Hybrid models of hydraulic systems for hardware-in-the-loop simulation. Part 1: Theory

1 Hybrid models for hardware-in-the-loop simulation of hydraulic systems Part 1: theory J A Ferreira1*, F Gomes Almeida2, M R Quintas2and J P Estima de Oliveira3 1Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal 2IDMEC–Polo FEUP, University of Porto, Porto, Portugal 3Department of Electronic Engineering, University of Aveiro/IEETA, Aveiro, Portugal Abstract: Physical modelling of hydraulic systems results in systems of differential and algebraic equations (DAEs) that are normally stiff. This is because they often include multiple temporal scales and present complex and non-linear behaviour. The simulation of these stiffDAEs in real time demand small time steps, in order to achieve algorithm stability, because explicit fixed step solvers are usually applied. Modelling some fast dynamics as instantaneous changes in order to reduce the model’s stiffness has been an area of research in the last few years. The description of the dynamic behaviour as piecewise continuous modes, interspersed with discrete transitions, together with the reduction in the model complexity, facilitates the use of fixed time step integration methods and thus allows real-time simulation. The main goal of this work was to obtain not too complex models in order to allow the models to be used in hardware-in-the-loop experiments. This paper proposes the use of the statecharts formalism to describe hybrid behaviour in hydraulic systems and presents semiempirical models of a valve controlled hydraulic cylinder intended to test real controller performance on a hardware-in-the-loop setup. These semiempirical models require less computing power, and it is easier to adjust the model parameters. Keywords: fluid power, modelling, real-time simulation, hardware-in-the-loop simulation NOTATION K 9 p0 relative pressure gain at x : s=0 K 9 q0 flow gain at x : s=0 appiston acceleration Lcylinder maximum stroke Lv,Laspool velocity and accelerationAs1,As2 A1t,A2t pseudo-sections A1,A2cylinder chamber areas limits respectively Mconnected mass (load, pistonfn,vnnatural (angular) frequency FCO Coulomb frictional force and rod) Pirelative pressure at valve port iFffrictional force FLload applied force PLload pressure drop Pnnominal pressure dropFSStribeck friction gacceleration due to gravity P1,P2cylinder chamber relative pressuresglkc cylinder leakage conductance k1,k2,k3,k4,k5pseudo-section parameters P 9 Lrelative load pressure qij volumetric flowrate from port ik1t,k2t,k3t,k4t,k5t pseudo-section parameters Kvviscous friction coefficient to port j qlk leakage volumetric flowrate qlkc cylinder leakage volumetricThe MS was received on 20 February 2004 and was accepted after revision for publication on 25 May 2004. flowrate * Corresponding author: Department of Mechanical Engineering, Qin,Qout incoming and outgoing University of Aveiro, Campo Universitario, Aveiro 3810, Portugal. E-mail: jaff@mec.ua.pt volumetric flowrates respectively I03404 © IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 2 J A FERREIRA, F GOMES ALMEIDA, M R QUINTAS AND J P ESTIMA DE OLIVEIRA QLload volumetric flowrate be simulated in real time with decreasing costs. All these factors made possible the use of hardware-in-Qnnominal volumetric flowrate Qs,Qttank and source volumetric the-loop simulation (HILS) techniques [1], until recent years almost proprietary to the aerospace industries,flowrates respectively Q1,Q2volumetric flowrates of outlet with respect to other engineering fields. HILS refers to a technology in which some of the components of a pureports Ttemperature simulation are replaced with actual hardware. This type of procedure is useful, for example, to test a controller,u :normalized valve input µ[−1, 1] which, instead of being connected to the real equipment under control, is connected to a real-time simulator.vppiston velocity vSStribeck velocity Hydraulic systems normally present complex and non-linear dynamic behaviour and often include multipleVL1,VL2 enclosed volumes at lines 1 and 2 respectively temporal scales. Modelling these systems results in nonlinear equation systems that are usually stiff. WhenWin,Wout incoming and outgoing weight flowrates respectively using numerical simulation, the integration algorithms change their time step to handle these multi-time scalexppiston position x : snormalized valve spool position behaviours. However, these