Neuro- PI controller based model reference adaptive control for nonlinear systems

Transcription

1 MultiCraft International Journal of Engineering, Science and echnology Vol. 3, No. 6, 0, pp INERNAIONAL JOURNAL OF ENGINEERING, SCIENCE AND ECHNOLOGY 0 MultiCraft Liited. All rights reserved Neuro- PI controller based odel reference adaptive control for nonlinear systes R. Prakash, R. Anita Departent of Electrical and Electronics Engineering, Muthayaal Engineering College, Rasipura, ailnadu, INDIA-6360, prakashragu@yahoo.co.in Departent of Electrical and Electronics Engineering, Institute of Road and ransport echnology, Erode, ailnadu, INDIA-63836, anita_irtt@yahoo.co.in Abstract he ai of this paper is to design a neural network based intelligent adaptive controller. It consists of an online ultilayer back propagation neural network structure along with a conventional Model Reference Adaptive Control (MRAC).he training patterns for the Neural Network (NN) are obtained fro the conventional PI controller. In the conventional odel reference adaptive control (MRAC) schee, the controller is designed to realize plant output converges to reference odel output based on the plant which is linear. he NN is used to copensate the nonlinearity of the plant that is not taken into consideration in the conventional MRAC. he control input to the plant is given by the su of the output of conventional MRAC and the output of NN. he proposed Neural Network -based Model Reference Adaptive Controller (NN-MRAC) can significantly iprove the syste behavior and force the syste to follow the reference odel and iniize the error between the odel and plant output. he effectiveness of the proposal control schee is deonstrated by siulations. Keywords: Model Reference Adaptive Controller (MRAC), Artificial Neural Network (ANN), Proportional-Integral (PI) controller DOI: Introduction In the adaptive literature, the question of control of nonlinear systes with present-day sophistication and coplexities has often been an iportant research area due to the difficulties in odeling, nonlinearities and uncertainties. Model Reference Adaptive Control (MRAC) is one of the ain schees used in adaptive syste. Recently MRAC has received considerable attention, and any new approaches have been applied to practical process (Astro and Wittenark, 995). (Petros A loannou et al, 996).In the MRAC schee, the controller is designed to realize plant output converges to reference odel output based on assuption that plant can be linearzed. herefore this schee is effectively for controlling linear plants with unknown paraeters. However, it ay not assure for controlling nonlinear plants with unknown structure. In recent years, an Artificial Neural network (ANN) has becoe very popular in any control applications due to their higher coputation rate and ability to handle nonlinear syste. Soe of the relevant research work including ANN as a part of control schee is illustrated next. A robust Adaptive control of uncertain nonlinear syste using neural network is discussed in (Mofal and Calise, 997). Various types of NN have been efficiently utilized in identification of nonlinear systes (Chen et al., 99; (Guchi and Sakai, 99). A variety of algoriths are utilized to adjust the weight of the NN. In a typical ultilayered NN, the weights in the layers can be adjusted as to iniize the output error between the NNs output and the observed output. he back propagation algorith for efficiently updating the weight is useful in any applications such identification of nonlinear systes. Off-line iterative algorith can be eployed in such care of identification or odeling. However, in the aspect of control, the NN should work in on line anner. In the control syste structure, the output of NN is the control input to the nonlinear controlled syste. i.e., there is the

