Adaptive Neuro-Fuzzy Sliding Mode Control Based Strategy For Active Suspension Control

Transcription

1 th Internatonal Conference on Fronters of Informaton Technology Adaptve Neuro-Fuzzy Sldng Mode Control Based Strategy For Actve Suspenson Control Shahd Qamar 1 1 Department of Electrcal Engneerng COMSATS Insttute of Informaton Technology Abbottabad Pakstan Emal: shahdqamar@ct.net.pk Tarq Khan 2 and Laq Khan 1 2 Department of Electrcal Engneerng Federal Urdu Unversty of AST Islamabad Pakstan Emal: tarqslamabad@gmal.com laq@ct.net.pk Abstract Suspenson system of a vehcle s used to mnmze the effect of dfferent road dsturbances on rde comfort and to mprove the vehcle control. A passve suspenson system responds only to the deflecton of the strut. Whle the semactve system setup can dsspate energy from the system at an approprate tme n a way or amount that s rght for all the varables n the system. The man objectve of ths work s to desgn an effcent actve suspenson control for full car model wth 8-Degrees of Freedom (DOF) usng adaptve softcomputng technque. So n ths study an Adaptve Neuro- Fuzzy based Sldng Mode Control (ANFSMC) s used for full car actve suspenson system to mprove the rde comfort and vehcle stablty. ANFSMC s adapted n such a way as to estmate onlne the unknown dynamcs and provde feedback response. The detaled mathematcal model of ANFSMC has been developed and successfully appled to a full car model. The robustness of the presented ANFSMC has been proved on the bass of dfferent performance ndces. The analyss of MATLAB/SMULINK based smulaton results reveals that the proposed ANFSMC has better rde comfort and vehcle handlng as compared to passve or sem-actve suspenson systems. Keywords-Sldng Mode Control; Fuzzy Logc; Neural Network; Actve Car Suspenson; I. INTRODUCTION Suspenson system s a common property of all vehcles. Suspenson system solates the vehcle body from the road dsturbances to mprove rde comfort and good roadhandlng. Rde comfort and good road-handlng performance of a vehcle are generally analyzed by the dampng feature of the shock absorbers. A vehcle suspenson may be classfed as passve suspenson sem-actve suspenson and actve suspenson system. Passve suspenson system comprses sprngs and shock absorbers [1]. The sprngs are supposed to have a lnear feature and shock absorbers exhbt nonlnear afflaton between force and velocty. So n passve suspenson systems these components have fxed characterstcs and have no means for feedback control. Whereas the semactve suspenson system changes the dampng coeffcent by the electromagnetc regulator nsde the absorber. The mportant feature of the actve suspenson system s that a perpheral power source s appled to attan the desred suspenson objectve. The actuator n an actve suspenson system s placed as a secondary suspenson system for the vehcle. The controller drves the actuator whch depends on the proposed control law. The actve suspenson system gves the freedom to tune the whole suspenson system and the control force can be ntated locally or globally dependng on the system state. Also the actve suspenson system has the supplementary advantages because n ths suspenson system the negatve dampng can be afforded and a large range of forces can be produced at low veloctes. Thus these forces potentally allocate mprovement n the system performance. The selecton of control strategy s very mportant n the actve suspenson system. Wth proper control strategy t wll present mproved coalton between rde comfort and vehcle stablty. Intally many researchers assumed that the vehcle models are lnear but these models have some nonlneartes lke dry frcton on the dampers. These nonlneartes can affect the vehcle stablty and rde comfort. In the last few years researchers appled dfferent lnear control methods and nonlnear control methods to the vehcle suspenson models. The best performance assessments of varable suspenson system on a