variable-step methods are unsuitable for real-time simulation applications. For real-µ[−1, 1] zseal deformation (friction time simulation, a fixed-step integration algorithms must be used. The fixed-step methods mainly use explicitmodel) algorithms that generally have problems when solving stiffsystems. In fact, when some variables in the systemboil bulk modulus be1 effective bulk modulus for undergo fast changes, and the step size is too large, fixedstep algorithms may become unstable or the solutionchamber 1 be2 effective bulk modulus for may diverge. Reduction in the overall model stiffness can be achievedchamber 2 DPij pressure drop between port iby modelling some fast dynamics as instantaneous changes and representing the dynamic behaviour as piecewise con-and port j DPmpressure difference to the middle tinuous modes interspersed with discrete transitions [2]. These different continuous modes of operation can bepoint jdamping ratio described with expressive formalisms such as the hybrid bond graphs [3], hybrid automata [4] or hybrid Petrirmass density s0seal stiffness (friction model ) nets [5]. However, these are flat formalisms and so complex hybrid dynamics are difficult to describe and under-s1seal damping coefficient (friction model ) stand. Another formalism such as statecharts [6] added to hybrid features [7,8] is more suitable to describe complex dynamics due to its hierarchical approach to express behaviour. The capability of clearly describing,1 INTRODUCTION in a structured way, complex hybrid behaviours helps the specialist modeller in his or her task. It enables an easierHydraulic systems have been used, for a long time, in industrial manufacturing and in heavy machinery. evaluation of the impact and tradeoffs involved when fast continuous behaviours are substituted by discreteHydraulic hardware has undergone great evolution during the last few years, from hydromechanical devices transitions. Other additional problem, when modelling for real-time simulation, is the model complexity that,to sophisticated electrohydraulic systems controlled by microprocessors. The use of electronics and microassociated with limited step sizes, implies high performance computing hardware in order to guarantee stepprocessors contributes to improving the dynamic performance and to adding new features to traditional size restrictions. One way to reduce the computing power and consequently running the real-time simulation in low-systems. Hydraulic systems usually have complex dynamics and non-linearities that lead to hard tasks, even danger, cost hardware is to decrease the model complexity. This can be achieved by using semiempirical models for thethe parametrization of controllers and the testing of new control algorithms. The use of a new control schemes, components instead of using pure physical models. These semiempirical models should capture the most importantusually applied to non-linear systems, such as adaptive control, fuzzy logic or neural networks, to name just a characteristics of the system behaviour for control and simulation purposes. Semiempirical models may be usedfew, becomes possible due to the introduction of microprocessors in the control cycle and to the technological when a model of the input/output component behaviour is sufficient for simulation purposes. This is the usualevolution of hydraulic hardware. Also, with the evolution of the computing power, more complex systems can case when simulations are used for system design. If an I03404 © IMechE 2004Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 3HYBRID MODELS FOR HARD-IN-THE-LOOP SIMULATION OF HYDRAULIC SYSTEMS. PART 1 internal component behaviour description is needed, as be a compound AND state with substates B1 and B2. This process can proceed until low-level description isin the case of component design, then physical models must, in general, be used, compromising its real-time achieved. When orthogonal components are not truly independent, communication between them is specifiedcapabilities. These two complementary approaches, multi-mode by associating an action with a transition. This action is assumed to be broadcasted and so every system com-continuous behaviour and semiempirical models, facilitate the use of fixed-time step integration methods and thus ponent in the statechart will recognize the message. This broadcast communication mechanism allows, when oneallow real-time simulation