Active Vibration Damping in Hydraulic Construction Machinery Procedia Engineering 176 ( 2017 ) 514 – 528 1877 7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the[.]
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 176 (2017) 514 – 528 Dynamics and Vibroacoustics of Machines (DVM2016) Active vibration damping in hydraulic construction machinery Addison Alexandera,*, Andrea Vaccaa, Davide Cristoforib b a Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA CNH Industrial, Strada di Settimo 323, San Mauro Torinese 10099, Italy Abstract Hydromechanical systems are prone to significant oscillations, due to the ability of hydraulic oil to store potential energy This is extremely important when considering mobile hydraulic machinery, especially those machines which handle large loads Oscillations can negatively affect the stability of the payload, the comfort of the operator, and the overall safety of the system For the particular case of earthmoving machines, several systems have been designed in order to alleviate these oscillations and increase machine operability These systems include both passive and active designs which attempt to utilize the motion of the payload in such a way as to cancel out the effect of machine vibrations This paper seeks to assess the potential advantages of active oscillation control strategies with respect to current state of art passive strategies A reference case vehicle (wheel loader) is presented and analyzed in order to determine its typical vibrational behavior A simulation model for the reference machine is developed and used in assessing machine performance The effectiveness of the current passive vibration damping approach with respect to reducing the vibrations perceived by the operator in the cabin, as well as those affecting the payload, is presented Then, an active (electrohydraulic) control structure is presented using both acceleration and pressure feedback, including an adaptive controller constructed using an extremum-seeking algorithm To quantitatively compare the relative performances of these various systems, an appropriate objective function is defined Simulation results are presented for each of the considered control strategies, and their performances are compared The simulation indicates a performance of active vibration control systems roughly equivalent to that of currently implemented passive control strategies In some cases, the active control performance is actually two to three times as effective as the passive control © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license ©2016 The Authors Published by Elsevier Ltd (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2016) Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines Keywords:Vibration control; extremum seeking; hydraulics; construction machinery; electrohydraulic control; oscillation damping * Corresponding author Tel.: +1-765-477-1609; fax: +1-765-448-1860 E-mail address: addisonalexander@purdue.edu 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines doi:10.1016/j.proeng.2017.02.351 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 Introduction One of the prevalent issues related to the operation of mobile hydraulic construction machinery is the propensity of these systems to generate oscillations while traveling Conditions such as driving on uneven surfaces introduce vibrations into the machine, which can excite certain oscillatory modes, often causing strong low-frequency motion of the system This can have several negative effects, including decreasing implement and/or load stability, causing discomfort for the operator, and reducing the overall safety of the system Without an adequate system for reducing machine vibrations, productivity, safety, and machine life can all suffer Several solutions have been proposed in the past to address this issue, with varying degrees of success In general, these solutions fall into two different categories The first category is that of “passive” vibration damping These designs take advantage of the behavior of hydraulic systems, often incorporating specialized components or adding capacitive and/or resistive elements into the existing circuitry [1,2] Passive damping is typically effective in cancelling vibrations, but only in a very limited range of operating conditions Furthermore, by modifying the hydraulic circuit, the response dynamics of the system are often negatively impacted Also, the additional required hydraulic elements represent an added cost for the system Fig Two-body system showing chassis and implement These and other limitations of passive vibration damping systems inspired the development of “active” vibration control methods The term active refers to the fact that these systems utilize electrohydraulic setups that actively monitor various system parameters and generate electronic signals to control the motion of the hydraulic components in such a way that the machine oscillations are cancelled out [3] One of the main advantages of active control is that it often can be implemented in such a way that modifications to the basic layout of hydraulic system the reference machine are not required Such control strategies have previously been applied to several prototype machines in controlled environments, including those utilizing displacement-control architectures [4,5] This work, on the other hand, focuses on a more conventional hydraulic architecture for controlling actuators through hydraulic control valves The schemes presented in this paper use either machine acceleration or hydraulic pressure to synthesize the control signal The active ride control method put forth in this work utilizes a simple, non-model-based controller to damp the machine vibrations This simple control structure has several benefits, in that it can be transferrable from one system to another and the theory behind it is well understood However, this also means that the