Hybrid models for hardware-in-the-loop simulation of hydraulic systems Part 2: experiments

Transcription

1 1 Hybrid model for hardware-in-the-loo imulation of hydraulic ytem Part 2: exeriment J A Ferreira1*, F Gome Almeida2, M R Quinta2 and J P Etima de Oliveira3 1Deartment of Mechanical Engineering, Univerity of Aveiro, Aveiro, Portugal 2IDMEC Polo FEUP, Univerity of Porto, Porto, Portugal 3Deartment of Electronic Engineering, Univerity of Aveiro/IEETA, Aveiro, Portugal Abtract: The ue of new control cheme for hydraulic ytem ha been the object of tudy during the lat few year. A imulated environment i the cheaet and fatet way of evaluating the relative merit of different control cheme for a given alication. Real-time imulation allow arametrization and tet of the erformance of real controller. Thi aer decribe the et-u of a real-time imulation latform to erform hardware-in-the-loo imulation exeriment with the hydraulic model rooed in the comanion aer (Part 1). A et of arametrization technique are rooed for the emiemirical model of a valve-controlled hydraulic cylinder. Manufacturer data heet and/or exerimental meaurement were ued to adjut the model arameter. Some of thee were directly calculated and other were etimated through the ue of otimization technique. Cloed-loo control exeriment were then erformed on the real-time imulation latform and on the real ytem, in order to evaluate the real-time erformance of the develoed model. Keyword: fluid ower, modelling, real-time imulation, hardware-in-the-loo imulation OTATIO K9 flow gain at q0 x: =0 Kˆ, Kˆ etimated vicou friction vn v A, A A, A eudo-ection coefficient for negative and 1 2 1t 2t A, A cylinder chamber area oitive velocitie reectively 1 2 f, v natural (angular) frequency L cylinder maximum troke n n F frictional force L, L ool velocity and acceleration f v a F load alied force limit reectively L Fˆ, Fˆ etimated Coulomb frictional M connected ma ( load, iton COn CO force for negative and oitive and rod) velocitie reectively P relative reure at valve ort i i Fˆ, Fˆ etimated Stribeck friction for P load reure dro Sn S L negative and oitive velocitie P nominal reure dro n reectively P, P cylinder chamber relative 1 2 g acceleration due to gravity reure g cylinder leakage conductance P9 relative load reure dro lkc L k, k, k, k, k eudo-ection arameter q volumetric flowrate from ort i ij k, k, k, k, k eudo-ection arameter to ort j 1t 2t 3t 4t 5t K9 relative reure gain at q leakage volumetric flowrate 0 x: =0 lk q cylinder leakage volumetric lkc The MS wa received on 20 February 2004 and wa acceted after flowrate reviion for ublication on 25 May q leakage flow at x =0 * Correonding author: Deartment of Mechanical Engineering, lk0 Univerity of Aveiro, Camo Univeritario, Aveiro 3810, Portugal. Q load volumetric flowrate L jaff@mec.ua.t Q nominal volumetric flowrate n