of stiffsystems. part generates an event, that all the other parts sense it, acting in response if it is so specified. Other enhancement over the FSM formalism is the2 BEHAVIOUR DESCRIPTION WITH THE STATECHARTS FORMALISM association of an event action with a transition, when it is fired, or with a state, while the state is entered or exited. Continuous activity, usually expressed with differentialTo overcome the above limitations of finite state machine (FSM) formalism, Harel [6] proposed statecharts as and algebraic equations (DAEs), can also be associated with a state for modelling continuous behaviour whena visual formalism for the specification and modelling of complex reactive systems. The graphical syntax for the state is active. This action and activity concepts allow the modelling of hybrid systems; actions capturestatecharts has been developed quite early; however, the definition of formal semantics is not yet established. the discrete systems’ features while activities describe the continuous part. Initialization of the state variables ofIn accordance with the types of system to be modelled, several variants of statecharts have been proposed [9]. DAEs can be carried out by associating event actions with transitions or with the entrance or exiting of states.The main enhancements introduced by the statecharts formalism on the FSM were the use of hierarchy, This variant of statecharts is usually called hybrid statecharts and can be viewed as DAEs with its variableparallelism and broadcast communication. Hierarchy is a well-accepted approach for designing structure controlled by the discrete statechart features. Changing the DAE structure corresponds to substitutingand managing complex designs. In statecharts, hierarchy is used to group sets of states together, allowing higha set of continuous equations by another. This is described in a hybrid statechart by the continuous equationslevel description and stepwise development. Depth is achieved by an OR decomposition of a conventional (expressed with the continuous activity) that belong to different states. However, changing the equations in aFSM state, while orthogonality is introduced by an AND decomposition. Parallelism inside a statechart is DAEs can vary the index of the DAEs which can cause problems to numerical solvers.described by AND states, allowing modelling of concurrent activities in the same model through orthogonal Consider the example of a relief valve that limits the pressure in a hydraulic system. It is a hydromechanicalstates. These orthogonal states are all activated when an AND state is entered and are all deactivated when it closed-loop system but it is usually modelled by its (static) input/output characteristic [10]. The behaviouris exited. Figure 1 shows the high-level description of a system of the simple relief valve model can be described by considering that the valve has two possible stable states,with two states A and B. These states can be refined through state decomposition. State A will be a compound and also hysteresis when it changes from one state to another. The valve volumetric flowrate qrthrough theOR state with substates A1, A2 and A3. State B will valve orifice is assumed laminar and is represented by two conductances, one that is the leakage conductance when the valve is closed, glk , and the other the conductance when the valve is opened, gop . The interpretation of the relief valve statechart (Fig. 2) can be made in the following way: when the pressure difference DPis greater than the pressure required to open the valve, pOpen, the valve will be opened (qr=(DP−pClose )gop+DPg lk); when the pressure difference is smaller than the closed pressure pClose the valve will be closed (qr=DPg lk). 3 MODELLING A HYDRAULIC SYSTEM This section presents semiempirical and hybrid models for some hydraulic components and describes how the Fig. 1 Refining states by AND/OR decomposition statecharts formalism can be used to express the system’s I03404 © IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 4 J A FERREIRA, F GOMES ALMEIDA, M R QUINTAS AND J P ESTIMA DE OLIVEIRA Fig. 2 Behaviour description of a relief valve using statechart hybrid behaviour. The experimental system used for applied to the valve. The second block deals with the static behaviour and relates the volumetric flowratemodelling purposes consists of a hydraulic cylinder driven by a high-performance proportional valve. The two comthrough the valve with the input spool position and port pressures.plementary modelling approaches are used to model the proportional valve (semiempirical model ) and to model the hydraulic cylinder (hybrid statechart). 