quarter car model are examned by [2] but only gave nformaton about the heave of the model and seems overlooked the rattle space lmt. Varous lnear control technques are appled on a quarter car model [17] but dd not show any nformaton for large gan from road dsturbance to car body acceleraton. The passenger suspenson seat was taken nto account n ther control technque by [15]. The quarter car model descrbed the passenger suspenson seat wth nonlneartes lke shock absorber dampng bump stops and lnkage frcton. Snce ths model does not gve the suffcent nformaton about the vehcles angular moton therefore vbraton control and dynamc behavor of a half-car suspenson model s nvestgated by varous researchers n [5]. [6] used optmal control laws to compare the performances of the passve suspenson system and actve system suspenson on quartercar model half-car model and full-car model [7]. appled PID controller on an actve suspenson system. A study on /12 $ IEEE DOI /FIT

2 nonlnear actve suspenson system [8] [9] were carred out. Some comparson of PID controlled actve suspenson and sldng mode controlled actve suspenson s proposed [10]. Also PI sldng mode control [12] s appled on an actve car suspenson system. [16] examned the actve control of seat vbratons of a vehcle model usng varous suspenson alternatves. PID control technque s pertaned as a conventonal law. Snce ths control technque can be appled broadly and wdely t has performed sgnfcant role n control applcatons. But ths control method s senstve to parameter changes. If the plant changes ts parameters due to uncertantes then PID controller cannot update ther parameters accordng to plant parameters. On the other hand the adaptve PID controller can update ts parameters accordng to the models parameters. Because of ths adaptve PID controller has better performance than conventonal PID control. But on the hand adaptve PID control has not much nonlnearty as compared to fuzzy logc control to control the nonlnear system. Fuzzy logc control has been broadly consdered and executed n dfferent control systems [13] [14]. A major advantage for ths knd of control approach s that a precse depcton of the system s not essental the system reles on dfferent sensors vagueness ntrnsc n the measurements acqured by the varous sensors are oblgatory. Fuzzy logc control s perfect for ths sort of condton snce exact and accurate nput s not necessary. Because fuzzy logc control s a set of lngustc rules whch sgnfes human thoughts and arranges the estmaton to resolve control approaches for the whole process. Due to these benefts many researchers prefer to look nto ths knd of control approach to reduce the tradeoff between the rde comfort and vehcle stablty. In [15] the authors used a fuzzy logc controller tuned to ncrease the rde comfort of the vehcle. A varety of smulatons showed that the fuzzy logc control s effcent to gve a better rde qualty than other common control approaches for example skyhook control [17]. [18] presented a sldng mode controller for actve suspenson systems. But ths does not address the problem of robustness and models uncertantes. A varety of smulatons showed that the fuzzy logc and observer-based fuzzy sldng-mode control s profcent to gve a better rde qualty than other common control approaches [19]. In ths study ANFSMC control technque s used to enhance the rde comfort and vehcle stablty aganst the road dsturbances. The passenger seat s also ncorporated n the vehcle model to mprove the passengers comfortablty. The paper s dvded nto 6 sectons. Secton II dscusses the full vehcles model. Secton III dscusses the control problem Secton IV dscusses ANFSMC for full car suspenson control. Fnally smulaton results and concluson are gven n secton V and VI respectvely. Fgure 1. Full Car Model II. VEHICLE S MODEL The full car suspenson model s known to be a nonlnear system whch has eght-degrees of freedom. It comprses only a sprung mass attached