2 2 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA Q, Q tank and ource volumetric condition, including failure mode. Teting a control t flowrate reectively ytem rior to it ue in a real lant can reduce the cot Q, Q volumetric flowrate of outlet and the develoment cycle of the overall ytem. HILS 1 2 ort ha been ued with ucce in the aeroace indutry and u: normalized valve inut µ[ 1, 1] i now emerging a a technique for teting electronic v iton velocity control unit [4, 5]. Thi rocedure ha been alied to v Stribeck velocity olve ome ecific roblem but i eldom ued a a S, etimated Stribeck velocitie for latform to tet the real-time behaviour of hardware vˆsn vˆs negative and oitive velocitie comonent. The imlementation of HILS i imortant reectively for the erformance analyi of comonent or ytem, V, V encloed volume at line 1 and and alo for control algorithm validation. The real-time L1 L2 2 reectively code hould be generated through model decrition. x iton oition Thi code can be executed afterward in dedicated x: normalized valve ool oition hardware, in order to guarantee enough erformance for µ[ 1, 1] real-time execution. z eal deformation (friction model ) The following ection reent the hardware et-u b oil bulk modulu for the valve and cylinder model arametrization and the real-time imulation latform to erform HILS b effective bulk modulu for exeriment. e1 chamber 1 b effective bulk modulu for e2 chamber 2 DP reure dro between ort i and 2 HARDWARE SET-UP AD HARDWARE-I- ij ort j THE-LOOP SIMULATIO PLATFORM DP reure difference to the middle m oint A hydraulic aaratu that conit of a linear hydraulic j daming ratio actuator driven by a ervo-olenoid valve, a hown in eal tiffne (friction model ) Fig. 1, wa develoed for identification of model arameter and to erform HILS exeriment. The ytem i 1 0 eal daming coefficient (friction model ) equied with a et of enor to meaure the ytem reure and iton oition. The valve ort and cylinder chamber reure P, P, P and P are meaured uing 1 2 t four analogue reure enor. The cylinder rod oition 1 ITRODUCTIO i acquired with a linear digital encoder with 1 mm of reolution. The velocity wa obtained by differentiation of The ue of new control cheme for hydraulic ytem ha the oition ignal. All the enor and the valve electrical been the object of tudy during the lat few year [1]. It inut are connected to a low-cot DSP-baed real-time i commonly acceted that a imulated environment i card (RTC) from dspacea [6], model DS1102, in uch the cheaet and fatet way for the evaluation of the a way that real-time control and data acquiition can be relative merit of different control cheme for a given erformed. alication. Modelling and real-time imulation of com- To erform HILS exeriment (ee ection 4), two lex ytem till are, according to Burrow [2], area to DS1102 board, intalled in two different eronal exlore. In fact, and a tated by Lennevi et al. [3], with comuter, were ued a hown in Fig. 2. The control the growing comuting ower, more and more comlex algorithm run in one of the RTC, the other being ytem can be imulated in real time, with decreaing reonible to run the real-time imulation of the cylinder cot. and valve model. The real ytem i then connected to Hardware-in-the-loo imulation ( HILS) refer to a the controller, through a double witch, to acquire the technology in which ome of the comonent of a ure data ued in the HILS erformance evaluation. imulation are relaced with the reective hardware comonent. Thi tye of rocedure i ueful, for examle, to tet a controller which, intead of being connected to the real equiment under control, i connected to a 3 PARAMETER IDETIFICATIO AD real-time imulator. The controller mut think that it i working with the real ytem and o the accuracy of the imulation and it electrical interfacing to the controller PARTIAL RESULTS Thi ection reent the trategie and exeriment mut be adequate. Thi technology rovide a mean for erformed for the identification of the arameter of the teting control ytem over the full range of oerating hybrid model rooed in Part 1 [7].

3 HYBRID MODELS FOR HARDWARE-I-THE-LOOP SIMULATIO OF HYDRAULIC SYSTEMS. PART 2 3 Fig. 1 Hydraulic tet bed (draft and real ytem) Fig. 2 HILS latform 3.1 Valve model ued for the arameter etimation. The block diagram Sool motion model arameter model, hown in Fig. 3, wa imulated over a frequency range from 10 to 300 Hz in te of 10 Hz. The arameter The ool motion model reroduce the frequency were adjuted uing three Bode amlitude curve reone amlitude with a econd-order model with available in the manufacturer data heet (5, 25 and 50 acceleration and velocity aturation, with the hae lag er cent of maximum amlitude). A variable frequency adjuted with a delay. The leat-quare method wa (and amlitude) ine wave u: wa alied to the inut of Fig. 3 Dynamic model for ool oition with velocity and acceleration limit

