EJSR_57_1_14

European Journal of Scientific Research

ISSN 1450-216X Vol.57 No.1 (2011), pp.156-174

© EuroJournals Publishing, Inc. 2011

http://www.eurojournals.com/ejsr.htm

Design of Intelligent Adaptive Control using

Neural Network and Fuzzy Logic Controller

R. Prakash

Department of Electrical and Electronics Engineering

Muthayammal Engineering College, Rasipuram, Tamilnadu, India-636102

E-mail: [email protected]

R. Anita

Department of Electrical and Electronics Engineering

Institute of Road and Transport Technology, Erode, Tamilnadu, India-638316

E-mail: [email protected]

Abstract

In this paper, two novel intelligent model reference adaptive control schemes are

proposed. First is the Neural Network-based Model Reference Adaptive Control scheme

(NN-MRAC) and second is the Fuzzy logic Controller-based Model Reference Adaptive

Control scheme (FLC-MRAC). The NN-MRAC scheme formed to replace the classical PI

controller used in conventional model reference adaptive scheme by a neural network. The

FLC-MRAC schemes formed to replace the classical PI controller used in conventional

model reference adaptive scheme by a fuzzy logic controller. The proposed schemes can

significantly improve the system behavior and force the system to follow the reference

model and minimize the error between the model and plant output. A detailed simulation

comparison between the conventional and new schemes is carried out with an example.

Superior performance has been obtained using the neural network and fuzzy logic

controller used in MRAC scheme.

Keywords: Model Reference Adaptive Controller (MRAC), Neural Network (NN), Fuzzy

Logic Controller (FLC), Proportional-Integral (PI) controller

1. Introduction In the adaptive literature, the question of control of nonlinear systems with present- day sophistication

and complexities has often been an important research area due to the difficulties in modeling,

nonlinearities and uncertainties. Model Reference Adaptive Control (MRAC) is one of the main

schemes used in adaptive system. Recently Model Reference Adaptive Control has received

considerable attention, and many new approaches have been applied to practical process [1], [2].In the

MRAC scheme, the controller is designed to realize plant output converges to reference model output

based on assumption that plant can be linearized. Therefore this scheme is effectively for controlling

linear plants with unknown parameters. However, it may not assure for controlling nonlinear plants

with unknown structure. In recent years, an Artificial Neural Network (ANN) and Fuzzy logic

techniques has become very popular in many control applications due to their higher computation rate

and ability to handle nonlinear system. Some of the relevant research work including ANN as a part of

Design of Intelligent Adaptive Control using Neural Network and Fuzzy Logic Controller 157

control scheme is illustrated next. A robust adaptive control of uncertain nonlinear system using neural

network is discussed in [3] .Various types of NN have been efficiently utilized in identification of

nonlinear systems [4],[5]. A variety of algorithms are utilized to adjust the weight of the NN. In a

typical multilayered NN, the weights in the layers can be adjusted as to minimize the output error

between the NN’s output and the observed output. The back propagation algorithm for efficiently

updating the weight is useful in many applications such identification of nonlinear systems. Off-line

iterative algorithm can be employed in such care of identification or modeling. However, in the aspect

of control, the NN should work in on line manner. In the control system structure, the output of NN is

the control input to the nonlinear controlled system. i.e., there is the unknown nonlinear system

between the NN and the output error. In this case, in order to apply any learning rules, it is need the

derivatives of the system output with respect to the input [6], [7] presented a simple structure of NN

based feed forward controller which is equivalently an inverse of the controlled system after the NN

completes learning of the weights which are adjusted to minimize the feedback error. Narendra and

parthasarathy [8] has shown in general indirect approach to nonlinear discrete time neuro – control

scheme which consists of identification and adaptive control by using the [9] and [10] that the NN –

based adaptive control algorithm can cooperate well with identification of the nonlinear functions to

realize a nonlinear adaptive control when the nonlinear adaptive control when the non linear control

scheme is feedback linearizable. Kamalsudan and Ghandakly [11] presented a fighter aircraft pitch

controller evolved from a dynamic growing RBFNN in parallel with a model reference adaptive

controller. The abilities of a neural network for nonlinear approximation and development for

nonlinear approximation and the development of a nonlinear adaptive controller based on neural

networks has been discussed in many works [12], [13]. The use of neural networks for identification

and control of non linear system has been demonstrated in [14] discusses a direct adaptive neural

network controller for a class of non linear system. An Adaptive Inverse Model Control System

(AIMCS) is designed for the plant, and two Radial Basis Function (RBF) neural networks are utilized

in the AIMCS discussed in [15]. An adaptive-neuro-fuzzy-based sensor less control of a smart-material

actuator is presented in [16].It is well known that fuzzy technique has been widely used in many

physical and engineering systems, especially for systems with incomplete plant information [17]-[22].

In addition to fuzzy logic, it has been widely applied to controller designs for nonlinear systems [23]-

[27]. A novel fuzzy model reference based controller for controlling nonlinear plants can be found in

[28]. Hugang Han [29] proposed an adaptive fuzzy controller for a class of nonlinear system with

disturbance. A problem of Fuzzy-Approximation-Based adaptive control for a class of nonlinear time-

delay systems with unknown nonlinearities and strict-feedback structure is discussed in [30]. Cheng-

Wu Chen et al [31] discussed a proposed a method of stability analysis for a GA-Based reference

ANNC which is capable of handling problems in a nonlinear system.

