Neural Network Identifier with Iterative earning for Turbofan Engine Rotor Speed Control Syste QIAN Kun PANG Xiangping I Bangyuan Departent of Aerial Instruent and Electric Engineering The First Aeronautical Institute of Air Force Xinyang, China qiankun_0306@163.co Abstract This paper proposed a new neural network algorith with fuzzy iterative learning controller and applied to a certain turbofan engine rotor speed control syste. A dynaic neural network was used to identify the plant on-line. The control signal was then calculated iteratively according to the responses of a reference odel and the output of identified plant. A fuzzy logic block with four very siple rules was added to the loop to iprove the overall loop properties. Experiental results deonstrate the proposed control strategy provides better disturbance reection and transient properties than those achieved by conventional echanical-hydraulic controller(mhc) and analogue engine electronic controller(aeec). At the sae tie, it can iprove transitional quality in control syste, and eet the deands of high perforance and high control accuracy in turbofan engine. Keywords Aerial Engine; Neural Network Identifier(NNI); Iterative earning Controller(IC); Trans-diensional earning(td); Fuzzy ogic Copensation(FC) I. INTRODUCTION In recent years, with the rapid developent of odern control theory and the application of super large-scale integration and icroprocessor in aerial engine electronic controller, full authority digital electronic controller (FADEC) has been an iportant developing direction in high perforance aeroengine control syste. Coparing with conventional echanical-hydraulic controller and analogue engine electronic controller(aeec), FADEC not only has the siple configuration, but also apply coplicated and anvanced control algorith to aeroengine control syste. It can realize ulti-variables and ulti-loops decoupling control in syste. So it eets the deands of high perforance guideline and high control accuracy in turbofan engine[1],[]. Neural networks are probably the ost discussed intelligent control paradig used today in odel identification probles and in controller design[3],[4]. Integrated with neural network application in control field, this paper proposed a new neural network algorith with fuzzy logic copensation and applied to an aeroengine rotate speed control syste. Experiental results deonstrate the proposed control strategy is effective. II. CONTRO MODE DESIGN Figure.1 depicts the block diagra of the proposed closed-loop control schee. The reference input signal is r. The control goal is that the plant output signal y follows as closely as possible the output signal y of the reference odel. The reference odel of the plant is an ideal odel that has the desired characteristics related to the rise tie, overshoot, steady-state error, etc. u r IC 1 Z u f u u n e( k 1) TD Reference Model FC Aeroengine e n NNI y ( k 1) y e y n ( k 1) y n y X / net Figure.1 Neural network Control block with fuzzy logic copensation Ignoring aeroengine cobustion delay, the dynaic odel of rotor speed control in a saple for as[5],[6]: X n ( s) K ( τ s 1) = (1) X ( s) T s T s 1 f 1 Where X n and X f are low copressor rotor speed and fuel respectively. After discretization, the odel can be rewritten as: y ( 1 0 k k 1) = a y a y ( 1) 978-1-444-1674-5/08 /$5.00 008 IEEE CIS 008
where b1u b0u ( k=0,1, () u and y are scalars. Trans-diensional learning(td) is a Windows 3.1 artificial neural network. TD allows users to perfor pattern recognition by utilizing software that allows for fast, autoatic construction of Neural Networks, ostly alleviating the need for paraeter tuning. By supporting ulti-shot learning over standard one-shot learning, ultiple data sets (characterized by varying input and output diensions) can be learned increentally, resulting in a single coherent network. This can also lead to significant iproveents in predictive accuracy. A neural network identifier(nni) for the on-line identification deterines on-line an approxiate current non-linear odel of the plant. This odel is necessary for good loop control. An iterative learning controller (IC) produces a control signal u n, which is cobined with the output signal of the fuzzy logic block(fb) to produce the actual plant input signalu = u n u. III. NEURA NETWORK IDENTIFIER The dynaic NN for plant odel identification has n input nodes, hidden-layer nodes and l output node. The weight atrix for the input-to-hidden layer is W (n1), the input pattern vector X (n1) l, the hidden-to-output weight atrix is V (1) l, the output signal vector of the hidden-layer is net (1), Here n=1 and =p. The input layer and the hidden layer have each a 1 node constant to cater for biases of the neurons in the subsequent layer. These two nodes do not have feedback signals. The output y n of NNI is the predicted syste output. The values of variables are considered at oents t k =k*τ (τ is the sapling interval). k=1,,. To siplify notation we will use u to denote the value u(t k ). Thus, at t=t k we have the syste I/O values u and y. We define