2 45 unknown nonlinear syste between the NN and the output error. In this case, in order to apply any learning rules, we need the derivatives of the syste output with respect to the input (Yaada and Yabuta, 99). (Kawalo, et al 987) presented a siple structure of NN based feed forward controller which is equivalently an inverse of the controlled syste after the NN copletes learning of the weights which are adjusted to iniize the feedback error. (Narendra and parthasarathy, 990) has shown in general indirect approach to nonlinear discrete tie neuro control schee which consists of identification and adaptive control by using the (Chen, 990) and (Liu and chen, 993) that the NN based adaptive control algorith can cooperate well with identification of the nonlinear functions to realize a nonlinear adaptive control when the nonlinear adaptive control schee is feedback linearizable. (Kaalsudan and Ghandakly, 00) presented a fighter aircraft pitch controller evolved fro a dynaic growing RBFNN in parallel with a odel reference adaptive controller. he abilities of a neural network for nonlinear approxiation and developent for nonlinear approxiation and the developent of a nonlinear adaptive controller based on NNs has been discussed in any works (Calise, et al, 00).(Arciniegas et al,997). A Neural Network Internal Model Control (NN- IMC) strategy is investigated in (otok R. Biyanto et al, 00) by establishing inverse and forward odel based neural network (NN). he use of NNs for identification and control of non linear syste has been deonstrated in (Ahed, 000) discusses a direct adaptive neural network controller for a class of non linear syste. An online Radial Basis-Function Neural Network (RBFNN) in parallel with a MRAC is discussed in (Kaalasadan and Ghandakly, 007). (Yujia Zhai et al, 00) proposed a nonlinear odel predictive control (NMPC) ethod to control the elevation and travel of a three degree of freedo (DOF) laboratory helicopter using successive linearization to approxiate the internal odel of the syste. An adaptive-neuro-fuzzy-based sensorless control of a sart-aterial actuator is presented in (Sadighi and Ki, 0). An Adaptive Inverse Model Control Syste (AIMCS) is designed for the plant, and two Radial Basis Function Neural Networks (RBF) NNs are utilized in the AIMCS discussed in (Yuan Xiaofang et al, 00). (Xiang-Jie Liu et al, 004) discussed an Adaptive Inverse Model Control Syste (AIMCS) and it is designed for the plant, and two RBF NNs are utilized in the AIMCS. A MRAC-based current control schee of a Peranent agnet (PM) synchronous otor with an iproved servo perforance is presented in (Cho et al, 009). (Fadali et al, 00) presented a robust adaptive control approach using MRAC for autonoous robot systes with rando friction. An adaptive output-feedback control schee is developed for a class of nonlinear Single Input Single Output (SISO) dynaic systes with tie delays (Mirkin et al, 00). A neuro-sliding ode approach based on MRAC is proposed in (Huh and Bien, 007). In particular, the adaptive tracking control architecture proposed in (Sanner and Slotine, 99) evaluated a class of continuous-tie nonlinear dynaic systes for which an explicit linear paraeterization of uncertainty is either unknown or ipossible. he adaptive controller is used in various practical applications have attracted uch attention in the field of control engineering. his is due to their proising potential for the tasks of tackling the presence of unknown paraeters or unknown variation in plant paraeters with better perforance 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 can not stabilize the closed-loop control syste. A solution to this proble is to incorporate dead-zone technique in the adaptive controller. With this approach, the controller will stop updating the control paraeters when the identifier error is saller than soe threshold. hus, it can prevent the estiated paraeters fro being infinity. However, the regulation error of the syste will only be asyptotically bounded if large threshold is used, resulting in undesirable closed-loop perforance. All control techniques have their individual characteristics. Hence, cobining the erits of the adaptive control with that of the neural network control theories and then designing a new stabilizing controller will have better perforance than that based on one control theory PI controllers are widely used in industrial control systes applications. hey have a siple structure and can offer a satisfactory perforance over a wide range of operation. herefore, the ajority of adaptation schees described in the literature for MRAS eploy a siple fixed-gain linear PI controller to generate the estiated output. However, due to the continuous variation in the plant paraeters and the operating conditions, in addition to the nonlinearities present in the plant, PI controllers ay not be able to provide the required perforance. Not uch attention has been devoted to study other types of adaptation echaniss used to iniize the error to obtain the estiated output. In this paper, this point is addressed by presenting a neural network to replace the classical PI controller used in the conventional MRAC schee. he NN -MRAC schee is proposed as nonlinear optiizer, which ensures plant output trajectory tracks the reference odel output trajectory and tracking error is zero with iniu tie as possible. Fro the designed PI controller training patterns are generated and it is used to train the artificial BPN neural network. he trained neural network connected in parallel with an MRAC and it output the appropriate control signals for achieving the desired response. he control input given by the plant is the su of the output of adaptive controller and the output of neural network. he neural network is used to copensate the nonlinearity of the plant that is not taken into consideration in the conventional MRAC. he role of odel reference adaptive controller is to perfor the odel atching for the uncertain linearized syste to a given reference odel. he network weights are adjusted by ultilayer back propagation algorith which is carried out in online. Finally to confir the effectiveness of proposed ethod, it is copared with the siulation results of the conventional MRAC. he paper is organized as follows. Section proposes the structure of an MRAC design. Section 3 describes the PI controllerbased odel reference adaptive controller and Section 4 describes the discussion of the proposed schee. Section 5 analyses the result and discussion of the proposed Neural Network-based Model Reference Adaptive Control (NN-MRAC) schee and the conclusions are given in section 6. In this paper, the proposed NN-MRAC schee is designed by using parallel cobination of the conventional MRAC syste and NN controller.