Fuzzy Logic (FL) technique has been proposed to replace PI controllers in different error

minimization applications [32], [33]. Various applications of FL have shown a fast growth in the past

few years. FLC has become popular in the field of industrial control applications for solving control,

estimation, and optimization problems [34]. An adaptive control approach for time-varying permanent-

magnet synchronous motor (PMSM) systems with chaotic behavior is discussed in [35]. Observer-

based model reference output feedback tracking control design for switched linear systems with time

delay is investigated in [36]. A learning approach of combining MRAC with the use of fuzzy systems

as reference models and controllers for control dynamical systems can be found in [37]. A hybrid

approach by combining fuzzy controller and neural networks for learning-based control is proposed in

[38].The adaptive controller is used in various practical applications have attracted much attention in

the field of control engineering. This is due to their promising potential for the tasks of tackling the

presence of unknown parameters or unknown variation in plant parameters with better performance

than those of constant gain feedback control law. In general, the external load disturbances always

exist, although it is bounded. So, the controller without considering the disturbances cannot stabilize

the closed-loop control system. A solution to this problem is to incorporate dead-zone technique in the

adaptive controller. With this approach, the controller will stop updating the control parameters when

158 R. Prakash and R. Anita

the identifier error is smaller than some threshold. Thus, it can prevent the estimated parameters from

being infinity. However, the regulation error of the system will only be asymptotically bounded if large

threshold is used, resulting in undesirable closed-loop performance. All control techniques have their

individual characteristics. Hence, combining the merits of the adaptive control with that of the neural

network control theories and then designing a new stabilizing controller will have better performance

than that based on one control theory

PI controllers are widely used in industrial control systems applications. They have a simple

structure and can offer a satisfactory performance over a wide range of operation. Therefore, the

majority of adaptation schemes described in the literature for MRAS employ a simple fixed-gain linear

PI controller to generate the estimated output. However, due to the continuous variation in the plant

parameters and the operating conditions, in addition to the nonlinearities present in the plant, PI

controllers may not be able to provide the required performance. Not much attention has been devoted

to study other types of adaptation mechanisms used to minimize the error to obtain the estimated

output. In this paper, this point is addressed by presenting two novel intelligent model reference

adaptive control schemes are proposed to replace the classical PI controller used in conventional model

reference adaptive scheme by a neural network or fuzzy logic controller. A NN- MRAC scheme is

proposed to improve the tracking performance. Furthermore, a FLC-MRAC is proposed as another

nonlinear optimizer, which ensures plant output trajectory tracks the reference model output trajectory

and tracking error is zero with minimum time as possible.

The neural network and fuzzy logic controller is used to compensate the nonlinearity and

disturbance of the plant that is not taken into consideration in the conventional MRAC. The role of

model reference adaptive controller is to perform the model matching for the uncertain linearized

system to a given reference model. The paper is organized as follows. Section 2 proposes the structure

of an MRAC design. Section 3 describes the PI controller-based model reference adaptive controller

and Section 4 and 5 describe the discussion of the proposed schemes. Section 6 analyses the result and

discussion of the proposed schemes and the conclusions are given in section 7.

2. Structure of an MRAC design The MRAC is one of the major approaches in adaptive control. The desired performance is expressed

as a reference model, which gives the wished response to an input signal. The adjustment mechanism

changes the parameters of the regulator by minimizing the error between the system output and the

reference model.

2.1. The Plant Model and Reference Model System

To consider a Single Input and Single Output (SISO), Linear Time Invariant (LTI) plant with strictly

proper transfer function

)(

)(

)(

)()(

sR

sZK

su

sysG

P

p

P

p

P == (1)

where up is the plant input and yp is the plant output .Also, the reference model is given by

)(

)(

)(

)()(

sR

sZK

sr

sysG

m

mm

mm == (2)

where r and ym are the model’s input and output. Define the output error as

mp yye −= (3)

Now the objective is to design the control input Umr such that the output error, e goes to zero

asymptotically for arbitrary initial condition, where the reference signal r(t) is piecewise continuous

and uniformly bounded. The plant and reference model satisfy the following assumptions


Assumptions

1. Zp(s) is a monic Hurwitz polynomial of degree mp

2. An upper bound n of degree np of Rp(S)

3. The relative degree n*= np - mp of G(s)

4. The sign of the high frequency gain Kp are known

5. Zm(s), Rm(s) are monic Hurwitz polynomials of degree qm, pm respectively, where pm ≤ n

6. The relative degree nm*= pm- qm of Gm(s) is the same as that of G(S), i.e., nm*= n*

2.2. MRAC with Relative Degree n =1

As in Ref [1] the following input and output filters are used,

pguF += 11 ωω� (4)

pgyF += 22 ωω�

where F is an )1(*)1( −− nn stable matrix such that det )( FSI − is a Hurwitz polynomial whose roots

include the zeros of the reference model and that (F,g) is a controllable pair. It is defined as the

“regressor” vector T

p

TTry ],,,[ 21 ωωω = (5)

In the standard adaptive control scheme, the control Umr is structured as

ωθ T

mrU = (6)

where TC ],,,[ 0321 θθθθ = is a vector of adjustable parameters, and is considered as an estimate of a

vector of unknown system parameters θ*

.