controller relies heavily on an online optimization method in order to work properly for any given system To verify the feasibility of the the proposed controller, and to gain an understanding of the system behavior, a simulation model was created A basic schematic of this system model is shown in Fig It includes considerations for rigid body motion and hydraulic system dynamics, as well as a simple tire deflection model Oscillations are introduced into the system through vibrations represented as vertical motion of the tire/road interface The tires themselves are modeled as a spring-damper connection between the road surface and the axle of the machine Using the simulation model, the effectiveness of the current passive vibration damping approach is analyzed The existing passive system is based on the addition of a capacitive element (accumulator) and a resistive element (4/4 515 516 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 spool valve) into the hydraulic circuit These elements work together in a way similar to the shock absorbers on an automobile suspension The resistive component damps the transmitted vibrations between the implement and the chassis, while the capacitive component can reduce both the amplitude and frequency of the transmitted vibrations In order for it to effectively optimize the controller parameters, a numerical objective function was defined which allows different controller performances to be compared This objective function attempts to quantify the oscillations in the system over a given period of time A well-defined objective function is also necessary for implementing the non-model-based adaptive controller Nomenclature Variables A area a gain of sinusoidal perturbation B valve constant CH hydraulic capacitance c damping rate of tire F force f function describing dynamic system h high-pass filter pole location J moment of inertia k spring rate of tire, extremum-seeking algorithm integrator gain M moment m mass p pressure Q net flow into control volume t time x displacement in the x-direction y displacement in the y-direction, output of dynamic system z measured quantity α hydraulic cylinderchamber area ratio β wheel loader boom angle γ isentropic exponent of a gas Δ change in parameter θ rotational displacement, parameter estimate ξ damping ratio of second-order system τ time constant of first-order system ω frequency of sinusoidal perturbation ωn natural frequency of second-order system Subscripts A atm acc B command ext gas i net oil related to the cylinder chamber of the hydraulic piston atmospheric pressure related to the hydraulic accumulator related to the piston chamber of the hydraulic piston the value sent into a dynamic system as a command external to current system related to the gas in the hydraulic accumulator related to component i the net value of a term (in minus out) related to the hydraulic oil in the system Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 PRC pilot pre pump raise rod W x y z related to the passive ride control (PRC) system related to the pilot line of a valve related to the pre-charge pressure of the hydraulic accumulator occurring at the hydraulic pump related to the raising action of the hydraulic piston related to the rod of the hydraulic piston related to the wheels of the wheel loader occurring in or about the x-direction occurring in or about the y-direction occurring in or about the z-direction initial value Reference Machine For the purposes of determining the performance of the active vibration damping method used in this paper, a reference machine was needed which could be a representative case for describing the behavior of mobile construction equipment.The reference machine used for this work is a Case 621F wheel loader This is a twelvemetric ton wheel loader with articulated steering and a loading bucket capable of holding 1.9 m3 of material It has a four-speed transmission with a maximum speed of 38.6 km/h This research is primarily focused on the hydraulic actuation of the wheel loader implement (boom and bucket with linkages) Therefore, no considerations are given to the other actuators on the machine or the transmission system The hydraulic circuit controlling the implement motion is a post-compensated load-sensing (LS) system, in which the LS supply pump serves the boom and bucket as users Fig Boom control system schematic, including passive ride control (PRC) The reference machine is also equipped with a passive ride control (PRC) setup capable of damping vibrations under certain operating conditions The actual hydraulic schematic of this system is shown in Fig In this case, the oscillation reduction is accomplished by the addition of a hydraulic capacitance and a hydraulic resistance into the existing circuit which controls the position and motion of the boom This capacitance takes the form of an accumulator (labeled as #13 in Fig 2) connected to the boom control circuit via a pilot-operated 4/4 spool valve The inclusion of the accumulator and valve has a significant effect on the dynamic behavior of the system For instance, the system now includes the pressurized gas within the accumulator, which has a much higher compressibility than the hydraulic oil This allows fluid to flow in and out of the accumulator as the changing pressure causes the volume of the gas to expand and contract This flow means that the system with the PRC 517 518 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 enabled is more pliable; that is, it allows a wider range of relative motion between the wheel loader frame and the implement By adjusting the orifice (#10) on the pilot line of the 4/4 spool valve (#9), the dynamics of this flow, and hence the dynamics of the moving implement, can be modified even further (i.e to achieve a desirable behavior) The primary effect of allowing a greater motion of the boom is that the wheel loader no longer behaves in theory as a