4 4 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA the dynamic model. The outut ool oition x: wa then ued to evaluate the outut gain in decibel, G. n Thi gain wa then comared with the data heet gain at the ame frequency and amlitude, Gr. The cot n function F i calculated for each et of model arameter v, j, L and L. The model arameter were elected n v a for the minimum value of the function F. Becaue mot of the valve action take lace near the middle oition, a weighting factor of four wa alied on the 5 er cent quadratic error when calculating the cot function value: u: =A in in (2 f n t), A out = x: (1) where n={1, 2,, 29, 30}, fn =10n and t i the variable time. The amlitude gain G=20 log (A /A ) i ued to out in calculate the cot function: F(v, j, L, L )=4 30 (G Gr )2 n n n v a 2 K n=1 Ain =5% + 30 (G Gr )2 n n 2 K n=1 Ain =25% + 30 (G Gr )2 n n (2) 2 K n=1 Ain =50% The following arameter et minimize the cot function for the elected model: v = rad/, j=0.48, n L = and L = v a The imulation reult (dotted curve) reented in Fig. 4 how that the amlitude effect of non-modelled dynamic behaviour are more viible for frequencie higher then 200 Hz. To adjut the hae curve for the different amlitude a delay wa ued. The aroach for the delay etimation wa identical with that ued for the amlitude reone arameter. Analying the reult (Dt= ) reented in Fig. 4, it can be con- cluded that very good reult are obtained for the 5 er cent inut variation (for the valve alication frequency range) Static arameter The tatic model equation rooed in Part 1 of the aer [7] for a ymmetrical but unmatched valve ue four eudo-ection function A 1 (x: ), A 2 (x: ), A 1t (x: ) and A 2t (x: ) and a follow: A 2 (x: )=k 1 x: +k 2 + k 3 x:2 +k 4 x: +k 5 A 1 (x: )= k 1 x: +k 2 + k 3 x:2 k 4 x: +k 5 A 1t (x: )=k 1t x: +k 2t + k 3t x:2 +k 4t x: +k 5t A 2t (x: )= k 1t x: +k 2t + k 3t x:2 k 4t x: +k 5t (3) The k arameter of A i 1 (x: ), A 2 (x: ), A 1t (x: ) and A 2t (x: ) and can be etimated in order to reroduce the valve reure gain and the valve flow gain. The valve ued ha the following tatic meaured characteritic: Q =25.5 l/min, P =35 bar, P =70 bar, K9 =28 l/min, n n qo K =36.5, q =1.36 l/min, where K9 i the relative 0 lk0 0 reure gain at x: =0, K9 i the flow gain at q0 x: =0, P n i the nominal reure dro, q i the leakage flow at lk0 x: =0, Q i the nominal volumetric flowrate and P i n the ource reure. A characteritic of thi tye of valve i that the chamber reure may not intercet at P /2, a can be een later in Fig. 5a. The actual valve ha the intercetion oint at 43 bar for P =70 bar, thu having a difference DP =8 bar relative to P /2. Uing equation (2) and (4) m (reented in Part 1) and conidering that ort 1 and 2 are cloed (reure gain meaurement), i.e. Q =Q =0, 1 2 the following relation can be et for the reure difference at the middle oint: DP m = P 2 A 2 (0)2 A 2t (0)2 A 2 (0)2+A 2t (0)2 (4) Uing again equation (2) and (4) of Part 1 and Q 1 =Q 2 =0, the relative load reure i given by A P9 (x )= 1 (x: )2 L A 1 (x: )2+A 1t (x: )2 A 2 (x: )2 A 2 (x: )2+A 2t (x: )2 where P L =P 1 P 2 and P9 L =P L /P S. The reure gain i then defined a (5) Fig. 4 Dataheet ( ) and imulated ( ) Bode diagram for amlitude and hae lag reone (by courtey of K9 = qp9 L (x : ) Eaton Cororation) 0 qx: K x: =0 (6)

5 HYBRID MODELS FOR HARDWARE-I-THE-LOOP SIMULATIO OF HYDRAULIC SYSTEMS. PART 2 5 Fig. 5 Real and imulated reult of the tatic valve model When meauring the flow gain that i connecting ort 1 to ort 2 (ee Fig. 3 of Part 1) with a null reitance, the load flowrate Q can be exreed a Q or by Q. Then L 1 2 uing equation (2) and (4) of Part 1 and the chamber reure difference to the middle oint, DP, the load in flow i given by the following equation when Q =Q : L 1 Uing Q L =Q 2, the flow gain can alo be exreed by K9 = qa 2t (x : ) q0 qx: K x: =0 SP 2 +DP m qa 2 (x : ) qx: K x: =0 SP 2 DP m Q L (x: )=A 1 (x: )S P 2 DP m A 1t (x : )S P 2 +DP m The flow outide the origin area can be adjuted with the nominal flow Q n and nominal reure P n, which (7) can be meaured for a ecific valve or are available in the manufacturer data heet, a A 2 (x: )#A 1t (x: )#0 The flow gain can be written a for x: =1: (9) K9 = qq L (x : ) = q0 qx: K qa 1 (x : ) x: =0 qx: K x: =0 SP 2 DP m Q n P n =A 1 (x: ) x: =1 (10) qa 1t (x : ) qx: K x: =0 SP 2 +DP m (8) Q n P n =A 2t (x: ) x: =1 (11)