3 46. Structure of an MRAC design he MRAC is one of the ajor approaches in adaptive control. he desired perforance is expressed as a reference odel, which gives the wished response to an input signal. he adjustent echanis changes the paraeters of the regulator by iniizing the error between the syste output and the reference odel.. he Plant Model and Reference Model Syste. o consider a Single Input and Single Output (SISO), Linear ie Invariant (LI) plant with strictly proper transfer function y ( ) Z ( s ) P s p G ( s ) = = K () P u p ( s ) R P ( s ) where u p is the plant input and y p is the plant output. Also, the reference odel is given by y ( s ) Z ( s ) G ( s ) = = K () r ( s ) R ( s ) where r and y are the odel s input and output. Define the output error as e = y p y (3) Now the objective is to design the control input U r such that the output error, e goes to zero asyptotically for arbitrary initial condition, where the reference signal r(t) is piecewise continuous and uniforly bounded. he plant and reference odel satisfy the following assuptions: Assuptions:. Z p (s) is a onic Hurwitz polynoial of degree p. An upper bound n of degree n p of R p (S) 3. he relative degree n* = n p - p of G(s) 4. he sign of the high frequency gain K p are known 5. Z (s),r (s) are onic Hurwitz polynoials of degree q, p respectively, where p n 6. he relative degree n * = p - q of G (s) is the sae as that of G(S), i.e., n * = n*.. Relative Degree n = As in Ref [] the following input and output filters are used, ω& F + (4) = ω gu p ω& = F ω + gy p where F is an ( n )*( n ) stable atrix such that det ( F) reference odel and that (F,g) is a controllable pair. It is defined as the regressor vector SI is a Hurwitz polynoial whose roots include the zeros of the ω = [ ω, ω, y p, r] (5) In the standard adaptive control schee, the control U r is structured as U = θ ω (6) r where θ = [ θ, θ, θ3,c 0 ] is a vector of adjustable paraeters, and is considered as an estiate of a vector of unknown syste paraeters θ *. he dynaic of tracking error * ~ e = G ( s) (7) where p θ ω K P = * p and K ~ θ * = θ ( t ) θ represents paraeter error. Now in this case, since the transfer function between the paraeter error θ ~ and the tracking error e is strictly positive real (SPR) [], the adaptation rule for the controller gain θ is given by & * θ = Γeω sgn( p ) (8) where Γ is a positive gain.

4 47.3. Relative Degree n = In the standard adaptive control schee, the control U r is structured as U r = θ ω + θ& Φ = θ ω θ Γ φe sgn( K p / K ) (9) where θ = [ θ, θ, θ3,c 0 ] is a vector of adjustable paraeters, and is considered as an estiate of a vector of unknown syste * paraeters θ. he dynaic of tracking error is * ~ e = G ( s)( s + p ) p θ φ (0) where K P = 0 * p and K ~ θ * = θ ( t) θ represent the paraeter error. ( s)( s p0) G + is strictly proper and Strictly Positive Real(SPR). Now in this case, since the transfer function between the paraeter error θ ~ and the tracking error e is SPR, [] and the adaptation rule for the controller gain θ is given θ& = Γ φe sgn( K p / K ) () where e = y p- y and Γ is a positive gain. he adaptive laws and control schees developed are based on a plant odel that is free fro disturbances, noise and unodelled dynaics. hese schees are to be ipleented on actual plants that ost likely to deviate fro the plant odels on which their design is based. An actual plant ay be infinite in diensions, nonlinear and its easured input and output ay be corrupted by noise and external disturbances. It is shown by using conventional MRAC that adaptive schee is designed for a disturbance free plant odel and ay go unstable in the presence of sall disturbances. 3. PI Controller-based Model Reference Adaptive Controller he PI algorith reains the ost popular approach for industrial process control, despite continual advances in control theory. his is because the PI algorith has a siple structure which is conceptually easy to understand and ipleent in practice but also the algorith provides adequate perforance in the vast ajority of applications. A PI controller ay be considered as an extree for of a phase lag copensator. he transfer function of PI Controller is generally written in the Parallel for given by () or the ideal for given by (3). U pi ( S ) K i G PI ( S ) = = K P + () E ( S ) S = K P ( + ) (3) i where U pi (s) is the control signal acting on the error signal E(s), K p is the proportional gain, K i is the integral gain and i is the integral tie constant. he two ter functionalities are highlighted by the following. he proportional ter-providing an overall control action proportional to the error signal through the all pass gain factor. he integral ter reducing steady state errors through low frequency copensation by an integrator he disturbance and nonlinear coponent are added to the plant input of the conventional odel reference adaptive controller, in this case the tracking error has not reaches to zero and the plant output is not tracked with the reference odel plant output. he conventional MRAC fails copletely under the action of the external disturbance and nonlinearities, where a degradation in the perforance due to overshoot is observed. he disturbance is considered as a rando noise signal. o iprove the syste perforance, the PI controller-based Model Reference Adaptive Control schee (PI-MRAC) is proposed. In this schee, the controller is designed by using parallel cobination of conventional MRAC syste and PI controller. he Block diagra of PI- MRAC schee is shown in Fig.. he control input U p of the plant is given by the following equation, U p = U r + U pi (4) where U r is the output of the adaptive controller and U pi is the output of the PI controller. U θ r = ω (5) where θ is the update law vector, and ω is the paraeter vector.

