                                (4)

 2  F2  gy p                                                                 IV. PI CONTROLLER-BASED MODEL REFERENCE
                                                                                           ADAPTIVE CONTROLLER
where F is an (n  1) * (n  1) stable matrix such as that
                                                                                The disturbance and nonlinear component are added to
det ( SI  F ) is a Hurwitz polynomial whose roots include                  the plant input of the conventional model reference adaptive
the zeros of the reference model and that (F,g) is a                        controller, in this case the tracking error has not come to
controllable pair. It is defined as the “regressor” vector                  zero and the plant output is not tracked with the reference
       T T
  [1 ,2 , y p , r ]T                                   (5)              model plant output. The large amplitude of oscillations will
    In the standard adaptive control scheme, the control u is               come with the entire period of the plant output and the
structured as                                                               tracking error has not come to zero .The disturbance is
                                                                            considered as a random noise signal. To improve the system
u   T                                                         (6)        performance, the PI controller-based model reference
                  [1 ,  2 ,  3 , C 0 ]T                                adaptive controller is proposed. In this scheme, the
where                        is a vector of adjustable                      controller is designed by using parallel combination of
parameters, and is considered as an estimate of a vector of                 conventional MRAC system and PI controller.
unknown system parameters θ* .
The dynamic of tracking error is                                                The transfer function of PI Controller is generally
              ~                                                             written in the “Parallel form” given (12) by or the “ideal
e  Gm ( s) p* T                                      (7)
                     *               k   p
                                                                            form’’ given by (13)
            P                                   ~      *
where               k m
                           and    ( t )        represents              GPI (S ) 
                                                                                         U pi ( S )
                                                                                                       KP 
                                                                                                               Ki                                         (12)
parameter error. Now in this case, since the transfer function                            E (S )               S
                               ~
between the parameter error  and the tracking error e is                                              K P (1 
                                                                                                                   1
                                                                                                                      )
                                                                                                                                                         (13)
                                                                                                                   Ti
Strictly Positive Real (SPR) [1], the adaptation rule for the
controller gain θ is given by                                               where Upi(s) is the control signal, acting on the error signal
                                                                            E(s),Kp is the proportional gain, Ki is the integral gain and Ti
 
  e1 sgn p *                                        (8)              is the integral time constant.
where  is a positive gain.                                                     The block diagram of the PI controller-based model
                                                                            reference adaptive controller is shown in Fig. 1.
B. Relative Degree n =2
    In the standard adaptive control scheme, the control u is
structured as
                     T
u   T       T    T  e1 sgn( K p / K m )            (9)
                                             T
where   [1 ,  2 ,  3 , C 0 ] is a vector of adjustable
parameters, and is considered as an estimate of a vector of
                                                 *
unknown system parameters  .
   The dynamic of tracking error is
                       ~
 e  Gm (s)(s  p0 ) p* T                                    (10)
                                 k
            P    *
                         
                                     p
                                         *   ~
where                and    ( t )  
                                 k   m
                                                                                                            Fig. 1 PI controller-based MRAC
represents the parameter error. Gm (s)(s  p0 ) is strictly
proper and Strictly Positive Real (SPR). Now in this case,                      In the PI controller-based model reference adaptive
since the transfer function between the parameter error                     controller, the value for the PI controller gains Kp and Ki
                                                                            are calculated by using the Ziegler–Nichols tuning method.




                                                                       87                                                 http://sites.google.com/site/ijcsis/
                                                                                                                          ISSN 1947-5500
                                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                                Vol. 9, No. 2, February 2011