to the four unsprung masses M fr M fl M rr M rl (front-rght front-left rear-rght and rear-left wheels) at each corner. The sprung mass s allowed to have ptch heave and roll and where the unsprung masses are allowed only to have heave. For smplcty all other motons are gnored for ths model. Ths model has eght degrees of freedom and allocates the body acceleraton and uprght body dsplacement ptch and roll moton of the vehcle body. Full car s professonally ensurng passenger safety and rde comfort. Ths model s consderng only one seat and ths s very mportant to take nto consderaton other fxed wth chasss [16]. The eght degrees of freedom conssts of (x 1 x 2 x 3 x 4 x 5 x 6 x 7 = θ x8 =φ) four wheels dsplacement seat dsplacement heave dsplacement ptch dsplacement and roll dsplacement. The model of a full car suspenson system s shown n fgure 1. The suspensons between the sprung mass and unsprung masses are modelled as nonlnear vscous dampers and sprng components and the tyres are modeled as smple nonlnear sprngs wthout dampng elements. The actuator gves forces that determne the dsplacement of the actuator between the sprung mass and the wheels. The dampers between the wheels and car body sgnfy sources of conventonal dampng lke frcton among the mechancal components. The nputs of full car model are four dsturbances comng through the tyres and the four outputs are the heave ptch seat and roll dsplacement [20] [21] [22] [23]. The full car model wll be used as a good approxmaton of the whole car. A. Mathematcal Modelng The general class of nonlnear MIMO system s descrbed by: p s p s y (r) = A(x)+ B j (x)u j + G j (x)z j (1) =1 =1 =1 =1 108

3 Where x = [y 1 ẏ 1... y r y p ẏ p... y rp 1 p ] T R r s the overall state vector whch s assumed avalable and r 1 +r r p = r. u =[u 1 u 2... u s ] T R s s the control nput vector y =[y 1 y 2... y p ] T R p s the output vector and z = [z 1 z 2... z s ] T R s s the dsturbance vector. A (x) = 1... p are contnuous nonlnear functons B j (x) =1... p j =1... s are contnuous nonlnear control functons and G j (x) =1... p j =1... s are contnuous nonlnear dsturbance functons. Let A =[A 1 (x) A 2 (x)... A p (x)] T (2) The control matrx s: b 11 (x)... b 1s (x) B(x) =..... b p1 (x)... b ps (x) The dsturbance matrx s: g 11 (x)... g 1s (x) G(x) =..... g p1 (x)... g ps (x) y (r) =[y (r1) 1 y (r2) 2... y p (rp) ] T p s p s (3) (4) y (r) = A(x)+B(x).u + G(x).z (5) A(.) R p p ; B(.) R p s ; G(.) R p s The generc nonlnear car model s ẏ = f(x)+b(x).u + G(x).z (6) y = h(x) (7) f(x) R (16 16) B(x) R (16 4) G(x) R (16 4) state vector x R(16 1) u R(4 1) and z R(4 1). The above matrces can be shown n state-space form wth state vector x that s also represented n row matrx form. f(x) =[A 1 (x) A 2 (x) A 3 (x)... A 16 (x)] x =[x 1 x 2 x 3... x 16 ] T A 1 (x) to A 8 (x) are velocty states and A 9 (x) to A 16 (x) are acceleraton states of four tres seat heave ptch and roll [16]. The dsturbance nputs for each tre ndvdually are represented n the form of z matrx. z =[z 1 z 2 x z z 4 ] T z n are n dsturbances appled to full car model. u n are n controllers output to full car model to regulate the car model dsturbances. y n are n states of car. r n are n desred outputs of the controller. Fgure 2. Road Profle III. CONTROL PROBLEM The am of ths control strategy s to mprove the rde comfort and vehcle stablty aganst the road dsturbances. The comfort s examned by the vertcal dsplacement and acceleraton felt by the passenger. The lfetme of elements of vehcle s conserved by keepng away from httng the rattle space lmts.e. to stay away from the allowable peak to peak dsplacement of the system. Hence the controller goal s to mnmze the dsplacement and acceleraton of the vehcle body wth reference to the open-loop to avod the suspenson travel should not httng the rattle space lmts. So the controller performance s good when t reduces the vehcle vbratons under road dsturbances. In ths