The dynamic of tracking error

ωθ T

m psGe~

)( *= (7)

Where m

p

K

KP =* and *)(

~θθθ −= t represents parameter error. Now in this case, since the

transfer function between the parameter error θ~

and the tracking error e is strictly positive real (SPR)

[1], the adaptation rule for the controller gain θ is given by

)sgn(1

∗Γ−= Pe ωθ� (8)

where Γ is a positive gain.

The adaptive laws and control schemes developed are based on a plant model that is free from

disturbances, noise and unmodelled dynamics. These schemes are to be 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 measured input and output may be corrupted by noise and

external disturbances. It is shown by using conventional MRAC that adaptive scheme is designed for a

disturbance free plant model and may go unstable in the presence of small disturbances.

3. PI Controller-Based Model Reference Adaptive Controller The PI algorithm remains the most popular approach for industrial process control, despite continual

advances in control theory. This is because the PI algorithm has a simple structure which is

conceptually easy to understand and implement in practice but also the algorithm provides adequate

performance in the vast majority of applications. A PI controller may be considered as an extreme form

of a phase lag compensator. The transfer function of PI Controller is generally written in the “Parallel

form” given by (9) or the “ideal form’’ given by (10).

S

KK

SE

SUSG i

P

pi

PI +==)(

)()(

(9)

)1

1(i

PT

K += (10)


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 is the integral time constant. The “two term” functionalities are highlighted by the

following.

• The proportional term-providing an overall control action proportional to the error signal

through the all – pass gain factor.

• The integral term – reducing steady state errors through low – frequency compensation by

an integrator

The disturbance and nonlinear component are added to the plant input of the conventional

model reference adaptive controller, in this case the tracking error has not reaches to zero and the plant

output is not tracked with the reference model plant output. The conventional MRAC fails completely

under the action of the external disturbance and nonlinearities, where a degradation in the performance

due to overshoot is observed. The disturbance is considered as a random noise signal. To improve the

system performance, the PI controller based Model Reference Adaptive Controller (PI-MRAC) is

proposed. In this scheme, the controller is designed by using parallel combination of conventional

MRAC system and PI controller. The Block diagram of PI-MRAC scheme is shown in Fig.1. The

control input U of the plant is given by the following equation,

vUUU pimr ++= (11)

where Umr is the output of the adaptive controller ,Upi is the output of the PI controller and v is the

disturbance.

ωθ T

mrU =

where θ is the update law vector, and ω is the parameter vector.

The input of the PI controller is the error, in which the error is the difference between the plant

output yp(t) and the reference model output ym(t). The PI controller gains can be selected as high as

possible, but are limited by the noise. In this paper PI gains are obtained by trial and error method. In

this case also, the disturbance and nonlinear component is added to the input of the plant. The PI-

MRAC improves the system performance comparing to the conventional MRAC scheme. However

due to the continuous variation in the system parameters and the operating conditions, in addition to

the nonlinearities present in the system, PI-MRAC scheme may not be able to provide the required

performance

Figure 1: Block diagram of PI-MRAC

4. Neural Network-Based Model Reference Adaptive Controller In this scheme, the controller is designed by using parallel combination of conventional MRAC system

and neural network controller. The training patterns of neural network are extracted from the input and

output of PI controller of designed PI -MRAC scheme. The block diagram of proposed neural network-

based model reference adaptive controller (NN-MRAC) is shown in Fig. 2


This scheme is restricted to a case of Single Input Single Output (SISO) control, noting that the

extension to Multiple Input Multiple Output (MIMO) is possible. To keep the plant output yp converges

to the reference model output ym, it is synthesize the control input U by the following equation,

vUUU nnmr ++= (12)

where Umr is the output of the adaptive controller, Unn is the output of neural network and v is the

disturbance

Figure 2: Block diagram of the NN- MRAC

Stability of the system and adaptability are then achieved by an adaptive control law Umr

tracking the system output to a suitable reference model output, such as that the error e = yp-ym = 0

asymptotically. The NN provides an adaptive control for better system performance and solution for

controlling nonlinear processes.

The ANN controllers designed in most of the work use a complex network structure for the

controller. The aim of this work is to design a simple ANN controller with as low neurons as possible

while improving the performance of the controller. The inputs of the neural network are the error and

change in error. Here the multilayer back propagation neural network is used in the proposed method.

The multilayer back propagation network is especially useful for this purpose, because of its inherent

nonlinear mapping capabilities, which can deal effectively for real-time online computer control. The

NN of the proposed method has three layers: an input layer with 2 neurons, a hidden layer with 2

neurons and an output layer with one neuron.

Let xi be the input to the ith

node in the input layer, zj be the input to the jth

node in the hidden

layer, y be the input to the node in the output layers. Furthermore Vij be the weight between the input

layer and hidden layer, Wj1 is the weight between the hidden layer and the output layer. The relations

between inputs and output of NN is expressed as,

∑=

− +=n

i

ijiojinj VxVZ1

(13)

)( _ injj ZFz = (14)

∑ =− +=P

j jjin WzWY1 101

(15)

)( inYFy −= (16)

where F (.) is the activation function.