single rigid body but rather as two separate masses (implement and chassis) connected to each other through a hydraulic circuit which behaves in many respects like a spring-damper connection (see Fig 1) The motion of the wheel loader implement now produces its own forces which are reacted by the chassis of the wheel loader and which counteract the forces that cause the undesired oscillations in the machine By tuning the accumulator and valve parameters, the equivalent spring-damper connection between the chassis and the implement can be adjusted in order to reduce the machine oscillations within a wide range of operating conditions Once the parameters for the PRC have been set, this circuit can work well at the specified operating condition, but its performance will suffer when the system is very far from the design point To overcome this limitation of the PRC, an active ride control (ARC) system is desired A well-designed active control system should not be susceptible to the performance issues mentioned when the PRC is being used far from its design point, because the active control can generate different control signals for different operating conditions Machine Model The first step in assessing the machine behavior and the effect of the various oscillation reduction methods is the generation of a suitable simulation model for the system This model has several different objectives, but its main goals are as follows First, the model needs to include the rigid body dynamics of both the chassis and the implement of the reference machine Second, it must account for the effect of the tires, as they are the only contact points between the machine and the driving surface Finally, the model must incorporate the dynamics of the hydraulic system used to control the position of the boom, as the motion of this system will play a large role in the performance of the vibration control strategies 3.1 Vehicle Dynamics Model To generate the simulation model for the entire machine, it must be analyzed from a vehicle dynamics standpoint As mentioned in the discussion of the reference machine, when a vibration control strategy has been activated, the implement and chassis of the wheel loader are able to move relative to each other Therefore, this system is treated as two decoupled masses, a chassis and an implement, which are linked together via pin connections and a hydraulic cylinder Figure 1shows the full system with the implement portion of the machine circled Since they are treated as separate bodies, the chassis and the implement are represented as having distinct centers of gravity (labeled as CG1 and CG2, respectively) For the purposes of this research, each of these machine sections is treated as a rigid body Therefore, in terms of dynamics, each body is described by its own force balance (∑ 𝐹 ) = 𝑚 𝑥̈ ∑𝐹 (1) = 𝑚 𝑦̈ (∑ 𝑀 ) = 𝐽 𝜃̈ (2) , (3) Equations (1) through (3) are standard free-body motion equations which have been incorporated into the model to describe the motion of the system components In these equations, Fx and Fy represent the forces acting body i in the x- and y-directions, respectively (these directions are labeled in Fig 1), Mz represents the moments acting about the z-axis (extending out of the page), mi and Ji¬ are the mass and moment of inertia of body i The linear accelerations of body i in the x- and y-directions are shown as ẍ i and as ÿ i, respectively, and the rotational 519 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 acceleration about the z-axis is represented by θ̈ z,i By combining these equations with the appropriate kinematic constraints for the system (as done in [4]), this system reduces from a six degree-of-freedom model to one with only four degrees of freedom The forces and moments in (1)-(3) include both those exterior to the machine as well as reaction forces from one body to another Also considered is the force from the hydraulic cylinders (two acting in parallel) which connect the boom (implement) to the chassis It is this force which is used to counteract the machine oscillations, so its value is closely tied to the oscillation reduction strategy being used The model describing the cylinder force is described in detail in the next subsection of this paper To analyze the system behavior, an appropriate input for the system model must be determined In the case of this research, it was decided that the model input would be the height of the roadover time with respect to its starting height This is a reasonable analog to what the real-world system actually sees as an input, and in conjunction with the tire model described below, it translates well to a force input which will cause the dynamics model to behave appropriately Figure 3shows a typical road profile acquired from actual measurements on the reference machine, which begins with the machine remaining stationary for the first five seconds and then traveling over terrain Road Height Profile Front axle Rear axle 0.5 -0.5 -1 10 15 20 25 30 Time [s] Fig Representative road profile used as a model input (normalized) For this research, it was decided that an appropriate model for the tire dynamics is a spring-damper model This approach is widely used in literature due to its relatively simple construction and reasonable results [4,5,7] In this model formulation, the tire is treated as a spring-damper connection between the ground and the machine The road profile controls the lower side of the vertical spring-damper connection shown in Fig 1, so the motion of the center point of the wheel W is a function of the forces generated by the spring-damper tire model In this model, the tire is assumed to only exert a vertical force onto the machine This is because the primary input affecting the system vibrations is the height profile of the road Thus, the horizontal forces generated by the tire are neglected, as they not contribute in an important way to the vibrations