study a road profle s expressed as. a(1 cos8πt) 1 t t 16 and 17 t 18 z(t) = (b1 cos8πt) 3 t t 14 and 20 t 21 0 otherwse Where a =0.10 m and b =0.15 m are the ampltudes of two dfferent bumps on the road. These road profles are very helpful for observng the heave ptch and roll of the vehcle. Fgure 2 shows the road profle. The control problem s that the suspenson travel should be less than the ampltude of dsturbance.e m. The maxmum dsplacement of the road profle s 0.15 m. The tme delay between front and rear wheels s gven by: δ(t) = (s 1 + s 2 ) V Where s 1 =1.2 m and s 2 =1.4 m are the values of dstance between front wheels and rear wheels and V s the vehcle velocty whch s unform. (8) 109

4 IV. ADAPTIVE SLIDING MODE CONTROL BASED NEURO-FUZZY STRATEGY As sldng mode control s a nonlnear control strategy whch can provde robust state feedback for the nonlnear dynamc systems. The sldng mode control forces the systems state to stay on the swtchng surface. When the system states reach the sldng surface then the system stay nsenstve to nternal constrant oscllatons and rrelevant dsturbances [28]. The sldng mode control structure should satsfy two requrements.e. the closed-loop stablty and performance specfcatons. Consder the followng sldng mode surface by usng a sgn functon.e. Fgure 3. A nonlnear swtchng surface q = ksgn(s) (9) Where k s a constant and t s the maxmal value of the controller output. s s called swtchng functon because the control acton swtches ts sgn on the two sdes of the swtchng surface s =0. s s defned as [29] [31]. s =ė + λe (10) where e = y y ref here y and y ref are the actual and desred states. λ s a constant then sgn(s) s a dscontnuous functon gven as: { 1 f s < 1 sgn(s) = 1 f s > 1 Ths control strategy wll ensure that the system states move towards and stay on the sldng surface s =0from any ntal condton f the followng condton meets sṡ τ s (11) where τ s a postve constant that ensures the system trajectores wll meet the sldng surface. The aforementoned sgn functon for the sldng mode controller structure often cause chatterng n practce. Chatterng s undesrable because t may excte the hgh frequency response of the system. In order to resolve the chatterng ssue a boundary layer around the sldng surface s ntroduced [32]. Where q = q s (12) q s = k.sat( s ψ ) where ψ s a constant whch denotes the thckness of the boundary layer and sat( s ψ ) represents the saturaton functon whch s defned as: sat( s ψ )= { s ψ f s ψ 1 sgn( s ψ ) f s ψ > 1 Ths controller s actually a contnuous approxmaton of the deal relay control [29] [30]. The result of ths control scheme s that nvarance of sldng mode control s lost. The system robustness s a functon of the wdth of the boundary layer. A varaton of the above controller structure s to use a hyperbolc tangent functon nstead of a saturaton functon [33] [34]. q = k.tanh( s ψ ) (13) or t can be wrtten as (ė ) + λe + c q = k.tanh ψ (14) where ψ and c are the constant and λ s the thckness of the sldng surface. It s proven that f k s large enough the sldng mode controllers of (9) (12) and (14) are guaranteed to be asymptotcally stable. The nonlnear swtchng curve s shown n fgure 3. Ths nonlnear curve shows that the swtchng band around the swtchng lne s there to allevate chatterng. A. ANFSMC Structure The TSK fuzzy system s fundamentally adaptve and nonlnear n nature whch provdes robust performance for the parameter varatons and load dsturbances. The fundamental dea of the fuzzy modelng was gven by Zadeh n [35]. The proposed ANFSMC connects TSK fuzzy logc system wth sldng mode functons. In the ANFSMC lnear functon or constant n the consequent part of the lngustc rules n TSK fuzzy systems are replaced wth hyperbolc tangent functon to enhance the estmaton power of the neuro-fuzzy system by usng the nformaton of hyperbolc tangent functon. Each rule n a TSK fuzzy logc control can be a sldng mode controller. The sldng mode controller n each rule can have varous forms. The boundary layer and the coeffcents of the sldng surface become the coeffcents 110