The sigmoid function for the activation function is chosen as follows

ax

axF −

−+=

)exp(1

2)(

µ (17)

where µ > 0, a is a specified constant such as that a ≤ 0, and F(x) satisfies –a<F(x) <a

The aim of training to minimize the sum of square error energy function,


2][2

1)( kk ytkE −= (18)

The weight are updated by using

jinkk

j

j zYFytW

EW )()( 1

1

1 −−−=∂

∂−=∆ ηη

)()( 1

01

01 inkk YFytW

EW −−−=

∂

∂−=∆ ηη (19)

1

1)( j

k

kiinj

ij

ij WxZFV

EV ∑−−=

∂

∂−=∆ δηη

1

1

0

0 )( j

k

kinj

j

j WZFV

EV ∑−−=

∂

∂−=∆ δηη (20)

where η is the learning role

))]())(([(2)(

)(inin

in

in YFaYFaaY

YF

−+−=

∂

∂−

−

− µ (21)

))())(((2)(

)(injinj

inj

injZFaZFa

aZ

ZF−−

−

−+−=

∂

∂ µ (22)

The set of inputs and desired outputs of neural network are extracted from the PI controller of

designed PI controller based MRAC scheme. A back propagation neural network is trained till a certain

fixed error goal is reached. Here, the network is trained for an error goal of 0.0005.

Training the Back Propagation network requires the following steps:

1. Initialize the weights and biases in the network randomly.

2. Apply inputs to the network through the input nodes.

3. Apply the target output values.

4. Calculate the error between the output and the target output.

5. Repeat steps 1-4 until the error for the entire network is acceptably low.

6. The structure of the neural network for NN-MRAC scheme is shown in Fig. 3.

Figure 3: Structure of the neural network for NN-MRAC scheme

5. Fuzzy Logic Controller -Based Model Reference Adaptive Controller Various applications of Fuzzy Logic (FL) have shown a fast growth in the past few years. FLC has

become popular in the field of industrial control applications for solving control, estimation, and

optimization problems. In this section FLC is proposed to replace the PI controller of PI-MRAC

scheme and it used for error minimization. In the PI-MRAC scheme, the PI controller is generating a

quantity, in such a way so as to minimize a specified error. Therefore, FLC can replace the

conventional PI controller to solve the optimization problem. A Fuzzy-Logic Controller based Model

Reference Adaptive Controller (FLC-MRAC) scheme is proposed to improve the system performance.

The controller structure proposed in this paper for the FLC-MRAC is shown in Figure 4 which consists

of a parallel MRAC, and a FLC. While the MRAC forces the plant output to follow closely the output

of the model which represents the desired closed loop behavior, and the FLC used for various

operating conditions, the objective of the fuzzy logic control is to determine the control signal for


controlling nonlinear processes. The error and the change in error are given input to the FLC. The rules

and membership function of FLC are formed from the input and output waveforms of PI controller of

designed PI-MRAC.

Figure 4: Block diagram of the FLC-MRAC

To keep the plant output yp converges to the reference model output ym, it is synthesize to

control input U by the following equation,

vUUU fzmr ++= (24)

where Umr is the output of the adaptive controller ,Ufz is the output of the fuzzy logic controller and v is

the disturbance signal

ωθ T

mrU = T

C ],,,[ 0321 θθθθ =

T

p ry ],,,[ 21 ωωω =

where θ is the update law vector, and ω is the parameter vector.

The proposed FLC is a Mamdani-type rule base where the inputs are the error (e) and error

change (ce) which can be defined as

)()()( kykyke pm −=

)1()()( −−= kekekce

where ym(k) is the response of the reference model at kth

sampling interval, yp(k ) is the response of the

plant output at kth

sampling interval, e(k) is the error signal at kth

sampling interval, ce(k) is the error

change signal at kth

sampling interval.

FLC consists of three stages: fuzzification, rule execution, and defuzzification. In the first

stage, the crisp variables e(kT) and ce(kT) are converted into fuzzy variables error (e) and change in

error (ce) using the triangular membership functions. Each fuzzy variable is a member of the subsets

with a degree of membership varying between ‘0’ (non-member) and ‘1’ (full member).In the second

stage of the FLC, the fuzzy variables error (e) and change in error (ce) are processed by an inference

engine that executes a set of control rules containing in a rule base. 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. The feature of the proposed scheme is that the FLC can compensate for the

nonlinearity of the system to linearize the dynamics from the output of the adaptive controller to the

system output, while the role of the adaptive controller is to perform the model-matching for the

linearized system.


5.1. Construction of Fuzzy Rules

In this paper the fuzzy rules are formulated by using the input and output waveforms of the PI

controller of designed PI-MRAC scheme behavior and the experience of control engineers. Let us

consider an example of a PI controller input (error), change in error and PI controller output waveforms

are given by Fig.5. Fuzzy rules and membership for error (e) and change in error (ce) and output (Ufc)

are created by using the Fig. 5.The developed fuzzy rules are given in Table.1

Figure 5(a): PI controller input (error), (b) change in error, (c) PI controller output (Upi)

The membership functions for fuzzy variable error (e), change in error (ce) and output (Ufc) are

shown in Fig .6

Figure 6: Fuzzy controller input and output membership functions. (a) Error (e). (b)Change in Error (ce). (c)

Output (Ufc)

Table 1: Linguistic rule base

1 If error is ‘A’ and change in error is ‘A’ then the output is ‘D’

2 If error is ‘B’ and change in error is ‘B’ then the output is ‘F’

3 If error is ‘C’ and change in error is ‘D’ then the output is ‘H’

4 If error is ‘D’ and change in error is ‘F’ then the output is ‘J’

5 If error is ‘E’ and change in error is ‘C’ then the output is ‘A’

6 If error is ‘F’ and change in error is ‘I’ then the output is ‘K’

7 If error is ‘G’ and change in error is ‘C’ then the output is B

8 If error is ‘H’ and change in error is ‘H’ then the output is ‘I’

9 If error is ‘I’ and change in error is ‘C’ then the output is ‘C’

10 If error is ‘J’ and change in error is ‘E’ then the output is ‘E’

11 If error is ‘K’ and change in error is ‘G’ then the output is ‘G’


6. Results and Discussion In this section, the results of computer simulation for the conventional MRAC, PI-MRAC, NN-MRAC

and FLC-MRAC scheme is evaluated by applying inputs of varying magnitude plus nonlinearities and

disturbance in the plant. The same series of noise disturbance has been applied for each simulation.

