Indonesian Journal of Electrical Engineering and Computer Science V ol. 7, No . 2, A ugust 2017, pp . 434 441 DOI: 10.11591/ijeecs .v7.i2.pp434-441 434 Composite Nonlinear Feedbac k With Disturbance Obser ver f or Active Fr ont Steering Sarah ’Atifah Saruc hi 1 , Hairi Zamzuri 2* , Noraishikin Zulkarnain 3 , Mohd Hatta Mohammed Ariff 4 , and Norbaiti W ahid 5 1,2,4,5 Mala ysia-J apan Inter national Institute of T echnology , Univ ersiti T eknologi Mala ysia,J alan Sult an Y ah y a P etr a, 54100 K uala Lumpur , Mala ysia 3 F aculty of Engineer ing and Built En viroment, Univ ersiti K ebangsaan Mala ysia, 43600 Bangi S elangor , Mala ysia * corresponding author , e-mail: hair i.kl@utm.m y Abstract One of the dominant vir tue of St eer-By-Wire (SBW) v ehicle is its capability to enhance handling perf or mance b y installing Activ e F ront Steer ing (AFS) system without the dr iv er’ s interf erences . Hence , this paper introduced an AFS control str ategy using the combination of Composite Nonlinear F eedbac k (CNF) controller and Disturbance Obser v er (DOB) to achie v e f ast y a w r ate tr ac king response which is also rob ust to the e xistence of disturbance . The proposed control str ategy is sim ulated in J-cur v e and Lane change manoe vres with the presence of side wind disturbance via Matlab/S im ulink sotw are . Futher more , compar ison with Propor tional Integ r al Der iv ativ e (PID) and Linear Quadr atic Regulator (LQR) controllers are also conducted to e v aluate the eff ectiv eness of the proposed controller . The results sho w ed that the combined CNF and DOB str ategy achie v ed the f astest y a w r ate tr ac king capabilit y with the least impact of disturbance in the AFS system installed in SBW v ehicle . K e yw or ds: composite nonlinear f eedbac k, disturbance obser v er , activ e front steer ing, st eer-b y-wire Cop yright c 2017 Institute of Ad v anced Engineering and Science . All rights reser v ed. 1. Intr oduction Steer-By-Wire (SBW) is a steer ing system which remo v es mechanical linkages betw een steer ing wheel and front wheel systems with electronic components and wires . Due to the re- mo v al, an A ctiv e F ront Steer ing (AFS) system can be applied independently without the dr iv er’ s interf erence because there is no fix ed relationship betw een the steer ing wheel angle and the front wheels angle [1, 2]. The aim of AFS implementation is to enhance v ehicle manouv er ability and stability [3, 4]. Here , AFS is installed in SBW v ehicle f or y a w r ate tr ac king control to assist the dr iv ers to k eep the v ehicle on the desired path. CNF controller is a combination of linear and nonlinear f eedbac k la ws without an y s witch- ing element. According to the pre vious research findings , CNF has been pro v en to ha v e strong capabilites in achie ving f ast y a w r ate tr ac king perf or mance with minimal o v ershoot in AFS system [5, 6]. Ho w e v er , Hasan et. al addressed the CNF perf or mance issue when a side wind distur- bance is applied to the AFS system [7]. According to the results , the y a w r ate tr ac king response is major ly aff ected b y the disturbance . It means that the CNF cannot stand alone to o v ercome the e xistence of disturbance . This issue leads to the decreasing of the v ehicle handling perf or mance . Regarding the issue , an integ r at ion of CNF controller with obser v er such as reduced- order and e xtended state obser v ers is one of the solution to enhance the rob ustness of the control system [8, 9, 10]. Thus , this paper proposes the combinat ion of CNF and Disturbance Obser v er (DOB) in AFS system to impro v e the tr ansient perf or mance of y a w r ate tr ac king control and at the same time sim ultaneously reject the element of disturbance . DOB is chosen because it is widely used in SBW system due to its efficiency and design simplicity [11, 12]. This paper is organiz ed as f ollo ws . In the ne xt section, the mathematical model of SBW’ s front wheel system and v ehicle model are presented. Then, the f ollo wing section descr ibes the Receiv ed March 26, 2017; Re vised J uly 12, 2017; Accepted J uly 23, 2017 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 435 design of the control str ucture . The f our th section sho ws the sim ulation results and discussion. Finally , the conclusion and future w or ks are being concluded and suggested in the last section. 