5 of the rule output functon and have ther physcal meanngs. The th fuzzy sldng mode rule can be expressed as.e. IF x 1 s A 1 AND x 2 s A 2 AND... AND x s A nm (15) THEN y m s k.tanh( s ) =1... m ψ Where x 1 x 2... x m y 1 y 2... y m are the nput-output varables and A j s the membershp functon of th rule and jth nput. The ANFSMC structure s gven n fgure 4. In the antecedent part fuzzy reasonng process s performed and n the consequent part of the rule sldng mode control process s performed. Layer 1: In ths layer fuzzy reasonng process s performed. Ths layer accepts nput values. Its nodes transmt nput values to the next layer. Layer 2: In ths layer fuzzfcaton process s performed and neurons represent fuzzy sets used n the antecedents part of the lngustc fuzzy rules. The outputs of ths layer are the values of the membershp functons. Then Gaussan membershp functon s gven by: η j (x )=e (x gj ) 2 σ j 2 = m j = n (16) Where η j (x j ) shows the membershp functon g j and g j are the mean and varance of membershp functon of the jth term of th nput varable m and n are the number of nput sgnals and number of nodes n second layer respectvely. Layer 3: In ths layer each node represents a fuzzy rule. In order to compute the frng strength of each rule and mn operaton s used to estmate the output value of the layer..e. μ j (x) = η j (x ) (17) Where s the meet operaton and μ j (x) are the nput values for the next layer (consequent layer). Layer 4: In ths layer hyperbolc tangent functon are represented. Layer 5: Ths layer estmates the weghted consequent value of a gven rule.e. the hyperbolc tangent functon are multpled wth the thrd layers output value. Therefore the output value for ths layer s gven by: ( ) s p l = w l k.tanh (18) ψ Layers 67: In these layers the defuzzfcaton process s performed.e. n μ (x)p l l=1 u = n (19) μ (x) l=1 Where u s the output for the entre network. Fgure 4. Schematc dagram of back-propagaton learnng algorthm for ANFSMC 1) Parameters Updatng Learnng Rules: The ANFSMC learnng s to mnmze a gven functon or nput and output values by adjustng network parameters. Unknown parameters are mean g j and varance σ j of membershp functons n antecedent part λ l c l ψ l and w l are the update parameters n the consequent part of the rules. In ths study the gradent descent technque s used reduce the cost functon. To mnmze the error between the actual output value of the system and the desred value the gradent descent method can be expressed as: J = 1 n (y ref y ) 2 (20) 2 =1 Where y ref and y are the desred and current output values of the system respectvely. The update parameters w l λ l c l and ψ l of the consequent part of network and g l and σ l (j = n) of the antecedent part of the network can be formulated as: w l (t + l) =w l (t) γ w l (21) λ l (t + l) =λ l (t) γ λ l (22) c l (t + l) =c l (t) γ c l (23) ψ l (t + l) =ψ l (t) γ ψ l (24) g j (t + l) =g j (t) γ g j (25) σ j (t + l) =σ j (t) γ σ j (26) 111

6 Where γ represents the learnng rate. By usng chan rule the partal dervatves of the c l ψ l g j and σ j can be expressed as: w l λ l = y u p l (27) w l y u p l w l = y u p l (28) λ l y u p l λ l = y u p l (29) c l y u p l c l Fgure 5. Closed-loop control structure for actve suspenson = y u p l (30) ψ l y u p l ψ l = y u μ j (31) g j y u μ j g j = y u μ j (32) σ j y u μ j σ j Where the quantty y u s approxmated by a constant r [26] [27]. By takng the dervatve of the above equatons t gve = er μ (ė ) j + λ e + c ktanh w l μ j j (ė ) = e 2 μ + r w ksec 2 λ e + c h λ l ψ μ j ψ ψ (ė ) μ + = er w ksec 2 λ e + c h c l ψ μ j (ė ) μ + = er w ksec 2 λ e + c h ψ l ψ μ j ψ ψ (ė ) + λ e + c ψ 2 = er y j u μ (x ) 2(x gj) g j μ j σ 2 j = er y j u μ (x ) 2(x gj) 2 g j μ j σ 3 j (33) (34) (35) (36) (37) (38) Hence the equatons (33 38) gve the requred change for the