3.1.1 Spool motion The double-action cylinder has low-friction seals in The amplitude and phase frequency response are the order to minimize the stick–slip phenomena. The cylinder basis for the development of the model to describe the load is a mass Min the vertical position. Figure 3 prevalve spool motion. The hysteresis for this type of valve sents the schematic diagram of the valve spool and the is less then 0.5 per cent and the other disturbances such cylinder. as spool friction or flow forces are minimized due to the closed-loop control of the spool position through an electronic control card. The most important behaviour to be modelled is the frequency response of the spool 3.1 Valve model position with regard to the input signal, as the main use of the present model is for control experiments.The valve model is split into two main blocks with a serial connection. The first block represents the dynamic The main objective is to reproduce the frequency response amplitudes with a second-order model withpart where the electrical signal of the controller card is the input and the spool position the output. It describes acceleration and velocity saturation. The phase lag is adjusted with a delay as in reference [11].the different spool dynamics for different input amplitudes Fig. 3 Schematic diagram of the cylinder and valve I03404 © IMechE 2004Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 5HYBRID MODELS FOR HARD-IN-THE-LOOP SIMULATION OF HYDRAULIC SYSTEMS. PART 1 Fig. 4 Dynamic model for spool position with velocity and acceleration limits Several simulations were made for different model flow equations are given by complexities: with velocity saturation only; with velocity qs1=sgn (DPs1 )As1 (x : s) √ |DPs1| and acceleration saturation. Different non-linear limiter shapes, based on continuous and variable structure qs2=sgn (DPs2 )As2 (x : s) √ |DPs2| functions, were considered in the model presented in Fig. 4. The best results were obtained with a limiter q1t =sgn (DP1t )A1t (x : s) √ |DP1t| based on the arctangent function for the velocity and a saturation limiter for the acceleration [12]. It should be q2t =sgn (DP2t )A2t (x : s) √ |DP2t| noted that both limiters have a unitary derivative at (2) the origin. Aij is the pseudo-section of the port ito port jorifice. 3.1.2 Volumetric flowrate model These pseudo-section functions are implemented with hyperbolic functions. The main reason to use these The spool position controls the volumetric flowrate into types of function is the possibility of considering two the cylinder chambers with a non-linear function of the well-defined asymptotes. normalized spool position x : sand the pressure difference For a symmetrical and centred valve with complete DP. This flow, combined with leakage and compressible matching of the spool and valve orifices, the number of flows, controls the chamber pressures. Figure 5 presents different pseudo-section functions can be reduced [12]. a Wheatstone bridge representing the valve flowrates, In this case, the pseudo-sections are related by pressures and orifice sections. The valve orifice areas versus spool position x : sare As1(x : s)=A2t(x : s)=As2(−x : s)=A1t(−x : s) modelled with pseudo-section functions Aij (x : s)asin reference [11]. The volumetric flowrate is assumed to A characteristic of some other valves is that their orifices be always turbulent, the laminar flow being implicitly are symmetrical but not matched, leading to modelled by the pseudo-section curves, Aij (x : s). The volumetric flowrate qij through a restriction section from As1(x : s)=As2(−x : s), A1t(x : s)=A2t(−x : s) port ito port jis written as [13,14] Using this approach the following functions were used qij =sgn (DPij )Aij (x : s) √ |DPij |(1) for the pseudo-sections: where DPij =Pi−Pjis the pressure drop between the two ports and sgn (DPij ) is the sign of PiµPj. Considering the nomenclature presented in Figs 3 and 5, the valve As2(x : s)=k1x : s+k2+ √ k3x :2 s+k4x : s+k5, k3x :2 s+k4x : s+k50, Yx : sµ[−1, 1] As1(x : s)=−k1x : s+k2+ √ k3x :2 s−k4x : s+k5, k3x :2 s−k4x : s+k50, Yx : sµ[−1, 1] A1t(x : s)=k1t x : s+k2t + √ k3tx :2 s+k4tx : s+k5t, k3tx :2 s+k4tx : s+k5t0, Yx : sµ[−1, 1] A2t(x : s)=−k1x : s+k2t + √ k3tx :2 s−k4tx : s+k5t, k3tx :2 s−k4tx : s+k5t0, Yx : sµ[−1, 1] (3) with ki,kitµR. Using the notation in the valve diagrams presented in Fig. 5 Wheatstone bridge representation of valve flowrates, pressures and orifice pseudo-sections Figs 3 and 5, the tank flow Qt, the source flow Qsand I03404 © IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 6 J A FERREIRA, F GOMES ALMEIDA, M R QUINTAS AND J P ESTIMA DE OLIVEIRA the outlet flows Q1and Q2are formulated as follows: negligible and the cylinder internal leakage flowrate, which is assumed to be laminar, is given by qlkc =glkc(P1−P2), Qs=qs1+qs2 where glkc is the leakage conductance. The piston velocity is vp=dxp/dt, where xpis the piston position. Qt=q1t+q2t Q1=qs1−q1t 3.2.2 Effective bulk modulus Q2=q2t−qs2 Most of the times, the effective bulk modulus is made constant in simulations. However, when hydraulic (4) systems have to run over a wide pressure range, a value for bethat is pressure dependent, is needed to achieve satisfactory simulation results. To model the effective 3.2 Cylinder model bulk modulus, a pressure-dependent model proposed in This section presents the cylinder model including the reference [15] is used. The model assumes that the air piston dynamics, the effective bulk modulus and the seal volume mixed in the oil is negligible, that the oil temperfriction. The overall behaviour of the cylinder model is ature and pumping conditions are constant and that described with a hybrid statechart. rigid pipes are used. The effective bulk modulus can then be stated for both cylinder chambers: 3.2.1 Piston dynamics Considering the schematic diagram presented in Fig. 3, be1 =105+P1 BP1+C,be2=105+P2 BP2+C(9) the cylinder dynamics can be defined as where B[P−1 a] and Care constants related to the oil Map=P1A1−P2A2−Ff+FL(5) characteristics. where P1and P2are the cylinder chamber pressures, ap=dvp/dtis the piston acceleration, vpis the piston 3.2.3 Friction model velocity, FLis the total load force, Ffis the frictional The friction phenomena are highly non-linear and can force and Mis the total mass in motion (load, piston cause considerable steady state errors and low perand rod). formance in hydraulically controlled systems. Friction The inlet and outlet chamber flows are related to is the reaction tangential force between two sliding the piston velocity and the compressibility effects. The surfaces. In a hydraulic cylinder, most of the friction most important of these effects is the oil compressibility effects are generated in the contact of the seals with expressed in terms of the bulk modulus. The continuity the cylinder body. Different friction patterns occur for equation [13], normally taken for a constant oil bulk different velocities and motion states. For small velocities, modulus, can be generalized assuming isothermal conthe hydraulic fluid acts as a superficial layer and the ditions (see the Appendix) to use the pressure-dependent shear forces determine the friction. For high velocities effective bulk modulus and expressed as and low pressures, a permanent fluid layer is developed and the friction is related to hydrodynamic effects. The ∑Qin−∑Qout =dV0 dt+V0 b(P) dP dt(6) friction then depends on the fluid viscosity characteristics and also on the distribution of velocities along the fluid Considering the diagram presented in Fig. 3, the cylinder layer. In the past, several methods to model the friction flowrate can be stated by applying equation (6) to each were proposed. Most of these are static models and have cylinder chamber: different complexities [16]. However, in recent years, interest on dynamic models for friction grew, especially Q1=glkc(P1−P2)+A1vp+VL1 +A1xp be1(P1) dP1 dt(7) in the analysis of high-accuracy servo-systems and in the development of friction compensators for control purposes [17–20]. Q2=−glkc(P1−P2)+A2vp−VL2 +A2(L−xp) be2(P2) dP2 dtTo model the friction between the seals and cylinder body, the LuGre dynamic model was used. The LuGre (8) friction model [21] can describe complex friction behaviour as the pre-sliding displacement, the stick–slip motion, theIt should be noted that the volume in chamber 1 is V01=VL1 +A1xpand in chamber 2 this volume is Stribeck effects and frictional lag. The stick–slip motion consists of a limit cycle oscillation at low velocities thatV02 =VL2 +A2(L−xp). VL1 and VL2 represent the line volumes plus the cylinder dead volumes and