5 48 Fig. Block diagra of PI-MRAC schee he input of the PI controller is the error, in which the error is the difference between the plant output y p (t) and the reference odel output y (t). he PI controller gains can be selected as high as possible, but are liited by the noise (Vas, 998). In this paper PI gains are obtained by trial and error ethod. In this case also, the disturbance (rando noise signal) and nonlinear coponent is added to the input of the plant. he PI-MRAC schee iproves the syste perforance coparing to the conventional MRAC schee. However due to the continuous variation in the syste paraeters and the operating conditions, in addition to the nonlinearities present in the syste, PI-MRAC schee ay not be able to provide the required perforance. 4. Neural Network-based Model Reference Adaptive Controller o ake the syste ore quickly and efficiently adaptable than conventional MRAC syste and PI-MRAC schee, a new idea is proposed and ipleented. he new idea which is proposed in this paper is the Neural Network-based Model Reference Adaptive Controller (NN-MRAC). In this schee, the controller is designed by using parallel cobination of conventional MRAC syste and NN controller. he training patterns of NN are extracted fro the input and output of PI controller of designed PI -MRAC schee. he block diagra of proposed NN-MRAC schee is shown in Fig.. Fig. Block diagra of the proposed MRAC schee his schee is restricted to a case of Single Input Single Output (SISO) control, noting that the extension to Multiple Input Multiple Output (MIMO) is possible. o keep the plant output y p converges to the reference odel output y, it is synthesize the control input U n by the following equation, U = U + U (6) n r nn where U r is the output of the adaptive controller U = θ ω r

6 49 θ = [ θ, θ, θ3,c 0] (7) ω = [ ω, ω, y p, r] where θ is the update law vector, and ω is the paraeter vector. Stability of the syste and adaptability are then achieved by an adaptive control law U r tracking the syste output to a suitable reference odel output, such as that the error e = y p -y = 0 asyptotically. he NN provides an adaptive control for better syste perforance and solution for controlling nonlinear processes. he ANN controllers designed in ost of the work use a coplex network structure for the controller. he ai of this work is to design a siple ANN controller with as low neurons as possible while iproving the perforance of the controller. he inputs of the NN are the error and change in error. Here the ultilayer back propagation NN is used in the proposed ethod. he ultilayer back propagation network is especially useful for this purpose, because of its inherent nonlinear apping capabilities, which can deal effectively for real-tie online coputer control. he NN of the proposed ethod has three layers: an input layer with neurons, a hidden layer with neurons and an output layer with one neuron. Let x i be the input to the i th node in the input layer, z j be the input to the j th node in the hidden layer, y be the input to the node in the output layers. Furtherore V ij be the weight between the input layer and hidden layer, W j is the weight between the hidden layer and the output layer. he relations between inputs and output of NN are expressed as, n Z inj = Voj + xiv (8) ij i= z j = F( Z _ inj ) (9) Y = W0 z W (0) in + j = j j P y = F Y ) () ( in where F (.) is the activation function. Sigoid function is chosen for the activation function as follows a F( x) = a + exp( μx) where µ > 0, a is a specified constant such as that a 0, and F(x) satisfies a<f(x) <a he ai of training is to iniize the su of square error energy function given by he weight are updated by using E ΔW = η = η ( t y ) F ( Y ) z j k k in W j j E ( k ) = [ t k y k E ΔW0 = η = η ( tk yk ) F ( Y in) (4) W0 E ΔV ij= η = ηf ( Z inj) xi δ kw j V ΔV ij 0 j= = ηf ( Z inj) δ kw j V0 j k k E η (5) where η is the learning role F( Y ( Y ( Z in in F ( Z inj ) μ = [( a F( Y ) a inj ) = ) in μ ( a F( Z a ))( a + F( Y inj in ))( a + F( Z ))] inj )) ] () (3) (6) (7)