being considered Using this simplified tire dynamics model, then, the force acting on the machine at each axle due to the tire is as follows: 𝐹 = −𝑘 𝛥𝑦 − 𝑐 𝑦̇ , (4) where ky and cy are the equivalent (vertical) spring and damping rates for the tire, respectively, and ΔyW and ẏ W are the change in relative vertical displacement and velocity of the wheel center with respect to the road surface, respectively It can be seen that when the distance between the wheel center and the road surface decreases (or is decreasing), the vertical force acting on the machine at W increases, and it decreases in the opposite case 3.2 Boom Cylinder Hydraulic System Model One aspect of the machine simulation model which must be represented with a high degree of accuracy is the hydraulic circuit which controls the motion of the boom of the wheel loader implement It is integral to properly simulating the machine dynamics This system is shown in Fig 520 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 The motion of the boom itself relative to the chassis of the machine is directly controlled by the position of the cylinders on each side of it These cylinders are linked hydraulically, so their motion can be considered equal A typical dual-acting single-rod cylinder, like those used on the reference machine, is shown in Fig The motion of this cylinder is defined by a simple force balance equation 𝑚 = 𝐴 (𝑝 − 𝛼𝑝 ) − 𝐹 𝑥̈ (5) In equation (5), mrod represents the mass of the cylinder rod, ẍ rod is the acceleration of the cylinder rod, pA and pB are the pressures in the two cylinder chambers, AA is the area of the piston, α is the area ratio between the piston face in the rod-side cylinder chamber and the full piston face in chamber A, and Fext includes all external forces acting on the piston, including the inertial forces of the masses connected to the rod This force includes all inertias and motion effects from the chassis and implement which are connected to the cylinder It should also be noted that friction forces are neglected in this model, as the primary forces being considered are much larger Fig Schematic of hydraulic cylinder model It can be seen from (5) that the pressures in cylinder chambers A and B are perhaps the most important factors in determining the motion of the boom in terms of cancelling out vibrations Therefore, the pressure in each chamber needs to be defined for the model 𝑝̇ = 𝑝̇ = , , (𝑄 − 𝐴 𝑥̇ ) (6) (𝑄 + 𝐴 𝑥̇ ) (7) In these equations, pi represents the pressure in chamber i, CH,i is the hydraulic capacitance (volume of fluid divided by its bulk modulus) of the fluid in chamber i, Qi is the net fluid flow into chamber i, and ẋ rod is the velocity of the cylinder rod All other variables are the same as above In general, the hydraulic capacitance CH,i is a function of the cylinder stroke (as it changes with fluid volume) Therefore, these equations are valid only at a certain cylinder position Nevertheless, because they consider not only the piston chambers but the connected transmission lines (which also have a relatively high compliance), the volumes dealt with here are so large, it isreasonable to assumethat the capacitances are constant As this system does not have significant leakage flows, (7) can be further simplified to: 𝑝̇ = , (−𝛼𝑄 + 𝛼𝐴 𝑥̇ ), (8) where α is the same area ratio used in (5) above When giving a command to the valve that raises and lowers the boom, the flow into the cylinder is fairly well defined It can be modeled using a simple orifice equation and an appropriate dynamic equation for the spool displacement y 𝑄 =𝐵 𝑦 , +𝑦 𝛥𝑝 , (9) 521 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 where for orifice i: Qi is the flow through the orifice, Bi is the valve constant, yi and y0,i are the current displacement and initial position of the spool, and Δpi is the pressure difference across the orifice This is a very standard way of calculating the flow through a given valve However, in the case of this research, the valve pressure-flow characteristics were mapped based on experimental data available for the reference valve Because the circuit under consideration is a load-sensing hydraulic system, the pump is designed to give a proper amount of flow so that the pressure in the supply line is always at a constant offset above the pressure of the boom cylinder circuit Thus, Δp across the valve is more or less constant, and the flow through the valve is primarily a function of spool displacement To model the dynamics of the spool in the valve, a second-order dynamic is given 𝑌 (𝑠) = 𝐼(𝑠) (10) In this equation, Yi (s) is the Laplace transform of the spool position yi, I(s) is the Laplace transform of the input command current to the spool, ωn is the natural frequency of the system, and ζ is the damping ratio of the system This transfer function gives a second-order dynamic for the spool given a certain command current One final consideration for this system is that while the pump flow is controlled by a load-sensing circuit, it is not capable of changing flow instantaneously To model this dynamic, a first-order time constant has been modeled for the pump flow 𝑄 (𝑠) = (𝑠) , 𝑄 (11) where Qpump(s) is the Laplace transform of the actual flow given by the pump, Qcommand(s) is the commanded flow from the load-sensing circuit, and τpump is the time constant for this system In actual implementation, this is split into two different time constants, one for “stroking” and one for “de-stroking,” since the pump dynamics can be different depending on whether the commanded flow is increasing or decreasing 3.3 Passive Ride Control System Model The final aspect of the complete system model which needs to be simulated is the passive ride control (PRC) structure For the sake of elaborating on the system structure, a schematic of the PRC system is shown in Fig When in normal operation (with the 3/2 enabling valve #11 in the on position rather than