The results show the effectiveness of the proposed schemes and reveal its performance superiority to

the conventional MRAC technique. A detailed simulation comparison has been carried out using with

an example.

The system set of data is as follows:

A third order system with the transfer function

5.275

75.34)(

23

2

+++

++=

SSS

SSSG

is used to study and the reference model is chosen as

6116

75.34)(

23

2

+++

++=

SSS

SSSGM

which has relative degree n*= 1

The initial value of conventional MRAC scheme the controller parameters are chosen as θ(0) =

[3, 18,-8, 3]T. Umr is the control input of the plant for conventional MRAC

ωθ T

mrU =

where TC ],,,[ 0321 θθθθ = is the update law vector, T

p ry ],,,[ 21 ωωω = is the regressor vector and

pguF += 11 ωω�

pgyF += 22 ωω�

where F is an )1(*)1( −− nn stable matrix such that det )( FSI − is a Hurwitz polynomial whose roots

include the zeros of the reference model and that (F,g) is a controllable pair

In this example, the nonlinearity component backlash is given to the input of linear system is

shown in Fig. 7

Figure 7: Nonlinear System

The PI controller gains can be selected as high as possible, but are limited by the noise. In the

PI-MRAC scheme, the value of the PI controller gains Kp = 22and Ki =96, were shown to provide a

better performance for the PI-MRAC scheme. The U is the control input of the plant for the PI-MRAC

scheme

vUUU pimr ++=

The simulink model of the PI-MRAC scheme developed is given in Fig. 8

Figure 8: Simulink Model of the PI –MRAC


In the neural network-based model reference adaptive controller, the details of the trained

network are shown in Fig. 9.

The U is the control input of the plant for the NN-MRAC scheme.

vUUU nnmr ++=

Figure 9: Details of the trained network

The simulink model of the neural network-based model reference adaptive controller developed

is given in Fig .10

Figure 10: Simulink Model of the NN –MRAC

To obtain optimal performance compared to PI-MRAC scheme and NN-MRAC scheme, FLC-

MRAC is employed. In FL-MRAC scheme, the fuzzy variables ‘e’ and ‘ce’ are processed by an

inference engine that executes a set of control rules containing in (6x6) rule base as shown in Table.2.

The fuzzy rules and membership functions are formulated using the input and output waveforms of the

PI controller of designed PI-MRAC scheme and the experience of control engineers. Each variable of

the FLC has six membership functions. The following fuzzy sets are used: NH (Negative High), NL

(Negative Large), ZE (Zero), PS (Positive Small), PM (Positive Medium) and PH (Positive High).

The U is the control input of the plant for the FLC-MRAC scheme.

vUUU fzmr ++=

Table 2: Linguistic rule base

ce

e NH NL ZE PS PM PH

NH NH NL PS PS PM PM

NL NL NL PS PS PM PM

ZE PS PS PM PM PM PM

PS PS PS PM PM PM PH

PM PM PM PM PM PH PH

PH PM PM PM PH PH PH


The membership functions for fuzzy variable error (e), change in error (ce) and output (Ufc) are

shown in Fig.11.

Figure 11: Membership functions for fuzzy variable error (e), change in error (ce) and output (Ufc)

The simulink model of the FLC-MRAC scheme is given in Fig .12

Figure 12: Simulink Model of the FLC- MRAC system

Figs. 13 show the performance of the MRAC with input r (t) = 1.6. In this case there is no

disturbance and nonlinearities are given in the plant.

Figure 13: Response of the conventional MRAC scheme without disturbance and nonlinearities :( a) Plant and

model reference response; (b) Tracking error

(a) (b)

Figs. 14–17 show the performance of the MRAC, PI-MRAC, NN-MRAC and FLC-MRAC

schemes for example 1 with input r(t)= 1.6 plus disturbance v(t)=cos5.9t and nonlinearity component

backlash with dead bandwidth M=10 are given to the plant


Figure 14: Response of the conventional MRAC scheme with disturbance and nonlinearities (a) Plant and


(a) (b)

Figure 15: Response of the PI- MRAC scheme with disturbance and nonlinearities: (a) Plant and model

reference response; (b) Tracking error.