values of w l λ l c l ψ l g j and σ j respectvely. B. Onlne Adaptve Neuro-fuzzy Sldng Mode Control Algorthm Fgure 5 shows the closed-loop control structure for the proposed ANFSMC control. Ths structure s employed to update the parameters of the ANFSMC control. The calculatons at any nstant of tme can be descrbed n the followng steps. Step 1: Set the nput-output yref and y of the system. Step 2: Update the parameters of the ANFSMC scheme.e. g j σ j w l λ l c l and ψ l by usng equatons (21 26). Step 3: Calculate the output of the ANFSMC scheme by usng equaton (19). Step 4: Fnally output of the controller added wth dsturbances s gven to system. Step 5: Repeat steps (2-4) untl soluton converges. C. Smulaton Results In ths study t s assumed that the vehcle s movng wth unform velocty unless the road dsturbances create the undesred oscllatons n the vehcle body. The closed-loop structure for full car suspenson control s gven n fgure 5. In order to fulfll the am of the actve suspenson system the proposed actve suspenson strateges are successfully mplemented on full car suspenson system to mprove the vehcles stablty and passengers comfort. The comfort s examned by the vertcal dsplacement and acceleraton felt by the passenger. The controllers goal s to mnmze the dsplacement and acceleraton of the vehcle body wth reference to the open-loop so as to avod the suspenson travel httng the rattle space lmts. So the controller performance s good when t reduces the vehcle vbratons under road dsturbances. In ths secton the smulaton results of dsplacement and acceleraton of the heave ptch roll and seat (wth and wthout controller) are gven. These results are compared wth passve suspenson and semactve suspenson systems. The smulaton tme for the road profle s 24 seconds. The performance ndex (PI) used for evaluaton of dfferent 112

7 Fgure 6. Seat dsplacement wthout control Fgure 8. Heave dsplacement Fgure 7. Seat dsplacement wth control Fgure 9. Ptch dsplacement algorthms s gven by PI = 1 2 T 0 (Z T P QZ P )dt (39) where Z p s the vector for dsplacement or acceleraton Q s the dentty matrx. The Root Mean Square (RMS) value for dsplacement and acceleraton of heave ptch roll and seat has been calculated by z rms dsp. = z rms dsp. = 1 T [h(t)] 2 2 (40) t=0 1 T [h(t)] 2 2 (41) t=0 Fgures (6 7) show that the response of seat wth control (wc) and seat wthout control (woc) s mproved as compared to passve suspenson and sem-actve suspenson system. In passve suspenson and sem-actve suspenson the maxmum value for seat dsplacement s m and m whle for the ANFSMC control the maxmum value for seat dsplacement s m. Here the passenger comfort s ncreased by 71% as compared to passve suspenson and 60% as compared to sem-actve suspenson system. The response of seat wth controller s better than seat wthout controller. Also the settlng tme of ANFSMC controller s reduced and steady state response s mproved as compared Fgure 10. Roll dsplacement to passve suspenson. The seat wth controller ncreased the passenger comfortablty by 10%. Fgures (9 10) show that the response of heave ptch and roll s mproved as compared to passve suspenson and semactve suspenson system. In passve suspenson and semactve suspenson the maxmum value of dsplacement for heave s m and m whle for the ANFSMC control the maxmum value of dsplacement for heave s m. Here the value of heave s mproved by 79% as compared to passve suspenson and 68% as compared to sem-actve suspenson system. In passve suspenson and semactve suspenson the maxmum value of dsplacement for ptch s m and m whle for the ANFSMC control the maxmum value of dsplacement for ptch s 113