6 6 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA The leakage flow can be exreed a a function of and it occurring frequency (natural frequency of the the relative valve chamber reure, P9 =P /P and ytem) with the reult of the imulation of a linear 1 1 P9 =P /P, uing equation (2) and (3) of Part 1 when verion of the whole ytem. The exerimental block 2 2 Q =Q =0: diagram ued to meaure the natural frequency i hown 1 2 in Fig. 6. The ytem ha to run in cloed loo around X qlk (x: )=q +q becaue of the different cylinder area and becaue of the =A difficultie in etting the valve middle oition. The ytem 1 (x: ) P (1 P9 )+A 1 2 (x: ) P (1 P9 ) i linearized around [P P X V X9 ]T. Thee (12) value are obtained from the teady tate condition of q velocity and acceleration equal to zero, which occur for lk (x: )=q +q 1t 2t X9 =0.009 where P =P and P =P. In thi ituation =A 1t (x: ) P P9 +A 1 2t (x: ) P P9 (13) 2 the reulting force i zero, i.e. A P +Mg A P = and, with P =P +P [9], the equilibrium reure Auming the condition P9 #1 and P9 #0, and uing 1 2 equation (12) and (13), new relation can be tated for the leakage flow and leakage flow derivative at a certain ool oition. If the leakage flow curve i available, a meaurement at a certain oition (x: >0) can be ued; otherwie the leakage at x: =1 can be et to a very mall value or even zero: q lk P91 =1 P9 2 =0 are given by P 10 = A 2 P Mg A 1 +A 2, P 20 = A 1 P +Mg A 1 +A 2 (18) where g i the acceleration due to gravity. At the oition X =82 mm the chamber volume are 0 = P A 2 (x: ) (14) almot the ame. The cylinder area are A = m2 and A = m2. 2 The valve tatic characteritic at the linearized oint q lk = P A P91 =1 1t (x: ) (15) P9 2 =0 qq qa lk = P qx K 2 (x: ) P91 =1 qx: K P91 =1 P9 2 =0 P9 2 =0 have the meaured value (16) k q1 = qq 1 qx: K X90 = S P 2P n m3/; qq qa lk = P qx K 1t (x: ) (17) P91 =1 qx: K P91 =1 k = qq 2 q2 qx: P9 2 =0 P9 2 =0 K X90 = S P m3/ 2P n Uing equation (3) for the eudo-ection function, ten equation can be tated to olve for the k and k eudo- i it k = qp 1 =19P Pa, k = 1 qx: K qp 2 = 15.6P Pa ection arameter model. Thu, uing equation (4), 2 X90 qx: K X90 (5), (8), (9), (10), (11), (14), (15), (16) and (17), and conidering that the leakage flow and their derivative where k i the flow gain at X9, k i the flow gain q1 0 q2 are zero for x: =1 (where P9 =1 and P9 =0), the eudo- at 1 2 X9, k i the reure gain (in chamber 1 at X9, ection equation arameter k, [ee equation (3)], are and k i the reure gain in chamber 2 at i X9. The 2 0 a following: flow reure coefficient are then defined a k = 2.136, k = , k = k = k q2, k = k q1 k = , k = (19) 4 5 c2 k c1 k 2 1 k = 2.145, k = , k = t 2t 3t k 4t = , k 5t = The reult for the relative reure and load flowrate obtained from the imulation of the tatic valve model are reented in Fig Cylinder model The effective bulk modulu The effective bulk modulu b, wa etimated through the e comarion of the maximum cylinder iton acceleration Fig. 6 Block diagram to meaure the natural frequency