The control input U of the plant is given by the following                     U mr   T 
equation,                                                                                                                                     (17)
                                                                                 [1,  2 , 3 , C0 ]T
U  U mr  U pi                                                    (14)          [ 1 ,  2 , y p , r ] T
U mr   T                                                                        Stability of the system and adaptability are then achieved
where Umr is the output of the adaptive controller and Upi                     by an adaptive control law Umr tracking the system state x
is the output of the PI controller. The input of the PI                        to a suitable reference model such as that the error e = yp-
controller is the error, in which the error is the difference                  ym =0 asymptotically. The Fuzzy Logic Controller (FLC)
between the plant output yp(t) and the reference model                         provides an adaptive control for better system performance
output ym(t). In this case also, the disturbance (random                       and solution for controlling nonlinear processes.
noise signal) and nonlinear component is added to the input                        The plant output is compared with the model reference
of the plant .The PI controller- based model reference                         output. After comparison, the error and the change in error
adaptive controller effectively reduces the amplitude of                       are calculated and are given as input to the fuzzy controller.
oscillations of the plant output. In this case the tracking error
has not come to zero. The PI controller-based model                                  The error (e) and error change (ce) are defined as
reference adaptive controller improves the performance                         e(k )  ym (k )  y p (k )
compared with the conventional MRAC.                                           ce ( k )  e( k )  e( k  1)
                                                                               where ym(k) is the response of the reference model at kth
      V. FUZZY LOGIC CONTROLLER-BASED MODEL
                                                                               sampling interval, yp(k ) is the response of the plant output
         REFERENCE ADAPTIVE CONTROLLER
                                                                               at kth sampling interval, e(k) is the error signal at kth
    To make the system adaptable to more quickly and                           sampling interval, ce(k) is the error change signal at kth
efficiently than conventional MRAC system and PI                               sampling interval.
controller-based MRAC system, a new idea is proposed and                           FLC consists of three stages: fuzzification, rule
implemented. The new idea which is proposed in this paper                      execution, and defuzzification. In the first stage, the crisp
is the fuzzy logic controller- based model reference adaptive                  variables e(kT) and ce(kT) are converted into fuzzy
controller. In this scheme, the controller is designed by                      variables e and ce using the triangular membership
using parallel combination of conventional MRAC system                         functions. Each fuzzy variable is a member of the subsets
and fuzzy logic controller. The error and the change in error                  with a degree of membership varying between ‘0’ (non-
are given input to the fuzzy logic controller. The rules and                   member) and ‘1’ (full member).In the second stage of the
membership function of fuzzy logic controller are formed                       FLC, the fuzzy variables e and ce are processed by an
from the input and output waveforms of PI controller of                        inference engine that executes a set of control rules
designed PI controller based MRAC scheme. The block                            containing in a rule base. In this paper the control rules are
diagram of fuzzy logic controller-based model reference                        formulated using the knowledge of the PI controller of
adaptive controller is shown in Fig. 2.                                        designed PI controller-based MRAC system behavior and
                                                                               the experience of Control Engineers. The reverse of
                                                                               fuzzification is called defuzzification. The FLC produces the
                                                                               required output in a linguistic variable (fuzzy number).
                                                                               According to real-world requirements, the linguistic
                                                                               variables have to be transformed to crisp output. As the
                                                                               centroid method is considered to be the best well-known
                                                                               defuzzification method, it is utilized in the proposed method.

                                                                               A. Construction of Fuzzy Rules:
                                                                                  Consider an example of a PI controller input (error),
                                                                               change in error and PI controller output waveforms are
                                                                               given by Fig. 3.
                                                                                   By using the Fig.3, Fuzzy rules and membership for
              Fig. 2 Fuzzy logic controller-based MRAC system                  error (e) and change in error (ce) and output (Ufc ) are
    The state model of linear time invariant system is given                   created
by the following form                                                                The developed fuzzy rules are
 X (t )  AX (t )  BU(t )                                         (15)        1. If error is ‘A’ and change in error is ‘A’ then the output is
 Y (t )  CX (t )  DU (t )                                                            ‘D’
    This scheme is restricted to a case of Single Input Single                 2. If error is ‘B’ and change in error is ‘B’ then the output is
Output (SISO) control, noting that the extension to Multiple                           ‘F’
Input Multiple Output (MIMO) is possible. To keep the                          3. If error is ‘C’ and change in error is ‘D’ then the output is
plant output yp converges to the reference model output ym,                            ‘H’
it is synthesized to control input U by the following                          4. If error is ‘D’ and change in error is ‘F’ then the output is
equation,                                                                              ‘J’
U  U mr  U fc                                                    (16)        5. If error is ‘E’ and change in error is ‘C’ then the output is
                                                                                       A
where Umr is the output of the adaptive controller and Ufc
is the output of the fuzzy logic controller