as shown and accumulator #13 above its precharge pressure and below its maximum pressure), it can be seen that the 4/4 stabilizing spool valve (#9) controls the flow between the boom cylinders and the PRC system accumulator Therefore, the motion of this valve is an important component to the system dynamics When it is at the first stage (on the left), the PRC system is fully connected to the boom control cylinders The other three stages work to ensure that the PRC accumulator (#13) maintains the appropriate pressure The orifice to the left of the stabilizing valve (#10) is meant to control the dynamics of the spool in the valve; therefore, the pressure seen by the pilot line entering the left side of the valve is described by a first-order transfer function 𝑃 (𝑠) = 𝑃 (𝑠) , (12) where Ppilot and Praise are the Laplace-transformed functions of pressure at the pilot line of the valve and in the line connected to the raise chamber of the boom cylinder, respectively, and τPRC is the time constant associated with the orifice connecting those two lines The stabilizing valve’s spool displacement is therefore related to the pressure difference between the pilots on either side of the valve The flow through the valve, then, can be calculated using the same orifice equation (9) which is used for determining the flow into the cylinder Having determined all of these model expressions, the final component needed to model the behavior of the PRC system is the pressure in the PRC accumulator, as this pressure affects the flow through the stabilizing valve and therefore, the motion of the machine implement In general operation for the machine (line pressure above 522 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 accumulator precharge but below maximum system pressure), the pressure of the oil in the line is equal to the pressure of the gas in the accumulator 𝑝 , =𝑝 (13) , Since the pressure of the gas in the accumulator is known, the volume of that gas can also be determined using the isentropic relationship for an ideal gas 𝑉 =𝑉 , , , , , (14) where Vacc,gas and Vacc,pre are the current volume and precharge volume of the gas in the accumulator, respectively, pacc,pre and pacc,gas are the precharge and current pressures of the gas, and γ is the isentropic exponent for the gas Knowing the volume of the gas and the volume of the accumulator, the flows into and out of the accumulator can be determined The net flow into the accumulator Qacc,net can then be used in the pressure build-up equation of the accumulator to determine the oil pressure 𝑝 , = 𝛾∫ , , 𝑄 , 𝑑𝑡 , (15) Typically, the solution comes from a numerical integration, since the time evolution ofpacc.oil depends on the instantaneous value of the pacc,oil, which affects the bulk modulus For other operating conditions (i.e above the max system pressure or below the accumulator precharge), these expressions not hold But those conditions are not within the normal operation of the machine, so they fall outside the scope of this paper Proposed Control Structure Active ride control (ARC) works by generating an appropriate signal for the valve that controls the motion of the boom cylinder on the machine Due to this fact, the active control system consumes more system energy than the passive control, which does not demand any current for controlling valves That being said, the ARC system uses the standard hydraulic system for the wheel loader (i.e no hardware modifications are required) Thus, it is easily implementable on production machines such as the reference machine To synthesize a proper control signal for commanding the boom valve, information about the current state of the system must be available to the controller This feedback control setup is pivotal to the design of the ARC, and selecting the correct feedback signal is of utmost importance Using an improper feedback signal could cause the controller to underperform or even to have a negative impact on the system Fig ARC schematic with (a) acceleration feedback (ARCa) and (b) pressure feedback (ARC p) Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 For the current system, two potential feedback signals were identified The first signal, and perhaps the most intuitive, is the acceleration of the cab or boom of the machine This should be an acceptable feedback signal because the vibrations in the cab and implement of the wheel loader are essentially accelerations, and they are exactly the phenomena which the system is actually attempting to control From a controls perspective, it makes sense to directly measure the system state that is being targeted by the controller As discussed in Section 2, the complete machine can be considered as two separate bodies which have their own dynamic behaviors Therefore, there are two different locations where the acceleration can be measured to attain different information about the system Because of this, there are two different configurations for ARC using acceleration feedback (shortened to ARCa): using the acceleration in the wheel loader cab (chassis) and using the acceleration of the boom (implement) Figure 5a shows a simplified schematic of this setup The second feedback signal considered is the pressure in the raise side of the boom actuation cylinder A similar sensor configuration has been previously investigated for load-handling machines [8] The pressure in this line provides a different indicator of the forces acting on the machine Therefore, by examining the pressure in this line, it should be possible to generate a motion which can counteract the forces causing vibrations in the machine A simplified schematic of the ARC using pressure feedback (denoted ARCp elsewhere in this paper) is shown inFig 5b It is important to note that both the pressure- and acceleration-based ARC structures also include sensors which monitor the angle of the boom (denoted by β) Due to the difference in resistive loads