7 HYBRID MODELS FOR HARDWARE-I-THE-LOOP SIMULATIO OF HYDRAULIC SYSTEMS. PART 2 7 The linearized cylinder and valve equation are exreed in tate ace format and were imulated in the SimulinkA [10] environment: Cdṗ 1 dṗ 2 dv dẋ D= t v b e1 K 0 b e1 u A 0 V c1 V b b e2 K e2 A 0 V c2 V A 1 A 2 f M M M w t u K 0 V q1 1 b e2 K 0 V q2 2 dx 0 1 D+ v 0 0w 1 Cd 2 dv b e1 C dx : g D Fig. 7 Acceleration veru frequency lot DCd C dv dx D = C dv dx D (20) Fig. 8 Effective bulk modulu veru chamber reure where V =V +A X and V =V +A (L X ) are the equilibrium volume and where V = m3 01 have the value B= and C= : and V = m3 are ued for dead volume of the 02 line and valve chamber reectively. M rereent all b = 105+P (21) the ma in motion and equal 80 kg. The linearized e BP+C verion of the friction model (Part 1) [7] i only valid where B (Pa 1) and C are contant related to the oil for mall dilacement ( le than 15 mm) where the eal characteritic of the model rooed in reference [11]. deformation (variable z) i equal to the iton dilacement x ; i.e. it i aumed that the iton i in the tiction tate. The friction factor f i then intended to model all The cylinder leakage conductance the friction effect (valve and cylinder) that occur when The internal cylinder leakage i aumed laminar and i the ool velocity ign have fat change. rereented by a conductance defined a The effective bulk modulu b and friction factor f were e etimated by an otimization roce that minimize the g = q lkc ditance (in the acceleration frequency lane) between lkc P P 1 2 (22) the real and imulated iton maximum acceleration. The The leakage flowrate i meaured indirectly in the followamlitude of the acceleration ignal meaured with ing way. In the initial iton oition x =0, ort 2 of b = Pa, b = Pa and f=8100 /m e1 e2 the valve wa traed, ort 1 i oen to atmohere and are reented in Fig. 7. The iton acceleration wa the cylinder wa allowed to run in a free way with a meaured with a high bandwidth accelerometer from 1 to heavy load. The iton oition and chamber reure 130 Hz. The exerience hown in Fig. 6 wa reeated for were meaured over a long eriod Dt of time in order everal ource reure in order to evaluate the effective to obtain a contant velocity in teady tate, v. The bulk modulu a a function of the reure. Figure 8 how leakage conductance can then be calculated from the evolution of the real b with the chamber reure e and b calculated with equation (21). The arameter e for the equation (21) were obtained by otimization and g lkc = v A 2 P 2 (23)