(a) (b)

Figure 16: Response of the NN- MRAC scheme with disturbance and nonlinearities: (a) Plant and model

reference response; (b) Tracking error

(a) (b)


Figure 17: Response of the FLC- MRAC scheme with disturbance and nonlinearities: (a) Plant and model

reference response; (b) Tracking error

(a) (b)

Fig. 18 show the performance of the MRAC with input r (t) = 15sin0.7t without disturbance and

nonlinearities are given to the plant

Figure 18: Response of the conventional MRAC scheme without disturbance and nonlinearities :( a) Plant and


(a) (b)

Figs. 19–22 show the performance of the MRAC, PI-MRAC and MRAC scheme for example 1

with input r (t) = 15sin0.7t plus disturbance v (t) =25 sin 0.7t +12 cos5.9t and nonlinearity component

backlash with dead bandwidth M=15 are given to in the plant

Figure 19: Response of the conventional MRAC scheme with disturbance and nonlinearities (a) Plant and


(a) (b)


Figure 20: Response of the PI- MRAC scheme with disturbance and nonlinearities: (a) Plant and model


(a) (b)

Figure 21: Response of the NN- MRAC scheme with disturbance and nonlinearities: (a) Plant and model


(a) (b)

Figure 22: Response of the FLC- MRAC scheme with disturbance and nonlinearities: (a) Plant and model


(a) (b)

Figs. 13 and 18 show the response of the conventional MRAC scheme without disturbance and

nonlinearities. It is shown that the plant output is tracks with the reference model output and the

tracking error approaches the zero. The performance of the conventional MRAC, PI-MRAC, NN-

MRAC and FLC-MRAC scheme is evaluated by applying inputs plus disturbance and nonlinearities in

the plant. The results show the effectiveness of the proposed schemes to force the plant to follow the

model, under uncertainties. Extensive simulation tests were carried out to compare the four adaptation

schemes: conventional MRAC, PI – MRAC scheme, NN- MRAC scheme and FLC-MRAC. In the

simulation results of conventional MRAC, PI-MRAC NN-MRAC and FLC-MRAC schemes, the

dotted line and solid line represents the model reference trajectory and plant trajectory respectively. In


conventional MRAC scheme with disturbance and nonlinearities, the plant output is poor with large

overshoots and oscillations as shown in Figs. 14 and 19.

Figs. 15 and 20 show the response of the PI-MRAC scheme. In this case, the overshoots and the

oscillations are reduced compared to the conventional MRAC scheme. However, due to the continuous

variation in the system parameters and the operating conditions, in addition to the nonlinearities and

disturbance present in the system, PI-MRAC scheme may not be able to provide the required

performance. In the proposed NN-MRAC scheme, the overshoots and the oscillations are much

smaller, yielding a much better performance than the conventional MRAC scheme and PI-MRAC

scheme as shown in Figs.16 and 21. However, the application of the NN-MRAC scheme does not

considerably improve the steady-state performance. In the proposed FLC- MRAC scheme the plant

output has tracked with the reference model output and the tracking error becomes zero within 4

seconds with less control effort as shown in Figs.17 and 22, and which gives the optimal performance

than the other methods. The FLC- MRAC scheme improves the transient and steady state performance.

The responses performed by the MRAC scheme are observed to be inferior to that of the NN-

MRAC and FLC-MRAC schemes. Also, the response of the MRAC shows large overshoot and

oscillation. Further, the response of the output performed by the NN-MRAC and FLC-NRAC scheme

shows more satisfactory results for the bounded disturbances and nonlinearities with unknown as well

as time-varying characteristics than that of the MRAC. From the above simulations, it is shown that the

control algorithm using only MRAC scheme can guarantee that the tracking error approaches the zero

if there are no disturbances and uncertainties, and plant output converges to the reference model output.

However, it is said that only using the MRAC scheme will not stabilize the controlled systems with

disturbances and nonlinearities

From the simulation results, because of the existing bounded disturbances and nonlinearities,

the controlled system using the control algorithm only using the model reference adaptive controller

will be unstable. When using the neural network and the model reference adaptive controller in

coordination in which the control law is provide better performance and improve the steady state

performance. But when using the fuzzy logic controller and the model reference adaptive controller in

coordination in which the control law is used to cope with nonlinearities and bounded disturbances, the

controlled system can be robustly stabilized all the time. From the above discussions, the proposed

control algorithm both with the fuzzy logic controller and the conventional model reference adaptive

controller can be a promising way to tackle the problem of controlling the nonlinear systems and

bounded time-varying disturbances.

From the above simulations, it is shown that the control algorithm using only the model

reference adaptive controller will not stabilize the nonlinear controlled systems with disturbances.

From Figs.16 and 21, it is seen that the control algorithm both with the neural network control and the

model reference adaptive controller working in coordination to improve the steady state performance.

From Figs.17 and 22, it is seen that the control algorithm both with the fuzzy logic control and the

model reference adaptive controller working in coordination can cope up with the uncertain dynamic

system and bounded disturbances, but the control algorithm without the neural network or fuzzy logic

network compensating control cannot. The proposed NN- MRAC scheme shows better control results

compared to those by the conventional MRAC and PI-MRAC system. Moreover, the FLC- MRAC

scheme shows faster and optimal response compared to the PI-MRAC scheme and NN-MRAC

scheme.

From these simulation results it is observe that:

1. In conventional MRAC the plant output is not tracked with the reference model output.

The conventional MRAC fails completely under the action of the external disturbance and

nonlinearities, where a degradation in the performance due to overshoot is observed.

2. The PI-MRAC scheme, the overshoots and the oscillations are reduced compared to the

conventional MRAC scheme In the PI-MRAC scheme, the plant output is nearly track

with the reference model output. However it will not be able to provide the required

performance.


3. The proposed NN- MRAC scheme shows better control results compared to those by the

conventional MRAC and PI-MRAC system. The NN-MRAC scheme is improve the

transient performance. However, the NN-MRAC scheme does not considerably improve

the steady-state performance.