respective occurs because the frictional force is larger at rest than during motion. The pre-sliding displacement shows thatvalve chamber volumes be1 and be2 represent the compressibilities of the fluid, pipes and cylinder walls of the friction behaves like a spring when the applied resulting force is lower than the static breakaway force.chambers 1 and 2 respectively; i.e. they are the effective bulk moduli. The external leakages are considered to be The frictional lag means that there is hysteresis in the I03404 © IMechE 2004Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 7HYBRID MODELS FOR HARD-IN-THE-LOOP SIMULATION OF HYDRAULIC SYSTEMS. PART 1 frictional force versus velocity curves. The LuGre model Accurate modelling of the behaviour, when the piston reaches the extremes, implies the use of a mechanicalis based on the interpretation of the friction as the force generated by a set of bristles belonging to the two impact with fast dynamics that increases the model’s stiffness and makes impossible the real-time simulationsurfaces in contact. The elastic deformation, corresponding to small displacements, is described by having spring in low-cost hardware. In some situations the impact dynamics can be handled with a simple model to limitbehaviour given by the bristles. For large displacements, the plastic deformation is captured by the movement the cylinder work length. The way that the model should be implemented can be well described through a hybridof the bristle’s connections; i.e. some connections are broken and others established. The model formulation statechart. Using the hybrid statecharts formalism the cylinderis based on the average behaviour of the bristles in contact. In a hydraulic cylinder the seal can be considered behaviour can be organized in three parallel ‘tasks’. These correspond to the high-level description of theas the bristle of the LuGre model. For a steady state velocity the seal deflection (state variable z) is constant. AND state Cylinder with three orthogonal states Piston, BulkModulus and SealFriction (Fig. 7).The seal deformation (Fig. 6) is represented by a state variable zwhose dynamics are given by These states can be refined through state decomposition. For example, the state Piston, used to describe the piston and chamber pressure dynamics, can be a compound dz dt=vp−|vp| g(vp)z(10) OR state with substates StopLeft,Normal and StopRight (Fig. 8). where vpis the piston velocity and g(v) is given by The state decomposition process can proceed until a low-level description is achieved. For example the g(vp)=1 s0 (FCO +(FS−FCO )e−(vp/vS)2) (11) StopLeft and StopRight states are then decomposed in order to describe the cylinder behaviour when it is stopped FCO is the Coulomb frictional force, FSis the Stribeck at the extremes. The main functionality to handle the hard force, vSis the Stribeck velocity and s0is the seal cylinder stops is the restarting of the state variable vp stiffness. when the piston reaches one of the limits (xp<0or The frictional force is generated due to the bending xp>L). When such an event occurs, the cylinder ‘enters’ of the seal that acts as a spring and damper, being proa stop state, and its acceleration is set to zero. To ‘leave’ portional to the seal deflection, its rate of change and the stop state the applied force (hydraulic force, load piston velocity. The frictional force is then given by and friction) must invert its signal. During activities define the continuous state behaviour. The Normal state Ff=s0z+s1 dz dt+Kvvp(12) specifies that the piston acceleration apis calculated using the Newton second law, where fis the resulting force where s1is the damping factor of the seal motion and Kvapplied to the piston. When the StopLeft or StopRight is the viscous friction coefficient. state is entered, the action associated with the state For small displacements the model has a behaviour entrance resets the piston velocity state variable. At the identical with a spring with a stiffness coefficient s0and same time, and considering that the piston enters in a damping factor s1. The maximum seal deformation the StopRight state, the default state PosForceR is also occurs in the pre-sliding phase (velocity is zero) and is entered and becomes active, which makes active its congiven by FS/s0.tinuous activity, with the piston acceleration now set to zero. In the meantime, if the resulting force, evaluated 3.2.4 Cylinder model’s behaviour using a statechart in the During activity of the Piston state, inverts its signal, the piston acceleration is again calculated with In real-time simulation all modes of operation can be the Newton law, because the NegForceR state becomes tested including failure modes. For that reason the active. It should be noted that all the During activities piston displacement has to be limited between 0 and L. Fig. 7 High-level cylinder statechartFig. 