8 8 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA The iton oition and the reure in chamber 2 were meaured for a eriod of time Dt=200. The total dilacement, in thi eriod, wa 1504 mm, and the reure mean value wa P =5.28 bar. The value 2 obtained for the internal leakage conductance wa g = m3/ Pa. lkc Friction model Etimation of the tatic arameter F, F, v and K and CO S S v the dynamic arameter and for the LuGre friction 0 1 model (ee ection 3 in Part 1 [7]) are reented below. oitive velocitie. The new etimated arameter are then Fˆ COn =89.26, vˆsn = m/, Fˆ CO =110.2, vˆs = m/, (Fˆ Sn Fˆ COn )=160.3 Kˆ vn =1387 /m (Fˆ S Fˆ CO )=150.8 Kˆ v =818.4 /m where the ubcrit n and indicate negative and oitive velocitie reectively. The comarion of the meaured tatic frictional force and thoe obtained from the ymmetric and nonymmetric tatic friction model i reented in Fig. 9. (a) Identification of the tatic arameter. The tatic arameter are etimated from the velocity frictional force curve meaured with contant velocitie. The amle time wa 5 m, with the frictional force and velocitie (b) Identification of the dynamic arameter. The trategy being calculated with 20 amle in order to minimize for the identification of the dynamic arameter and 0 1 the noie effect. The exeriment at contant velocitie conit in matching the real hydraulic force with the were erformed with cloed-loo velocity control. equivalent hydraulic force, obtained for the ame con- At contant velocity (a teady tate ituation, a =0), dition, from the imulation of the non-linear valve with the latform in the horizontal oition, the friction lu cylinder model. The non-ymmetric tatic friction force can be meaured through the chamber reure arameter were ued. The identification ued oen- [ee equation (5) in Part 1]: loo exeriment, with the valve and cylinder model enhancing the viibility of the dynamic arameter. The F =P A P A (24) f ytem working in the horizontal direction wa excited with a inuoidal ignal with ufficient amlitude to lead The frictional force wa meaured for contant velocitie between 0.2 and 0.2 m/. the ytem in and out of the tiction tate; i.e. the At contant velocity the tate variable z of the friction reulting force hould be, during imulation, larger and model [equation (10) to (12) of Part 1] i contant, lower than the breakaway force. dz/dt=0, and the friction force can be etimated from An otimization method, uch a that ued for eti- mation of the tatic arameter, wa ued to identify the Fˆ +(Fˆ )e (v f=[fˆ CO S Fˆ CO /vˆs)2] gn (v )+Kˆ (25) vv dynamic arameter. The cot function i where Fˆ, Fˆ and Kˆ are the etimated tatic CO S, vˆs v arameter and Fˆ i the etimated frictional force. f For the arameter etimation the leat-quare method wa ued for the cot function cf: cf(f, F, ŝ)= n [F (k) F (k, ŝ)]2 (27) h hm h hm k=1 where F (k) i the k amle of the real hydraulic force h (amle time equal to 10 m) and F (k, ŝ) i the cf= n [F (v ) Fˆ )]2 (26) hm f i f(v i hydraulic force that reult from the model imulation i=1 with the ame initial condition, for the ame time intant. where v are the meaured velocitie. i The utilization of the hydraulic force a the comarion The cot function wa calculated for each arameter force reult from the following imlification. The net et (Fˆ, Fˆ Kˆ given by the Simlex algorithm CO S, vˆs, v) acceleration force i given by ued in the fminearch function of the MATLABA [12] otimization toolbox [13]. Initial value for the arameter were obtained from the meaured velocity veru M dv dt =F h F (28) f frictional force curve. The tatic arameter to be ued are thoe that minimize the cot function. With the ma ued in the tet (iton lu rod), a the For a ymmetrical friction model, i.e. the ame maximum value of M dv /dt are le then 0.05, thi model arameter for oitive and negative velocitie, force i negligible when comared with the hydraulic and the etimated arameter are frictional force. Fˆ =101.8, Fˆ =153.0 The comarion of the hydraulic force, the cylinder CO S Fˆ CO chamber reure, the ool oition and the iton vˆs=0.019 m/, Kˆ v=1090 /m A the meaured frictional force denote different arameter for different ign of velocity, the model can be enhanced with different arameter for negative and velocity, when imulating the model with the nonymmetrical friction tatic arameter, i reented in Fig. 10. The etimated dynamic arameter are = /m and = /m. 1

9 HYBRID MODELS FOR HARDWARE-I-THE-LOOP SIMULATIO OF HYDRAULIC SYSTEMS. PART 2 9 Fig. 9 Frictional force veru velocity teady tate curve Fig. 10 Comarion between the real and imulated ytem when uing the non-ymmetrical friction tatic model