2. System Modeling 2.1. SBW’ s Fr ont Wheel System (a) (b) Figure 1. SBW’ s front wheel system a) Mechanism, b) Bloc k diag r am T ab le 1. F ront wheel system par ameter v alue P ar ameter Definition V alue Unit P ar ameter Definition V alue Unit sw Steer ing angle - r ad B m Motor damping coefficient 0.007 N ms=r ad f w F ront wheel angle - r ad J f F ront wheel iner tia 1.36 k g m 2 m Motor angle - r ad R Motor electr ical resistance 3.1124 O hm V V oltage - v L Motor electr ical inductance 1.6663 H enr y i Motor current - A y r Rac k displacement - m m r Rac k Mass 2 k g B r Rac k damping coefficient 25 N ms=r ad J m Motor iner tia 0.0012 k g m 2 B k Kingpin damping coefficient 70 N ms=r ad K s Lumped torque stiffness 0.257 N m=r ad r p Pinion gear r adius 0.1 m K b Motor emf constant 0.2319 V s=r ad r l Offset of king pin axis 0.69 m K l Steer ing linkage stiffness 26e2 N m=r ad Figure 1 sho ws the mechanism and b loc k diag r am of front wheel system while T ab le 1 lists the par ameter’ s details [13]. Basically , this system consiste d of steer ing, motor , r ac k, pinion and front wheels , as sho wn in Figure 1(a). The equations f or the system can be e xpressed as , Motor displacement and current: m = 1 J m ( B m _ m + K s i ) ; _ i = 1 L ( R i + K b _ m + V ) (1) Rac k and pinion : y r = 1 m r  2 K l r l 2 y r K s r p 2 y r B r _ y r K s r p m (2) F ront wheel displacement: f w = 1 J f K l f w y r r l B k _ f w (3) Based on Figure 1(b), these equations can be represented in the f ollo wing tr ansf er function f or ms , Composite Nonlinear F eedbac k With Disturbance Obser v er f or ... (Sar ah ’Atif ah Sar uchi) Evaluation Warning : The document was created with Spire.PDF for Python.
436 ISSN: 2502-4752 G 1 ( s ) = m ( s ) sw ( s ) = ( 2 : 274 10 13 ) s 2 + (2 : 365 10 11 ) s s 3 + 506 : 2 s 2 + 11360 s + 34390 s 3 + 506 : 2 s 2 + 11360 s (4) G 2 ( s ) = y r ( s ) m ( s ) = ( 3 : 553 10 15 ) s + (1 : 75 10 4 ) s 2 + 12 : 5 s + (1 : 805 10 5 ) (5) G 3 ( s ) = f w ( s ) y r ( s ) = (1 : 421 10 14 ) s + 1015 s 2 + 51 : 47 s + 1471 (6) 2.2. V ehic le Model Figure 2. Linear v ehicle model T ab le 2. V ehicle model par ameter P ar ameter Definition V alue Unit P ar ameter Definition V alue Unit l F Distance of F ront Wheel to COG 1.14 m F ! Cross wind F orce 2000 N m l R Distance of Rear Wheel to COG 1.64 m F y F F ront wheel later al f orce - N m f w F ront wheel angle - r ad Y a w r ate - r ad l ! Exter nal F orce P oint 0.5 m F y R Rear wheel later al f orce - N m V ehicle body slip angle - r ad m V ehicle Mass 1529.98 k g C f F ront Wheel Cor ner ing Stiffness 54500 N =r ad I z Y a w Iner tia 4000 k g m 2 C R Rear Wheel Cor ner ing Stiffness 42600 N =r ad v V elocity 22.22 ms 2 Figure 2 sho ws the 2-DOF linear v ehicle model while T ab le 2 lists the par ameter’ s details . The v ehicle model is used as the v ehicle plant to in v estigate the handling perf or mance . It consid- ers 2-DOF of the v eh icle body in later al and y a w motion. Assuming the v elocity to be constant, the linear v ehicle model can be presented in the f ollo wing state space f or m [14, 15, 16]: _ x b = A b x b + B b u b + E b F ! (7) where , A b = 2 6 6 4 2( C F + C R ) mv 1 2( l R C R l F C F ) mv 2 2( l R C R l F C F ) I z 2( l 2 F C F + l 2 R C R ) I z v 3 7 7 5 B b = 2 6 6 4 2 C F mv 2 l F C F I z 3 7 7 5 , E b = 2 6 6 4 1 mv l ! I z 3 7 7 5 x b = 2 4 3 5 , u b = f w . IJEECS V ol. 7, No . 2, A ugust 2017 : 434 441 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 437 3. Contr oller Design Figure 3. Proposed control str ucture T ab le 3. P ar ameter of the control str ucture P ar ameter Definition P ar ameter Definition c Correctiv e steer ing angle G 4 ( s ) T r ansf er function of nominal y a w Actual y a w r ate C 2 ( s ) Y a w r ate tr ac king controller r ef Desired y a w r ate C 1 ( s ) Wheel synchronization controller e Y a w r ate error D Disturbance compensator control input R 2 ( s ) Ref erence model G 1 4 ( s ) In v erse tr ansf er function of nominal y a w ! Side wind disturbance ^ ! Estimated side wind disturbance Figure 3 sho ws the o v er all vie w of the proposed control str ucture , which includes wheel synchronisation and AFS control systems . Meanwhile , T ab le 3 sets out the par ameters used in the proposed control str ucture . F ront wheel system needs a controller to control the motor position in order to steer the front wheels . Theref ore , CNF is also implemented as the wheel synchronisation controller to ensure that the front wheel angle is ab le to synchronise with the steer ing wheel angle commanded b y the dr iv er , as discussed in detail in [17]. 3.1. Composite Nonlinear Feedbac k According to Figure 3, in y a w r ate tr ac king control str ategy , an additional correcte d angle c obtained fro m the CNF controller C 2 ( s ) is added to the steer ing input sw to k eep the actual y a w r ate response closely tr ac k the desired y a w r ate response r ef gener ated b y ref erence model R 2( s ) . The CNF controller is designed based on SBW’ s front wheel and linear v ehicle model systems . Consequently , the equations of the systems is represented in t he f ollo wing state space f or m where the input u = sw and output y = . _ x = Ax + B u y = C x (8) Composite Nonlinear F eedbac k With Disturbance Obser v er f or ... (Sar ah ’Atif ah Sar uchi) Evaluation Warning : The document was created with Spire.PDF for Python.