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                                                                                                               ISSN 1947-5500
                                                                     (IJCSIS) International Journal of Computer Science and Information Security,
                                                                     Vol. 9, No. 2, February 2011


6. If error is ‘F’ and change in error is ‘I’ then the output is                       In this proposed fuzzy logic controller- based MRAC
        ‘K’                                                                         method, tracking error became zero within 6 seconds and no
7. If error is ‘G’ and change in error is ‘C’ then the output is                    oscillation has occurred. The plant output has tracked with
        B                                                                           the reference model output. This method is better than
8. If error is ‘H’ and change in error is ‘H’ then the output is                    conventional MRAC system and PI controller -based
        ‘I’                                                                         MRAC system
9. If error is ‘I’ and change in error is ‘C’ then the output is                                     VI. RESULTS AND DISCUSSION
        ‘C’
10. If error is ‘J’ and change in error is ‘E’ then the output is                     In this section, the results of computer simulations for
        E                                                                           conventional MRAC, PI controller-based MRAC and fuzzy
                                                                                    logic controller-based MRAC system are reported. The
11. If error is ‘K’ and change in error is ‘G’ then the output
                                                                                    results show the effectiveness of the proposed fuzzy logic
        is ‘G’
                                                                                    controller-based MRAC scheme and reveal its performance
                                                                                    superiority to the conventional MRAC technique.
                                                                                    Example 1:
                                                                                        In this example, the nonlinearity of backlash which is
                                                                                    followed by linear system is shown in Fig. 5




                                                                                                             Fig. 5 Nonlinear System

                                                                                        The disturbance (random noise signal) is also added to
                                                                                    the input of the plant
                                                                                       As an example, the system taken for the simulation is the
                                                                                    Lateral Dynamic Model of a Boeing 747 airplane.
                                                                                       The transfer function for the Lateral Dynamic Model of a
                                                                                    Boeing 747 airplane System is given by
                                                                                                0.5s 3  0.2608s 2  0.1223s  0.05832
                                                                                    G(s) 
           Fig. 3 PI controller input (error), change in error and                            4
                                                                                             s  0.6358s 3  0.9389s 2  0.5116  0.003674
                         PI controller output (Upi)                                 and the reference model are given by,
                                                                                                   1
  The FLC has two inputs: error e(kT) and change in error                            G m s  
                                                                                                s  3 
ce(kT) and one output Ufc(kT). The membership functions                                 The simulation was carried out with MATLAB and the
for fuzzy variable error (e), change in error (ce) and output                       input is chosen as r(t)= 55sin0.7t.The initial value of the
(Ufc) are shown in Fig.4.                                                           conventional MRAC scheme controller parameters are
                                                                                    chosen as (0) = [0.5, 0, 0, 0]T . The conventional model
                                                                                    reference adaptive controller is designed by using the
                                                                                    equations (6) and (8).
                                                                                        The simulations are done for the conventional MRAC,
                                                                                    PI controller- based MRAC and fuzzy logic controller-based
                                                                                    MRAC system with random noise disturbance and nonlinear
                                                                                    component are added to the plant.
                                                                                       In the PI controller-based model reference adaptive
                                                                                    controller, the value of the PI controller gains Kp and Ki are
                                                                                    equal to 10 and 75 respectively. In the fuzzy logic
                                                                                    controller- based model reference adaptive controller, each
                                                                                    universe of discourse is divided into six fuzzy sets: NH
                                                                                    (Negative High), NL (Negative Large), ZE (Zero), PS
                                                                                    (Positive Small), PM (Positive Medium) and PH (Positive
                                                                                    High).
                                                                                      The fuzzy variables e and ce are processed by an inference
                                                                                    engine that executes a set of control rules which are
                                                                                    contained in a (6x6) rule base as shown in Fig.6. The control
                                                                                    rules are formulated using the knowledge of the PI
Fig. 4 (a) Membership functions of the fuzzy variables error (e), (b) change        controller of designed PI controller based MRAC scheme
                     in error (ce), and output (Ufc)
                                                                                    behavior and the experience of Control Engineers.