7 50 he set of inputs and desired outputs of NN are extracted fro the PI controller of designed PI controller based MRAC schee. A back propagation NN is trained till it reaches a certain fixed error. Here, the network is trained to reach an error goal of raining the Back Propagation network requires the following steps:. Initialize the weights and biases in the network randoly.. 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 -4 until the error for the entire network is acceptably low. he structure of the NN for NN-MRAC schee is shown in Fig Results and Discussion Fig. 3 Structure of the NN for proposed NN-MRAC schee In this section, the results of coputer siulation for the conventional MRAC, PI-MRAC and NN-MRAC schees are evaluated by applying input of varying agnitude under nonlinearities and disturbances in the plant. he sae series of noise disturbance has been applied for each siulation. he results show the effectiveness of the proposed NN-MRAC schee and reveal its perforance superiority to the conventional MRAC technique. A detailed siulation coparison between the three schees has been carried out using with two exaples. 5.. Exaple. In this exaple, the nonlinearity coponent of backlash and disturbances (rando noise signal) in the input of linear syste are shown in Fig.4 Fig. 4 Nonlinear Syste he results of coputer siulation are obtained by using MALAB environent for the conventional MRAC, PI-MRAC and NN-MRAC schees with MALAB for tie duration t= [0, 50] s A third order syste with the transfer function S + 4S G ( S) = 3 S + 5S + 7S +.5 is used to study and the reference odel is chosen as S + 4S S) = G M ( 3 S + 6S + S + 6 which has relative degree n*= he input to the reference odel is chosen as r(t)= he initial value of conventional MRAC schee the controller paraeters are chosen as θ(0) = [3, 8,-8, 3]. U r is the control input of the plant for conventional MRAC schee denoted by

8 5 U = r where θ ω θ = [ θ, θ, θ3,c 0] is the update law vector, ω = [ ω,, y, r] ω p is the regressor vector and ω& = F ω + gu p ω& = F ω + gy p where F is an ( n )*( n ) stable atrix such that det ( SI F) is a Hurwitz polynoial whose roots include the zeros of the reference odel and that (F,g) is a controllable pair he PI controller gains can be selected as high as possible, but are liited by the noise. In the PI-MRAC schee, the value of the PI controller gains K p = 54 and K i =9, were shown to provide a better perforance for the PI-MRAC schee. he U p is the control input of the plant for the PI-MRAC schee U p = U r + U pi he siulink odel of the PI-MRAC schee developed is given in Fig. 5 Fig.5 Siulink Model of the PI-MRAC schee In the NN-MRAC schee, the details of the trained network are shown in Fig. 6 Fig.6.Details of the trained network of Exaple

9 5 he siulink odel of the proposed NN-MRAC schee developed is given in Fig.7 Fig.7 Siulink Model of the NN-MRAC schee Figs 8-0 shows the perforance of the MRAC, PI-MRAC and proposed NN-MRAC schees of Exaple with input of r(t)= under disturbance and nonlinearity coponent of backlash in the plant. (a)

10 53 (b) Fig. 8 Response of the conventional MRAC schee :(a) Plant and odel reference response; (b) racking error (a) (b) Fig. 9 Response of the PI- MRAC schee :(a) Plant and odel reference response; (b) racking error.