438 ISSN: 2502-4752 where , A = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 B m J m 0 K s J 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 K b L 0 R L 0 0 0 0 0 0 0 K s m r r p 0 B r m r K l m r r 2 l + K s m r r 2 p 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 K l J f r l B k J f K l J f 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 C F mv 2( C F + C R ) mv 1 2( l R C R l F C F ) mv 2 0 0 0 0 0 0 2 l F C F I z 2( l R C R l F C F ) I z 2( l 2 F C F + l 2 R C R ) I z v 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 B T = 0 0 1 L 0 0 0 0 0 0 ; x T = _ m m i _ y r y r _ f w f w CNF consists of linear u L and nonlinear u N f eedbac k la ws . The o v er all of the la ws u o is e xpressed as [10], u o = u L + u N (9) In linear f eedbac k par t, the damping r atio is set to be small so that the system could achie v e the ref erence input closely and ha v e a f ast r ising time . While in the nonlinear f eedbac k par t, the damping r atio w as increased to reduce the o v ershoot resulted from the linear par t. The details of linear f eedbac k la w is as f ollo ws: u L = F x + Gr (10) Here , r is the step input command or ref erence . F is the controller tuning par ameter to gener ate responses with f ast r ising time . While G is a scalar which is giv en as: G = h C ( A + B F ) 1 B i 1 (11) On the other hand, the nonlinear f eedbac k la w can be descr ibed as , u N = ( r ; y ) B 0 P ( x x e ) (12) Here , P is the solution of the f ollo wing L ypuno v equation, ( A + B F ) 0 P + P ( A + B F ) = W (13) where W is a positiv e definite matr ix. In this study , W is simplified as I . The equation f or x e is descr ibed as , x e = ( A + B F ) 1 B Gr (14) Based on Equation 12 , ( r ; y ) is a nonpositiv e function locally Lipschitz in x which can be e x- pressed as , ( r ; y ) = 'e  0 j h r j (15) where , > 0 and ' > 0 are the tuning par ameters to minimise o v ershoot. IJEECS V ol. 7, No . 2, A ugust 2017 : 434 441 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 439 3.2. Disturbance Obser ver Based on Figure 3, the function of DOB is to eliminate the side wind disturbance ! eff ect without aff ecting the input sw from the steer ing wheel b y pro viding the estimated disturbance ^ ! , which is then used to perf or m the compensation through negativ e f eedbac k loop . Firstly , the y a w model der iv ed from linear v ehicle model is defined as the nominal model G 4 ( s ) . F rom Equation 7, the tr ansf er function of nominal y a w model G 4 ( s ) is giv en as f ollo ws where the input is front wheel angle , f w and the output is y a w r ate , . G 4 ( s ) = ( s ) f w ( s ) = (2 C F l F mv ) s + 4 C F C R ( l F v + l R ) mI z v s 2 + (2( C F + C R ) I z + 2( C F l 2 F + C R l 2 R ) v ) s + a 0 (16) where , a 0 = (4 C F C R ( l F + l R ) 2 + 2( C R l R C F l F )) mv 2 In DOB design procedure , f w is calculated based on G 2 ( s ) and G 3 ( s ) . F or an easier procedure’ s e xplaination, firstly let G 2 ( s ) and G 3 ( s ) assumed as 1. Based on Figure 3 pre viously , the linear v ehicle model can be e xpressed as , = G 4 ( s )( f w + ! ) (17) where ! is the side wind e xter nal disturbance . The estimated disturbance ^ ! is giv en b y , ^ ! = G 4 ( s )) 1 ( G 4 ( s )( f w + ! )) f w (18) The selection of Lo w pass filter L p ( s ) deter mined the disturbance rejection perf or mance at lo w frequencies in the closed-loop system. The L p ( s ) order is chosen to be at least equal to the G 4 ( s ) order f or causality of L p ( s ) =G 4 ( s ) [18]. The equation of ^ ! m ultiplied b y L p ( s ) is as f ollo ws , ^ ! = L p ( s )[ G 4 ( s )) 1 ( G 4 ( s )( f w + ! )) f w ] (19) where L p ( s ) is designed as second order tr ansf er function. 