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                                                                                                                      ISSN 1947-5500
                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                 Vol. 9, No. 2, February 2011




                         Fig. 6 Fuzzy rules table
                                                                                                            8(b)
   The membership functions for fuzzy variable error (e),
change in error (ce) and output (Ufc) are shown in Fig. 7




                                                                                                            8(c)




 Fig. 7 Membership functions for fuzzy variable error (e), change in error
                         (ce) and output (Ufc)


    The results for the conventional MRAC, PI controller-                                                   8(d)
based MRAC and fuzzy logic controller -based MRAC
system are given in Fig. 8




                                                                                                           8( e )


                                   8(a)




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                                                                    Vol. 9, No. 2, February 2011




                                     8(f)

Fig. 8 Simulation results:8(a).Plant output yp(t) (solid lines) and the                                     Fig. 9 Fuzzy rules table
Reference model output ym (t) (dotted lines) of the conventional MRAC
system for the input r(t)= 55sin0.7t. 8(b).Plant output yp(t) (solid lines) and
the Reference model output ym (t )(dotted lines) of the PI controller-based
MRAC scheme for the input r(t)= 55sin0.7t. 8(c). Plant output yp(t) (solid
lines) and the Reference model output ym (t )(dotted lines) of the fuzzy
logic controller-based MRAC scheme for the input r(t)= 55sin0.7t.
8(d).Tracking error e for the conventional MRAC.8 (e).Tracking error e for
the PI controller-based MRAC scheme and 8(f) Tracking error e for the
fuzzy logic controller -based MRAC scheme.

Example 2:
     In this example, the nonlinearity of Dead zone is
followed by linear system.The disturbance (random noise
signal) is also added to the input of the plant. A second order
system with the transfer function is given below
                1
G(S ) 
          S 2  3S  10
is used to study and the reference model is chosen as
                    5
G M (S ) 
             S 2  10S  25
    The initial value of conventional MRAC scheme
controller parameters are chosen as (0) = [3, 18,-8, 3]T.
The conventional model reference adaptive controller is                                          Fig. 10 Fuzzy memberships used for simulation
designed by using the equations (9) and (11). The simulation
was carried out with MATLAB and the input is chosen as
r(t)= 20+5sin4.9t. In the PI controller based model reference                              The results for the conventional MRAC, PI controller-
adaptive controller, the value for the PI controller gains Kp                          based MRAC and fuzzy logic controller- based MRAC
and Ki are equal to 8 and 85 respectively.                                             system are given in Fig .11.
    In the fuzzy controller based model reference adaptive
controller, seven linguistic variables are used for the input
variable error and change in error.
   They are Extremely Negative (EN), High Negative
(HN), Medium Negative (MN), Small Negative (SN), zero
(ZE), Medium Positive (MP) and High Positive (HP).
    The seven linguistic variables are used for the output
variable as Very Low(VL),Low(L),Nearly Low(NL),
Medium(M),Medium High(MH),High(H) and Extremely
positive(EP).
    The control rules are formulated using the knowledge of
the PI controller of designed PI controller-based MRAC
                                                                                                                     11 (a)
scheme behavior and the experience of Control Engineers.
The fuzzy variables e and ce are processed by an inference
engine that executes a set of control rules which are
containing in a (7x7) rule base as shown in Fig. 9. The
membership functions for fuzzy inputs error (e), change in
error (ce) and fuzzy output (Ufc) are shown in Fig. 10.