11 54 (a) (b) Fig. 0 Response of the NN-MRAC schee :(a) Plant and odel reference response; (b) racking error 5.. Exaple. In this exaple, the nonlinearity coponent of Dead zone and disturbances (rando noise signal) in the input of linear syste Consider a second order syste with the transfer function. G ( S) = S + 3S 0 is used to study and the reference odel is chosen as 5 G M ( S) = S + 0S + 5 which has relative degree n*= he input to the reference odel is chosen as r(t) = 0+5sin4.9t. he output error is e = y y and the U r is the control input of the plant for conventional MRAC denoted by p U r = θ ω + θ& Φ = θ ω θ Γ φe sgn( K p / K ) where [ θ, θ, θ3,c 0 ] ω = [ ω, ω ω& = F ω + gu p θ = is the update law vector,, y, r] is the regressor vector and ω& = F ω + gy p where F is an ( n )*( n ) stable atrix such that det ( SI F) is a Hurwitz polynoial whose roots include the zeros of the reference odel and that (F,g) is a controllable pair he initial value of the conventional MRAC schee controller paraeters are chosen as θ(0) = [0.5, 0, 0, 0]. p

12 55 he PI controller gains can be selected as high as possible, but are liited by the noise. In the PI-MRAC schee, the value of the PI controller gains K p = 8 and K i =9, were shown to provide an optial perforance for the PI-MRAC schee. he U p is the control input of the plant for the PI-MRAC schee U p = U r + U pi he siulink odel of the proposed NN-MRAC schee developed is given in Fig he U n Fig. Siulink Model of the proposed NN-MRAC schee is the control input of the plant for the NN-MRAC schee. U = U + U n r nn In the proposed NN-MRAC schee, the details of the trained network are shown in Fig.. Fig. Details of the trained network of Exaple Figs 3-5 shows the perforance of the MRAC, PI-MRAC and proposed NN-MRAC schees of Exaple with input of r(t) = 0+5sin4.9t under disturbance and nonlinearity coponent of Dead zone in the plant.

13 56 ( a ) (b) Fig. 3 Response of the conventional MRAC schee :(a) Plant and odel reference response; (b) racking error (a)

14 57 (b) Fig. 4 Response of the PI-MRAC schee :( a) Plant and odel reference response; (b) racking error (a) (b) Fig. 5 Response of the NN-MRAC schee :(a) Plant and odel reference response; (b) racking error he perforance of the conventional MRAC, PI-MRAC and NN-MRAC schee is evaluated by applying inputs of varying agnitude under nonlinearities and disturbance in the plant. he results show the effectiveness of the NN-MRAC schee to force the plant to follow the odel, under uncertainties. Extensive siulation tests were carried out to copare the three adaptation