4. Sim ulation and Result 4.1. Sim ulation Set up 0 1 2 3 4 5 6 7 8 9 10 −1 −0.5 0 0.5 1 1.5 time (s) angle (rad)     J−curve Lane change (a) 0 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 2000 time (s) Force (N) (b) Figure 4. Manoeuvres a) J-cur v e and Lane change b) Side wind disturbance The perf or mance of the proposed control str ucture is e v aluated in sim ulation using Mat- lab/Sim ulink softw are . As sho wn in Figure 4(a), the sim ulation is conducted in tw o types of ma- noeuvres which are J-cur v e and Lane change . Then, side wind disturbance as in Figure 4(b) is pur posely added to the manoeuvres to in v estigate the rob ustness of the proposed controller . Moreo v er , compar ison betw een the o utput responses of CNF controller and DOB (CNF-DOB), Propor tional Integ r al Der iv ativ e cont roller and DOB (PID-DOB), and Linear Quadr at ic Regulator Composite Nonlinear F eedbac k With Disturbance Obser v er f or ... (Sar ah ’Atif ah Sar uchi) Evaluation Warning : The document was created with Spire.PDF for Python.
440 ISSN: 2502-4752 controller and DOB (LQR-DOB) based systems are carr ied out to compare and analyz ed the ro- b ustness and eff ectiv eness of the proposed control str ucture . Dur ing sim ulation, the v ehicle is assumed r unning in constant speed 80 k m=h at nor mal road condition. The y a w r ate ref erence model is der iv ed as [15, 16, 19], r ef = nv (1 + T s s ) L (1 + K s v 2 )( T f w s + 1) sw (20) Here , K s is the stability f actor , T s is the desired time constant, n is the steer ing r atio , T f w is the dela y time and sw is the steer ing wheel angle . 4.2. Sim ulation Results and Discussion 0 1 2 3 4 5 6 7 8 9 10 0 0.05 0.1 0.15 0.2 0.25 time (s) yaw rate (rad/s)     Reference CNF PID LQR (a) 0 1 2 3 4 5 6 7 8 9 10 −0.2 −0.1 0 0.1 0.2 time (s) yaw rate (rad/s)     Reference CNF PID LQR (b) Figure 5. Sim ulation results a) Y a w r ate response dur ing J-cur v e , b) Y a w r ate response dur ing Lane change Figure 5 depicts the output responses of y a w r ate tr ac king perf or mances dur i ng J-cur v e and Lane change manoeuvres . Based on the figure , the f astest r ising and settling time with the smallest margin of steady state error of y a w r ate tr ac king response is accomplished b y CNF-DOB control method, f ollo w ed b y PID-DOB and LQR-DOB . Moreo v er , the influence of the e xter nal side wind di s t urbance in CNF-DOB based system is reduced b y 87% . The results sho w that the combination of CNF and DOB is ab le to o v ercome the disturbance issue compared to the findings in [7], where the tr ac king perf or mance is major ly aff ected b y the e xistence of disturbance . 5. Conc lusion In this paper , the combination of CNF and DOB is successfully proposed as AFS controller in SBW v ehicle . Based on the sim ulation results , it can be concluded that the CNF-DOB based system is ab le to enhance the SBW v ehicle handling p erf or mance b y producing the f astest y a w r ate tr ac king responses with least disturbance eff ects compared to PID-DOB and LQR-DOB . As f or the fut ure w or k, e xper iment should be conducted to v alidate the proposed control method in a real time condition. Ac kno wledg ement The w or k presented in this study is funded b y Ministr y of Higher Education, Mala ysia under Research Univ ersity Gr ant, Univ ersiti T eknologi Mala ysia (v ote no: 13H73) and P er usahaan Otomobil Nasional (PR O T ON) Sdn. Bhd (v ote no: 4C099). Ref erences [1] M. Hosaka and T . Mur akami, “Y a w Rate Control of Electr ic V ehicle using Steer-b y-Wire Sys- tem, Adv anced Motion Control, 2004. AMC ’04. The 8th IEEE Inter national W or kshop , pp . 31–34, 2004. IJEECS V ol. 7, No . 2, A ugust 2017 : 434 441 Evaluation Warning : The document was created with Spire.PDF for Python.
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