vectors s( 1) u( s( ) u( k )...... S = s( p) = u( k p) (3) s( p 1) y(...... s( p) y( k p) 1 1 x( 1) X =, h( 1) net = (4)...... x( n) h( ) et x( 1)=u, and by using three positive real paraeters α,β,γ, we define a recursive relation for the f calculation of x as x( i1)=α*s( i)β*x(k-1, i1)γ*h(k-1, i) (5) where x(0, i1)=0, i=1,,, k=1,,, also Z ( k ) = W T X ( k ) (6) net ( k ) = f ( Z ( k )) (7) Here, f is a nonlinear sigoid function vector. The NN output y n at k-th tie interval is linear in net as follows. T y ( k 1) = V net( (8) n In (5), αis the forward gain, βis the selfish feedback gain on the input layer and γis the feedback gain fro the hidden layer to the input layer. We define the error function J = en / = ( y y n ) /,so that the necessary gradients and updates of the network paraeters are given by = = en net (9) net = = en (10) net V = V ( V (11) V = η =η*e n *net [1μ*net T *net] -1 (1) Wi = Wi Wi (13) Wi = η i =η*e n *V *Z *[1-Z ]*X (14) Here, η is the learning rate; μ is a sall positive coefficient; subscripts; i, indicate the i-th node in the input layer and the -th node in the hidden layer, respectively; k eans the k-th saple control period. IV. ITERATIVE EARNING CONTROER Our obective is to control the plant so as that its output y follows the response of the reference odel y. At tie t k we can deterine y (k1), which is the next value of the odel output. Since the current neutral network odel of the plant is identified by NNI, we can directly calculate u(k1) by the iterative algorith in order to obtain the NNI output y n close to y (k1). To do this we will look for u(k1) that will ake the expected output of NNI equal to y (k1). The value of u(k1) will be obtained iteratively according to [5], [6]. During the calculation of the iterative values we assue that the syste does not change its characteristics. Here, the NN odel serves as a known invariant nonlinear odel of the plant. We will use the PD control structure to calculate the next value of u using the current iterative value of u, as well as the current and previous iterative values of e=y -y n. Soe explanations of the notation are necessary. et the
control tie interval be T k =[t k, t k τ]. Here, t k1 =t k τand it represents the next sapling oent. During T k the iteration calculation is run. et kk correspond to the current iteration step. The current oent at the kk-th iterative step is t=t k Δ kk-1, whereδ kk-1 is the tie necessary to perfor the total of kk iterations. Also, notation u( t) represents the kk-th iteration value of u. The error during the kk-th control iterative input is denoted by e( t). The iterative calculation of the control signal u is given by u(kk1,t)=u(t)k p *e(t) k d *[e(t)-e(kk-1,t)], t=t k (15) e(t)=y (t)-y n (t), t=t k (16) Here k p and k d are the PD paraeters. The whole iteration session has to be finished during T k. The whole iteration control step is calculated as follows: a) kk=1;e(0,k1)=0; b) u ˆ( k 1) = u(, where û is the estiated value of u; c) calculate y n (k1) by(5)~(8) d) e(k1)=y (k1)-y n (k1) e) if e(k1) ε c, then GO TO g), ESE: ˆ( k 1) = uˆ( k 1) k * e( k 1) u p k d *[ e( k 1) e( kk 1, k 1)] f) kk=kk1;if kk-1 <τ RETURN to step b). g) u ( k 1) = uˆ( k 1),END iterations. V. FUZZY OGIC BOCK In the proposed control structure the PD type fuzzy logic block(fb) is used. The FB acts as a daper in the loop. The output of the FB is governed by u f = k F e, e ) (17) fu fuzzy ( Here u f is the FB output and k fu is the gain; e, e are the error signal and its derivative; F fuzzy is a non-linear function whose output signal represents crisp values resulting fro internal fuzzy logic processing of the FB. The crisp input signals e and e are noralized to the range [-1,1]. Siple Gaussian ebership functions for the noralized values of e and e are used. et N and P denote 'negative' and 'positive' respectively; then the ebership functions are µ N (x)=exp(-10(x0.3) ) µ P (x)=exp(-10(x-0.3) ) (18) TABE.I. \ e FUZZY OGIC CONTRO RUES e N P N NB N P P PB The four fuzzy rules used in the design of the FB are represented by the following Tab 1. where NB and PB denote 'negative big' and 'positive big', respectively. As a result of the fuzzy inference echanis, the output fuzzy value is produced. The ebership functions for the noralized output values are: μ NB (x)=[1exp(6(x0.3))] -1 μ PB (x)=[1exp(-6(x-0.3))] -1 μ N (x)=exp(-1.5(x0.3) ) μ P (x)=exp(-1.5(x-0.3) ) (19) After the output fuzzy value is obtained, it is defuzzyfied, denoralized, and ultiplied by the gain k fu to produce u f. VI. EXPERIMENTA RESUTS Our experients are based on a odel of the aeroengine rotor speed control syste used in laboratory. Obviously, Ignoring aeroengine cobustion delay, the odel can be siplified to a control syste of the second order as expression (). The proposed rotor control syste configuration shows as figure.. the control tie interval is τ =0.0s. The reference discrete odel with good perforance and realization for rotor speed control syste in certain turbofan engine can be taken as y ( k 1) = 1.8953y( 0.8978y( 0.0107u 0.010u( (0) figure. The proposed speed