15 58 schees: conventional MRAC, PI-MRAC schee and NN-MRAC schee. In the siulation results of conventional MRAC, PI- MRAC and NN-MRAC schees, the dotted line and solid line represents the odel reference trajectory and plant trajectory respectively. In conventional MRAC schee, the plant output is poor with large overshoots and oscillations as shown in Figs. 8 and 3. Figs. 9 and 4 show the response of the PI-MRAC schee. In this case, the overshoots and the oscillations are uch saller, yielding a uch better perforance than the conventional MRAC schee. However, due to the continuous variation in the syste paraeters and the operating conditions, in addition to the nonlinearities present in the syste, PI-MRAC schee ay not be able to provide the required perforance. In the proposed NN-based MRAC schee, the plant output has tracked with the reference odel output and the tracking error becoes zero within 6 seconds with less control effort as shown in Figs.0 and 5. he responses perfored by the control algorith only with the odel reference adaptive controller are observed to be inferior to that of the control algorith both with NN controller and the odel reference adaptive controller. Also, the response of the control algorith only with the odel reference adaptive controller shows large overshoot and oscillation. Further, the response of the output perfored by the control algorith both with the NN controller and the odel reference adaptive controller shows ore satisfactory results for the bounded disturbances with unknown as well as tie-varying characteristics than that of the control algorith only with the odel reference adaptive controller. Fro the siulation results, because of the existing nonlinearities and bounded disturbances, the controlled syste using the control algorith only using the odel reference adaptive controller will be unstable. But when using the NN and the odel reference adaptive controller in coordination in which the control law is used to cope with nonlinearities and bounded disturbances, the controlled syste can be robustly stabilized all the tie. Fro the above discussions, the proposed control algorith both with the neural network and the conventional odel reference adaptive controller can be a proising way to tackle the proble of controlling the nonlinear systes and bounded tie-varying disturbances. Fro the above siulations, it is shown that the control algorith using only the odel reference adaptive controller will not stabilize the nonlinear controlled systes with disturbances. Fro Figs.0 and 5, it is seen that the control algorith both with the neural network control and the odel reference adaptive controller working in coordination can cope up with the uncertain dynaic syste and bounded disturbances, but the control algorith without the neural network copensating control cannot. Copared to the conventional MRAC, PI-MRAC schee and NN-MRAC schee still show a faster response during transients. Moreover, the NN-MRAC schee shows faster response copared to the PI-MRAC schee. An optial response was obtained for the NN-MRAC schee copared to the PI MRAC schee. he proposed NN- MRAC schee shows better control results copared to those by the conventional MRAC and PI-MRAC schee. Fro these siulation results it is observe that:. In conventional MRAC the plant output is not tracked with the reference odel output. he conventional MRAC fails copletely under the action of the external disturbance and nonlinearities, where a degradation in the perforance due to overshoot is observed.. he PI-MRAC iproves the transient and steady state perforances copared with the conventional MRAC. In the PI- MRAC schee, the plant output is nearly track with the reference odel output. However it will not be able to provide the required perforance. 3. he proposed NN-MRAC design approach can keep the plant output in track with the reference odel and tracking error becoes zero within 6 seconds. he proposed NN-MRAC controller gives better perforances in ters of steady-state error, settling tie and overshoot. Hence it can be concluded that the proposed NN-MRAC schee is ore robust perforance than the classical MRAC and PI-MRAC schee. On the contrary, the proposed ethod has uch less error than the conventional ethod in spite of nonlinearities and disturbance. he siulation results have confired the efficiency of the proposed NN-MRAC schee for applying disturbances and nonlinearities Ipleentation issue. he proposed ethod can be widely used in ost of the industrial nonlinear and coplex applications such as achine tools, industrial robot control, position control, and other engineering practices. he proposed NN- MRAC is relatively siple and does not require coplex atheatical operations. It can be readily ipleented using conventional rnicroprocessors or icrocontrollers. he execution speed of the NN-MRAC schee can be iproved by using advanced processors such as Reduced Instruction Set Coputing (RISC) processors or Digital Signal Processors (DSP's) or ASIC's (Application Specific Integrated Circuits).. 6. Conclusion In this paper, a NN-MRAC schee is proposed to replace the PI controller of PI based MRAC by a neural network. In NN - MRAC the training patterns of neural network are extracted fro the PI controller of designed PI -MRAC schee. A detailed siulation coparison between the three schees has been carried out using with two exaples. he proposed NN-MRAC controller shows very good tracking results when copared to the conventional MRAC and the PI-MRAC syste. Siulations and analyses have shown that the transient perforance can be substantially iproved by proposed NN-MRAC schee In proposed NN-MRAC schee, the syste output tracks very closely the reference odel in spite of the disturbances and