8 0.013 m. Here the value of ptch s mproved by 70% as compared to passve suspenson and 57% as compared to sem-actve suspenson system. In passve suspenson and sem-actve suspenson the maxmum value of dsplacement for roll s m and m whle for the ANFSMC control the maxmum value of dsplacement for roll s m. Here the value of roll s mproved by 68% as compared to passve suspenson and 56% as compared to sem-actve suspenson system. Ths ncreased the vehcle stablty rde comfort and passenger comfortablty. Also the settlng tme of ANFSMC controller s reduced and steady-state response s mproved as compared to passve suspenson. Table I PERFORMANCE COMPARISON DOFs Control Algo. z rms dsp. Seat (woc) Seat (wc) Heave Ptch Roll z rms acc. Passve Sem-actve ANFSMC Passve Sem-actve ANFSMC Passve Sem-actve ANFSMC Passve Sem-actve ANFSMC Passve Sem-actve ANFSMC Table I shows the RMS values for dsplacement and acceleraton for the sad road profle. It can be seen that maxmum mprovement has been acheved n case of seat heave ptch and roll wth ANFSMC strategy. V. CONCLUSION In ths study the am s to gve the comfort rde and vehcle stablty aganst the road dsturbances. The detaled mathematcal modelng of the full car suspenson and proposed actve suspenson controllers are gven. Smulaton results show that ANFSMC control strateges for actve suspenson gves better rde comfort and vehcle stablty than sem-actve and passve suspenson system. The parameters of the proposed ANFSMC have been adjusted usng onlne adaptaton by mnmzng the cost functon. The performance of the actve control strategy s observed by the seat heave ptch and roll moton of the vehcle body. It s also observed that the ANFSMC control strategy s more robust and t mproves the rde comfort and vehcle stablty. VI. ACKNOWLEDGEMENT The authors would lke to thanks COMSATS Insttute of Informaton Technology Abbottabad Pakstan for facltatng us to complete ths research work. PI REFERENCES [1] A Gua C. Seatzu and G. Usa Sem actve Suspenson Desgn Wth an Optmal Gan Swtchng Target Vehcle System Dynamcs vol. 31 pp [2] Redfeld RC and Karnopp DC Optmal performance of varable component suspensons Vehcle System Dynamcs vo. 17 no. 5 pp [3] M. Bgarbegan W. Melek and F. Golnaragh A novel neurofuzzy controller to enhance the performance of vehcle semactve suspenson systems Vehcle System Dynamcs vol. 46 n0. 8 pp [4] C.F. Ncolas Landaluze E. Castrllo M. Gaston and R. Reyero Applcaton of fuzzy logc control to the desgn of sem-actve suspenson systems Proc. of 6th IEEE IntI. Conference on Fuzzy Systems Barcelona Span pp [5] Thompson AG and Davs BR. Computaton of the rms state varables and control forces n a half-car model wth prevew actve suspenson usng spectral decomposton methods Journal of Sound and Vbraton vol. 285 pp [6] M. Ahmadan and C.A. Pare A quarter-car expermental analyss of alternatve sem-actve control methods Journal of Intellgnet Materal Systems and Structures vol. 11 no. 8 pp [7] Mouleeswaran Senthl kumar Development of Actve Suspenson System for Automobles usng PID Controller Proceedngs of the World Congress on Engneerng London U.K vol [8] Alleyne A. and Hedrck J.K. Nonlnear control of a quarter car actve suspenson Amercan Control Conference pp [9] Hanaf D. PID Controller Desgn for Semactve Car Suspenson Based on Model from Intellgent System Identfcaton Computer Engneerng and Applcatons (ICCEA) 2010 Second Internatonal Conference on vol. 2 pp [10] Guclu R. and Yagz N. Comparson of dfferent control strateges on a vehcle usng sldng mode control Iranan Journal of Scence and Technology vol. 28 no. B4 pp [11] Alleyne A. and Neuhaus PD and Hedrck JK Applcaton of nonlnear control theory to electroncally controlled suspensons Vehcle System Dynamcs vol. 22 no. 5 pp [12] Sam Y.M. and Osman J.H.S. and Ghan RA Proportonalntegral sldng mode control of a quarter car actve suspenson TENCON02. Proceedngs IEEE Regon 10 Conference on Computers Communcatons Control and Power Engneerng vol. 3 pp [13] R. Rad R. Tawegoum A. Rachd and G. Chasseraux Decentralzed temperature fuzzy logc control of a passve ar condtonng unt Proc. of 15th IEEE IntI. Medterranean Conference on Control and Automaton Athens Greece pp

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