control syste block for an aeroengine Syste dynaic paraeters, such as T 1 T K τ, will change in liited scope with the different flight altitude H and ach nuber M for aeroengine reference odel (1). So these dynaic paraeters are uncertain for aeroengine rotor control syste. By experient, in whole aeroengine flight envelope, their possible ranges are T1 [0.1, 0.], T [0.5, 1.5], K [0.1, 0.4], τ [0., 0.5]. In conventional aeroengine echanical-hydraulic controller, because hydraulic aplifier valve with speed feedback is plus overlap configuration, it leads to dead zone effect inevitably in aeroengine rotor speed control syste. the input saturation liit is [-6, 6]; the dead-zone gap is ±0.. All nuerical values of the siulation odel are obtained either by easureents or identification fro laboratory experients. The software environent used for these siulation experients is Matlab 6.0, with the Siulink package; nuerical integration is done by the Runge-Kutta 4 algorith. The size of neural network is 8 7 1; the learning rate of neural network is η=0.; the control iterative paraeters are
k p =0. and k d =0.01, the noralization factors for inputs e and e to the FB are k e =1 and k de =0.1 respectively, while the gain k fu =1. The axial nuber of iteration steps during the sapling interval is 0. The initial values of vectors S, X and net are all set to zero for the variable coponents; the initial weights of atrices W and V are taken at rando; the three gains for recursive calculations of X are α=0., β=0.5, γ =0.5. Figure.3 shows the rotor speed loop response in certain turbofan engine flight/train axiu condition when the step type reference input is ain fuel signal f in flight altitude H=0k. Fro the oent t=.5sec and until t=7.5sec, a step type disturbance signal is inected into the loop. Figure.4 and Figure.5 show enlarged sections for a better coparison of the transient properties and disturbance reection properties of the proposed control algorith and that of the conventional echanical-hydraulic controller(hmc). Rearkably, the proposed NNI with FC can eliinate steady-state error, and the conventional HMC exists steady-state error about 0.4%. turbofan engine flight/train axiu condition when the step type reference input is ain fuel signal f in static test. As seen fro Figure.6, for echanical- hydraulic controller, the surge occurred at steady-state point under the influent of coponents nonlinear characteristic and aeroengine cobustion delay. It led to a long surging tie and a bad transient properties. For analogue engine electronic controller(aeec), although it can eliinate steady-state error, it also led to a long surging tie and a less overshot. The proposed algorith brought about good control results, such a short surging tie and overshot restraint. So it can iprove transitional quality in control syste, and eet the deands of high perforance and high control accuracy in turbofan engine. Figure.5 Syste disturbance reection properties with the proposed algorith and speed feedback algorith Figure.3 oop response with step type reference input signal Figure.6 Syste response curve in ground testing Figure.4 Syste transient properties with the proposed algorith and speed feedback algorith Figure.5 shows the rotor speed loop response in certain VII. CONCUSION This paper proposed a new neural network algorith with fuzzy logic copensation and applied to an aeroengine rotate speed control syste. A dynaic neural network was used to identify the plant on-line. The control signal was then calculated iteratively according to the responses of a reference odel and the output of identified plant. A fuzzy logic block with four very siple rules was added to the loop to iprove
the overall loop properties. Experiental results deonstrate the proposed control strategy provides better disturbance reection and transient properties than those achieved by conventional MHC and AEEC. REFERENCE [1] He Ering, Civil Aerial Engine Control Theory and its Typical Systes. Beiing: National Defense Publishing House. 00. [] Zhang Sheng-liang, Xie Shou-sheng. Test Syste for FADEC of an aeroengine. Journal of Propulsion Technology, vol. 4(), pp. 190~19, April 003. [3] Yan Pingfan, Zhang Changshui, Artificial Neutral Networks and Analog Evolution Algorith. Beiing: Qinghua University Publishing House, 1999. [4] D.Sbarbaro, J.P.Segovia, S.Alcozer and J. Gonzales. Applications of Radial Basis Network Technology to Process Control[J]. IEEE Trans. Control Systes Technology, 000, 8(1): 14-0. [5] Xie Shousheng, Certain Afterburning turbofan engine, Xi an: The Air Force Engineering University Publishing House, 00. [6] Fan Siqi, Xu Yunhua, Aerial Propulsion Syste Control. Xi an: Northwestern Technical University. 1995 [7] K.. Moore, M. Dahleh and S. P. Bhattachargya. Iterative earning Control: A Survey and NewResults[J]. Journal of Robotic Systes, 199, 9(5): 563-594. [8] T. C. Chen and C. Y. iaw. Robust Speed controlled Induction Motor Drive Based on Model Reference with Neural Network[J]. International Journal of Knowledge-Based Intelligent Engineering Systes, 1999, 3(3): 16-171.