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11(b)                                                     11(f)

                      Fig. 11 Simulation results:11(a) Plant output yp(t) (solid lines) and the
                      Reference model output ym (t) (dotted lines) of the conventional MRAC
                      system for the input r(t)= 20+5sin4.9t. 11(b) Plant output yp(t) (solid lines)
                      and the Reference model output ym (t )(dotted lines) of the PI controller-
                      based MRAC scheme for the input r(t)= 20+5sin4.9t. 11(c) Plant output
                      yp(t) (solid lines) and the Reference model output ym (t )(dotted lines) of
                      the fuzzy logic controller-based MRAC scheme for the input r(t)=
                      20+5sin4.9t. 11(d) Tracking error e for the conventional MRAC. 11(e)
                      Tracking error e for the PI controller-based MRAC scheme. 11(f) Tracking
                      error e for the fuzzy logic controller- based MRAC scheme.


                          The nonlinear component and the disturbance (random
                      noise signal) are added to the plant input of conventional
                      MRAC. The plant output is not tracked with the reference
11(c)
                      model output and large amplitude of oscillations occur at the
                      entire plant output signal as shown in Fig. 8(a) and 11(a) and
                      also tracking error has not come to zero as shown in Fig.
                      8(d) and 11(d). But when the disturbance (random noise
                      signal) and non linear component are added to the input of
                      the plant of PI controller-based model reference adaptive
                      controller and it improves the performance comparing to the
                      conventional MRAC and also reduces the amplitude of
                      oscillations of the plant output as shown in Fig. 8(b) and
                      11(b).In this case also plant output does not track the
                      reference model output and the tracking error has not come
                      to zero as shown in Fig. 8(e) and 11(e).When the
                      disturbance (random noise signal) and nonlinear component
                      are added to the input of the plant of the proposed fuzzy
                      logic controller-based MRAC scheme, the plant output has
11(d)                 tracked with the reference model output as shown in Fig.
                      8(c) and 11(c).The tracking error becomes zero within 6
                      seconds with less control effort as shown in Fig. 8(f) and
                      11(f) and no oscillations has occurred. From the plots, one
                      can see clearly that the transient performance, in terms of
                      the tracking error and control signal, has been significantly
                      improved by the proposed MRAC using fuzzy logic
                      controller. The proposed fuzzy logic controller-based
                      MRAC schemes show better control results compared to
                      those by the conventional MRAC and PI controller -based
                      MRAC system. On the contrary, the proposed method has
                      much less error than conventional method in spite of
                      nonlinearities and disturbance.

                                                 VII. CONCLUSION
11(e)
                          In this section, the response of the conventional model
                      reference adaptive controller is compared with the PI
                      controller-based MRAC system and proposal model
                      reference adaptive controller using fuzzy logic controller.
                      The controller is checked with the two different plants. The
                      proposed fuzzy logic controller -based MRAC controller
                      shows very good tracking results when compared to the



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                                                           ISSN 1947-5500
                                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                                Vol. 9, No. 2, February 2011


conventional MRAC and the PI controller- based MRAC                                [20]    Yeong-Chan Chang, “Intelligent Robust Tracking Control for a
system. Simulations and analyses have shown that the                                       Class of Uncertain Strict-Feedback Systems,” IEEE Transactions
                                                                                           on Systems, Man, and Cybernetics, Part B: Cybernetics vol.31,
transient performance can be substantially improved by
                                                                                           no.1,.pp. 142 – 155, Feb. 2009
proposed MRAC scheme and also the proposed controller                              [21]    Chang-Chun Hua, Qing-Guo Wang and Xin-Ping Guan“Adaptive
shows very good tracking results when compared to                                          Fuzzy Output-Feedback Controller Design for Nonlinear Time-
conventional MRAC. Thus the proposed intelligent parallel                                  Delay Systems With Unknown Control Direction,” IEEE
controller is found to be extremely effective, efficient and                               Transactions on Systems, Man, and Cybernetics, Part B:
useful                                                                                     Cybernetics, vol.39, no.2,pp. 363 - 374, April 2009
                                                                                   [22]    Rong-Jong Wai and Zhi-Wei Yang, “Adaptive Fuzzy Neural
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       697,Oct. 2006.                                                                                 University, Chennai, India, in 2004. At present she is
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[18]   Shao-Cheng Tong, Xiang-Lei He and Hua-Guang Zhang, “A
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