6 Deformation of the cylinder seal I03404 © IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 8 J A FERREIRA, F GOMES ALMEIDA, M R QUINTAS AND J P ESTIMA DE OLIVEIRA Fig. 8 Low-level cylinder statechart with all the continuous activities and event actions defined of the active states constitute the DAEs that have to be goal was to develop not too complex and not too stiff hydraulic component models for real-time simulation.solved to simulate the system behaviour in the present continuous mode. With the broadcast communication The first step is a reduction in the model’s stiffness by considering some fast dynamics, such as the piston impactmechanism, all the actions and During activities are ‘sensed’ at the same time; i.e., in this case, all the on the cylinder extremes, as instantaneous changes. This results in models with multi-continuous modes,variables are ‘visible’ in all the states. It is interesting to point out that statecharts can be used interspersed with instantaneous transitions that can be successfully represented by the statecharts formalismto handle models with different complexities, appropriated to different types of simulation. For instance, the with hybrid features. The overall cylinder behaviour is described by a hybrid statechart that proves suitable tosubstates BetaCte and BetaPressure can define, in their During activities, different equations for the effective represent graphically the variable equation structure and also different complexities of the cylinder model.bulk moduli of the cylinder chambers. The model user can then select the bulk modulus equations to use in a The other approach is to reduce the overall model complexity by the use of semi-empirical component models.certain simulation by just changing the Comp variable to the desired complexity level. Thus, at the beginning A model of a hydraulic system composed of a highperformance proportional valve and a hydraulic cylinderof the simulation process, the transition T11 is taken, or not, defining in that way the bulk modulus equations to was fully developed. A semi-empirical valve model that describes the volumetric flowrates of proportional valvesbe used. with different orifice sections was proposed. The section orifices follow hyperbolic functions obtained with the spool position as input. The volumetric flowrate through4 CONCLUSIONS the valve orifices is considered to be always turbulent, being the laminar flow implicitly modelled in the sectionThe present work proposes two complementary approaches for the modelling of hydraulic systems to perform HILS functions. The use of a dynamic model to describe the cylinder seal friction is also proposed.experiments using low-cost real-time hardware. The main I03404 © IMechE 2004Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077 9HYBRID MODELS FOR HARD-IN-THE-LOOP SIMULATION OF HYDRAULIC SYSTEMS. PART 1 15 Yu, J., Chen, Z. and Lu, Y. The variation of oil effective Acknowledgement bulk modulus with pressure in hydraulic systems. Trans. ASME, J. Dynamic Systems, Measmt Control, March 1994, This work was funded by FCT under the programme 116, 146–149. POCTI. 16 Armstrong, B., Dupont, P. and Canudas de Wit, C. A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica, 1994, 30(7), 1083–1138. 17 Southward, S., Radcliffe, C. and MacCluer, C. Robust REFERENCES Nonlinear Stick-Slic Friction Compensation. Trans. ASME, J. Dynamic Systems, Measmt Control, December 1991, 1 Maclay, D. Simulation gets into the loop. Instn Electl Engrs 113, 639–645. Rev, May 1997, 109–112. 18 Lischinsky, P., Canudas de Wit, C. and Morel, G. Friction 2 Mosterman, P. 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Fluid Power Systems—Modeling Simulation, Analog and Microcomputer Control, 1989 (Prentice-Hall, b(P)=rAqP qrBT (16) UK). I03404 © IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part I: J. Systems and Control Engineering mi00003404 11-07-04 13:59:55 Rev 14.05 The Charlesworth Group, Huddersfield 01484 517077