4. The proposed FLC-MRAC design approach can keep the plant output in track with the

reference model and tracking error becomes zero within 4 seconds. The proposed FLC-

MRAC controller gives better performances in terms of steady-state error, settling time

and overshoot. The FLC-MRAC scheme is improve the both steady-state performance

and transient performance. Hence it can be concluded that the proposed FLC-MRAC

scheme is more robust performance than the other schemes.

On the contrary, the proposed method has much less error than the conventional method in spite

of nonlinearities and disturbance. The simulation results have confirmed the efficiency of the proposed

FLC-MRAC scheme for applying disturbances and nonlinearities.

6.2. Implementation Issue

The proposed method can be widely used in most of the industrial nonlinear and complex applications

such as machine tools, industrial robot control, position control, and other engineering practices. The

proposed FLC-MRAC is relatively simple and does not require complex mathematical operations. It

can be readily implemented using conventional microprocessors or microcontrollers. The execution

speed of the FLC-MRAC scheme can be improved by using advanced processors such as reduced

instruction set computing (RISC) processors or digital signal processors (DSP's) or ASIC's (application

specific integrated circuits).

7. Conclusion In this paper, two novel intelligent model reference adaptive control schemes is proposed to replace the

PI controller of PI based MRAC by a neural network and fuzzy logic controller. In NN -MRAC the

training patterns of neural network are extracted from the PI controller of designed PI -MRAC scheme.

In FLC-MRAC the fuzzy rules and membership functions are formed from the input and output

waveforms of PI controller of PI- MRAC scheme. A detailed simulation comparison has been carried

out using with an example. The proposed FLC-MRAC controller shows very good tracking results

when compared to the conventional MRAC and the PI-MRAC and NN-MRAC scheme. Simulations

and analyses have shown that the steady state performance and transient performance can be

substantially improved by proposed FLC-MRAC scheme In proposed FLC-MRAC scheme, the system

output tracks very closely the reference model in spite of the disturbances and nonlinearities. Thus the

FLC-MRAC controller is found to be extremely effective, efficient and useful. Due to its simple

operation, the proposed FLC-MRAC can be readily implemented using conventional microprocessors.

References [1] K.J. Astrom and B. Wittenmark Adaptive control (2nd Ed.) Addison-Wesley-1995.

[2] Petros A loannou, Jing sun. “Robust Adaptive control”, upper saddle River, NJ: Prentice-Hall

1996.

[3] M.B.Mofal and A.J Calise,” Robust adaptive control of uncertain nonlinear systems using

neural network”, in proc. Amer control conf 1997. PP.1996-2000

[4] Chen.S,Billings, S.A and Grant, P.M.,1991, “Nonlinear system identification using neural

network”. Int.J.control 51, 1191-1214

[5] Guchi,Y and Sakai, H, 1991, “A nonlinear regulator design in the presence of system

uncertainities using multilayered neural network”, IEEE Toans Neural network, 2, 427-432


[6] Yamada, T and Yabuta, T., 1992,“Neural network controller using autotunning method for non

linear function”. IEEE Trans. Neural Network,3, 595-601

[7] Kawalo, M. Furukawa.K and Suzuki, R., 1987, “A hierachical neural network for control and

learning of Voluntary movement”, Biol Cybern, 57, 169-185

[8] Narendra, K.S and parthasarathy, 1990, “identification and control of dynamic systems using

neural network”. IEEE Tans. Neural network 1, 4-27

[9] Chen, F.C, 1990, “Back propagation neural networks for non linear Self – tuning adaptive

control”, IEEE contr. Syst. Mag., 10,40-48

[10] Liu, c.c and chen, F.C., 1993, “Adaptive control of non – linear continuous – time systems

using neural networks- general relative degree and MIMO cases”, INT.J. control, 58, 317-335

[11] S.Kamalsudan and Adel A Ghandakly. “A Nueral Network Parallel Adaptive Controller for

Fighter Aircraft Pitch- Rate Tracking”,IEEE transaction on instrumentation and measurement.

Nov 2010.

[12] A.J.Calise, N. Hovakimyan and M. Idan, “Adaptive Output Feedback Control of Nonlinear

System Using Neural Networks”, Automatica vol. 37, No.8 pp1201-1211 Aug 2001.

[13] J.I. Arciniegas, A.H. Eltimashy and K.J. Cios, “Neural Networks Based Adaptive Control of

Flexible Arms”, Neurocomputing, vol.17 no.314, pp.141-157, Nov.1997.

[14] M.S. Ahmed “Neural Net-Based Direct Adaptive Controller a Class Of Nonlinear Plants”,

IEEE trans Autom. control. Vol.45, no, 1 pp-119-123, Jan 2000

[15] Yuan Xiaofang; Wang Yaonan; Sun Wei; Wu Lianghong, “RBF Networks-Based Adaptive

Inverse Model Control System for Electronic Throttle”, IEEE Transactions on Control Systems,

vol. 18, no. 3. pp. 750 - 756, May 2010

[16] Sadighi,A. Kim, W.“ Adaptive-Neuro-Fuzzy-Based Sensorless Control of a Smart-Material

Actuator”, IEEE/ASME Transactions on Mechatronics, vol.1, no.2, pp. 371 - 379, Jan. 2011

[17] J.Dong,Y.Wang and G.-H. Yang, Control synthesis of continuous time T–S fuzzy systems with

local nonlinear models, IEEE Trans.Fuzzy Syst., vol. 39, no. 5. pp. 1245–1258, Oct. 2009.