16 59 nonlinearities. hus the NN-MRAC controller is found to be extreely effective, efficient and useful. However, the application of the new adaptation schees does not considerably iprove the steady-state perforance. Developent of a neurofuzzy networkbased MRAC schee is recoended as the future works for iprove the steady state perforance of the syste with the presence of disturbances and nonlinearities. Due to its siple operation, the proposed NN-MRAC can be readily ipleented using conventional icroprocessors. References Astro K.J. and Wittenark B Adaptive control (nd Ed.) Addison-Wesley. Chen. S, Billings, S.A and Grant, P.M.,99, Nonlinear syste identification using neural network, Int. J. Control, Vol. 5, pp. 9-4 Chen, F.C, 990, Back propagation neural networks for non linear Self tuning adaptive control, IEEE contr. Syst. Mag., 0, Arciniegas J.I., A.H. Eltiashy and K.J. Cios, 997. Neural networks based adaptive control of flexible ars, Neurocoputing, Vol.7, No. 34, pp Ahed M.S Neural net-based direct adaptive controller a class of nonlinear plants, IEEE rans Auto. Control. Vol.45, No,, pp Biyanto.R., Babang L. Widjiantoro, Ayan Abo Jabal, itik Budiati 00. Artificial neural network based odeling and controlling of distillation colun syste, International Journal of Engineering, Science and echnology, Vol., No. 6, pp Calise A.J., N. Hovakiyan and M. Idan, 00. Adaptive output feedback control of nonlinear syste using neural networks, Autoatica, Vol. 37, No.8, pp. 0-. Cho, H.C.; Fadali, M.S.; Lee, K.S.; Ki, N.H., 009. Model reference adaptive control-based adaptive current control schee of a PM synchronous otor with an iproved servo perforance, IE on Electric Power Applications,Vol.3, No.. pp Fadali, M.S.; Lee, K.S.; Ki, N.H., 00. Adaptive position and trajectory control of autonoous obile robot systes with rando friction, IE on Control heory & Applications, Vol.4, No.. pp Guchi,Y and Sakai, H, 99, A nonlinear regulator design in the presence of syste uncertainities using ultilayered neural network, IEEE rans. Neural Network, Vol., pp Huh, S.-H and Bien, Z Robust sliding ode control of a robot anipulator based on variable structure-odel reference adaptive control approach, IE on Control heory & Applications, Vol., No.5. pp , Oct. 007 Kawalo, M. Furukawa.K and Suzuki, R., 987, A hierarchical neural network for control and learning of voluntary oveent, Biol Cybern, Vol. 57, pp Kaalsudan S. and Ghandakly A.A. 00. A neural network parallel adaptive controller for fighter aircraft pitch- rate tracking, IEEE ransaction on Instruentation and Measureent Kaalasadan S., A. Ghandakly, 007. A neural network parallel adaptive controller for dynaic syste control, IEEE ransactions on Instruentation and Measureent, Vol.56, No.5. pp Loannou P.A., Sun J., 996. Robust Adaptive control, Upper Saddle River, NJ: Prentice-Hall. Liu, C.C. and Chen, F.C., 993, Adaptive control of non linear continuous tie systes using neural networks- general relative degree and MIMO cases, Int. J. Control, Vol. 58, pp Mirkin, B.; Gutan, P.-O., 00. Robust adaptive output-feedback tracking for a class of nonlinear tie-delayed plants, IEEE ransactions on Autoatic Control, Vol.55, No.0, pp Mofal M.B. and Calise A.J Robust adaptive control of uncertain nonlinear systes using neural network, in Proc. Aer Control Cont. pp Narendra, K.S and parthasarathy, 990, identification and control of dynaic systes using neural network. IEEE ans. Neural network, 4-7 Sadighi,A. Ki, W. Adaptive-Neuro-Fuzzy-Based Sensorless Control of a Sart-Material Actuator, IEEE/ASME ransactions on Mechatronics, vol., no., pp , Jan. 0 Sanner R.M. and J,E. Slotine, Gaussian Networks for Direct Adaptive Control, IEEE trans neural networks vol3, no.6. pp , Nov99 Vas P., Sensorless Vector and Direct orque Control. New York: Oxford Univ. Press, 998. Xiang-Jie Liu; F. Lara-Rosano; C.W. Chan, 004. Model-reference adaptive control based on neurofuzzy networks, IEEE ransactions on Systes, Man, and Cybernetics, Part C: Applications and Reviews, Vol.34, No.3. pp Xiaofang Y.; Yaonan W.; Wei S.; Lianghong W., 00. RBF networks-based adaptive inverse odel control syste for electronic throttle, IEEE ransactions on Control Systes, Vol. 8, No. 3. pp Yaada, and Yabuta,., 99,Neural network controller using autotunning ethod for non linear function. IEEE rans. Neural Network, Vol. 3, pp Zhai Y., Nounou M., Nounou H. and Al-Haidi Y. 00. Model predictive control of a 3-DOF helicopter syste using successive linearization, International Journal of Engineering, Science and echnology,.vol., No. 0, pp. 9-9.

17 60 Biographical notes R.Prakash received his B.E degree fro Governent College of echnology, affiliated to Bharathiyar University, Coibatore, ailnadu, India in 000 and copleted his M.ech degree fro the College of Engineering, hiruvanandapura, Kerala, India, in 003. He is currently working for his doctoral degree at Anna University, Chennai, India. He has been a eber of the faculty Centre for Advanced Research, Muthayaal Engineering College, Rasipura, ailnadu, India since 008. His research interests include Adaptive Control, Fuzzy Logic and Neural Network applications to Control Systes. R.Anita received her B.E Degree fro Governent College of echnology in 984 and copleted her M.E Degree fro Coibatore Institute of echnology, Coibatore, India in 990, both in Electrical and Electronics Engineering. She obtained her Ph.D degree in Electrical and Electronics Engineering fro Anna University, Chennai, India, in 004. At present she is working as Professor and Head of Departent of Electrical and Electronics Engineering, Institute of Road and ransport echnology, Erode, India. She has authored over sixty five research papers in International, National journals and conferences. Her areas of interest are Advanced Control Systes, Drives and Control and Power Quality Received Deceber 00 Accepted April 0 Final acceptance in revised for July 0