10 10 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA 4 HARDWARE-I-THE-LOOP SIMULATIO the uual ring and damer comonent (ring tiffne EXPERIMETS equal to 1010 /m and the damer coefficient equal to 1010 /m ) and the eal friction model only conider A SimulinkA block imlementing the cylinder hybrid the vicou friction comonent. The overall ytem need tate chart [7] and the valve model wa ued. The model a third-order fixed-te olver with a 2 m te ize in wa imulated in real time with a third-order exlicit order to run roerly, negating real-time oeration with olver and a fixed te ize of 0.5 m. low-cot hardware. Cloed-loo oition control exeriment, with ointto-oint oition trajectory a the inut reference ignal, were erformed. Figure 11 how the comarion between the two exeriment when controlled by roortional 5 COCLUSIOS control, with the roortional contant equal to 50 and a moved ma of 80 kg. A model of a hydraulic ytem comoed of a higherformance The exeriment reented in Fig. 12 intend to evaluate roortional valve and a hydraulic cylinder the erformance of the real and imulated ytem when reented in Part 1 [7], wa fully arametrized. Mot the deired inut trajectorie are te and ram. In thi of the ued model are emiemirical with their ara- exeriment a reure ource with P =120 bar wa ued meter being calculated with imle method or by with a roortional gain K =100. otimization. The tatic valve arameter are calculated From the reult of the above exeriment it can be by olving a non-linear equation ytem. Thi equation aid that the ytem model reent a atifactory erformance ytem i ecified in order to reroduce the relevant at mall velocitie and at trajectorie with tatic characteritic available from the manufacturer high-frequency content. A imilar et of imulation wa data or from exerimental meaurement. The arameter roduced uing a commercial library of hydraulic com- of the dynamic art of the valve and of the friction model onent [14]. The cylinder end to are modelled with are determined with otimization technique. Fig. 11 HILS exerimental and imulated reult

11 HYBRID MODELS FOR HARDWARE-I-THE-LOOP SIMULATIO OF HYDRAULIC SYSTEMS. PART 2 11 Fig. 12 Exerimental and imulation reult for inut trajectorie with high frequency content The main goal of thi work wa to obtain not too 2 Burrow, C. R. Fluid ower ytem an academic ercomlex model allowing their ue in HILS exeriment. ective. JHPS J. Fluid Power Sytem, January 1998, The develoed model are reaonably accurate and the 29(1), whole ytem can be imulated in real time with a thirdfor the evaluation of control concet for vehicle drive 3 Lennevi, J., Palmberg, J. and Janon, A. Simulation tool order exlicit olver with a fixed te ize of 0.5 m. ytem. In Proceeding of the 4th Scandinavian Inter- Cloed-loo oition control exeriment were erformed national Conference on Fluid Power, Tamere, Finland, with the overall model running in a low-cot real-time Setember card from dspacea. The reult were comared with 4 Maclay, D. Simulation get into the loo. Intn Electl Engr the behaviour of the real ytem, with the comarion Rev., May 1997, being very atifactory. 5 Otter, M. M., Schlegel, M. and Elmqvit, H. Modelling and realtime imulation of an automatic gearbox uing Modelica. ACKOWLEDGEMET In Proceeding of the Euroean Simulation Symoium ( ESS 97), Paau, Germany, October DS1102 DSP Controller Board, Technical Manual (dspace Thi work wa funded by FCT under the rogramme gmbh, Paderborn). POCTI. 7 Ferreira, J. A., Gome de Almeida, F., Quinta, M. R. and Etima de Oliveira, J. P. Hybrid model for hardware-inthe-loo imulation of hydraulic ytem. Part 1: theory. REFERECES Proc. Intn Mech. Engr, Part I: J. Sytem and Control Engineering, 2004, 218(I0), Edge, K. A. The control of fluid ower ytem reonding 8 Ferreira, J. A. Modelação de Sitema Hidráulico to the challenge. Proc. Intn Mech. Engr, Part I: J. Sytem ara Simulação com hardware-in-the-loo. PhD thei, and Control Engineering, 1997, 211(I2), Univerity of Aveiro, Aveiro, Portugal, 2003.

12 12 J A FERREIRA, F GOMES ALMEIDA, M R QUITAS AD J P ESTIMA DE OLIVEIRA 9 Gome de Almeida, F. Model reference adative control of 12 MATLAB The Language of Technical Comuting, Techa two axe hydraulic maniulator. PhD thei, Univerity nical Manual. of Bath, Bath, Coleman, T., Branch, M. A. and Grace, A. Otimization Tool- 10 Simulink Dynamic Sytem Simulation for MATLAB, box, 1999 ( The Math Work, Inc., anch, Maachuett). Technical Manual. 14 Beater, P. Hylib Library of Hydraulic Comonent for Ue 11 Yu, J., Chen, Z. and Lu, Y. The variation of oil effective with Dymola, 2001 (Dynaim AB, Sweden). bulk modulu with reure in hydraulic ytem. Tran. ASME, J. Dynamic Sytem, Meamt Control, March 1994, 116,