[18] J.-H. Park,G.-T. Park,S.-H. Huh, S.-H. Kim and C.-J.Moon, Direct adaptive self- structuring

fuzzy controller for nonaffine nonlinear system, Fuzzy Sets and Systems, vol. 153, no. 3, pp.

429–445, Feb.2005.

[19] N. Al-Holou, T. Lahdhiri, D. S. Joo, J. Weaver, and F. Al-Abbas, Sliding mode neural network

inference fuzzy logic control for active suspension systems, IEEE Trans. Fuzzy Syst., vol. 10,

pp. 234–246, Apr. 2002.

[20] R.-J. Wai, M.-A. Kuo, and J.-D. Lee, Cascade direct adaptive fuzzy control design for a

nonlinear two-axis inverted-pendulum servomechanism, IEEE Trans. Syst., Man, Cybern., Part

B, vol. 38, no. 2, pp. 439–454, Apr. 2008.

[21] T.-H. S. Li, S.-J. Chang, and W.Tong, 2004, Fuzzy target tracking control of autonomous

mobile robots by using infrared sensors, IEEE Trans. Fuzzy Systems, vol. 12, no. 4, pp. 491-

501,Aug. 2004.

[22] K. Tanaka and M. Sano, A robust stabilization problem of fuzzy control systems and its

application to backing up control of a truck trailer, IEEE Trans. Fuzzy Syst., vol. 2, no. 1, pp.

119--134, Feb. 1994.

[23] S. Labiod and T. M. Guerra, Adaptive fuzzy control of a class of SISO nonaffine nonlinear

systems, Fuzzy Sets and Systems, vol. 158, no. 10, pp. 1126–1137, May. 2007.

[24] G. Feng, A survey on analysis and design of model-based fuzzy control systems, IEEE Trans.

Fuzzy Syst., vol. 14, no. 5, pp. 676–697, Oct. 2006.

[25] K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix

Inequality Approach, New York: Wiley, 2001.

[26] H. O.Wang, K. Tanaka, and M. Griffin, An approach to fuzzy control of nonlinear systems:

Stability and design issues, IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14--23, Feb. 1996.

[27] K. Y. Lian, and J. J. Liou, Output Tracking Control for Fuzzy Systems Via Output Feedback

Design, IEEE Trans. Fuzzy Syst., Vol. 14, No.5, pp. 628-639, Oct. 2006.


[28] Mojtaba Ahmadieh Khanesar and Mohammad Teshnehlab, Direct fuzzy model reference

controller for SISO nonlinear plants using observer, International Journal of Innovative

Computing, Information and Control, Volume 6, Number 1, January 2010

[29] Hugang Han, Adaptive Fuzzy Controller for a Class of Nonlinear Systems, International

Journal of Innovative Computing, Information and Control, Volume 1, Number 4, December

2005

[30] Bing Chen; Xiaoping Liu; Kefu Liu and Chong Lin, Fuzzy-Approximation-Based Adaptive

Control of Strict-Feedback Nonlinear Systems With Time Delays, IEEE Trans. Fuzzy Syst.,

vol.18, no. 5, pp. 883 – 892, Oct. 2010

[31] Cheng-Wu Chen and Po-Chen Chen, GA-based adaptive neural network controllers for

nonlinear systems, International Journal of Innovative Computing, Information and Control,

Volume 6, Number 4, April 2010

[32] S. Mir, M. E. Elbuluk, and D. S. Zinger, PI and fuzzy estimators for tuning the stator resistance

in direct torque control of induction machines, IEEE Trans. Power Electron., vol. 13, no. 2, pp.

279–287, Mar. 1998.

[33] B. Karanayil, M. F. Rahman, and C. Grantham, PI and fuzzy estimatorsfor on-line tracking of

rotor resistance of indirect vector controlled inductionmotor drive, Proc. IEEE Int. Electr.

Mach. Drives Conf., 2001,pp. 820–825.

[34] P. Vas, Artificial-Intelligence-Based Electrical Machines and Drives-Application of Fuzzy,

Neural, Fuzzy-Neural and Genetic Algorithm Based Techniques, New York: Oxford Univ.

Press, 1999.

[35] Hyun Cheol Cho, Kwon Soon Lee and M. Sami Fadali, Adaptive control of PMSM systems

with chaotic nature using lyapunov stability based feedback linearization, International Journal

of Innovative Computing, Information and Control, Volume 5, Number 2, February 2009

[36] Qing-Kui Li, Xiang-Jie Liu, Jun Zhao2 and Xi-Ming Sun, Observer based model reference

output feedback tracking control for switched linear systems with time delay: constant delay

case, International Journal of Innovative Computing, Information and Control, Volume 6,

Number 11, November 2010

[37] J. R. Layne and K. M. Passino, Fuzzy model reference learning control for cargo ship steering,

IEEE Contr. Syst. Mag., vol. 13, no. 12, pp.23–34, 1993.

[38] J. T. Spooner and K. Passino, Stable adaptive control using fuzzy systems and neural networks,

IEEE Trans. Fuzzy Syst., vol. 4, pp. 339–359, 1996

EJSR_57_1_14

Documents

controlling nonlinear plants

intelligent adaptive control

fuzzy logic controller

classical pi controller

nonlinear adaptive control

conventional mrac system

fuzzy logic

linear system