between raising and lowering the boom, as well as other factors, the boom has a tendency to drift from the desired angle during operation of the ARC system Therefore, the angle of the boom is treated as a feedback signal so that the controller can correct for drift and maintain the correct boom angle when it is not attempting to counteract vibrations Fig Basic control structure for ARC p setup Using the feedback of either pressure or acceleration signals, many different traditional control structures for the ARC can be used For the case of this paper, the control scheme considered is a simple proportional-derivative (PD) controller The PD control structure is a simple and well-understood control scheme, and it is well suited to the application at hand As the proportional control attempts to drive the current error to zero, the derivative component strives to cut down on the response time of the controller This is important for dynamic systems such as the reference machine, where the idea is to attenuate machine oscillations as rapidly as possible While stability analysis for this system is outside the scope of this paper, similar control strategies have previously been shown to be stable under comparable operating conditions [9] Therefore, it should lend itself well to a fairly aggressive optimization scheme Figure shows what this basic structure looks like for ARC using pressure feedback From this figure, it can be seen that the proportional and derivative gains (KP and KD) are determined by a gain scheduler, which is capable of modifying them in real-time based on the operating condition at hand As shown in the figure, the operating condition is determined using the operator command and the feedback signal The inclusion of the operating condition identification is one of the primary facets which sets the ARC apart from the PRC ARC can be adapted 523 524 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 to better suit a given situation, where PRC has been designed specifically for a certain condition and its performance can suffer when the system is not in that specific condition The high-pass (HP) filter shown in the figure is meant to remove the constant value of the pressure so that the controller only acts on the vibrations It also allows the pressure to change slowly, which permits standard operation of the implement without interference from the controller Another consideration for this system is the anti-drift boom angle control This is accomplished by a PI structure acting on the error between the desired boom angle and the current angle The resulting command signals are then summed to generate the control current i shown in the figure FromFig 6, it is possible to see that the operator command to the boom is still factored into the generation of the control signal Therefore, when the system does not have any vibrations to be damped, the boom control behaves as it would under normal operation For ARC using acceleration feedback (ARCa), the same structure is used, substituting an acceleration signal for the pressure signal in the figure above Perhaps the most difficult aspect of the control structure shown in Fig is the generation of the values for the gain scheduler, which sets the proportional, integral, and derivative gains of the PD and PI controllers based on the current operating condition Ideally, the gain scheduler must be populated with appropriate gains for every conceivable situation Therefore, some method must be used to find the best gain values for each operating condition It would be impractical to find the values by trial and error, so an automated optimization strategy is desired The strategy selected for use in this investigation is known as the extremum-seeking (ES) optimization approach This strategy has been successfully applied by the author’s research team for optimizing the gain scheduler parameters used in controlling hydraulic cranes [10,11] This strategy was chosen for several different reasons First, of course, it can independently find the optimal controller parameters for a given operating condition However, this means that if the operating conditions on the machine change significantly, the controller can adapt to better meet the new design point, which could be significantly different from the first Furthermore, using this strategy means that this system can even be transferred from one machine to another without drastic changes to the structure, and it should adapt to the new machine without much trouble These and other considerations make the ES strategy very appealing for this research ES optimization uses a gradient-based algorithm to adjust the input of a given function in such a way as to find an extremum (minimum or maximum) of that function That is to say, it determines the location of a function extremum by perturbing the function’s input and observing the gradient of the function In this way, given the proper optimization parameters, the ES algorithm should converge to an extremum of the function (assuming one exists) [6], though the location to which it converges may be a local extremum as opposed to a global extremum Objective Function Definition In order for the ES algorithm to properly optimize the controller parameters, it needs a numerical value for y, the output of the system Strictly speaking, there are three different objective functions which have been defined for this research Each of these uses a different measurement signal from the machine The first two each use the acceleration at a given location on the machine One location is inside the cab of the wheel loader, where the acceleration represents the vibrations felt by the machine operator The second location is the boom, which should be equivalent to the vibrations at the load Therefore, these two cost function values represent very different considerations: one for operator safety/comfort and the other for load stability Finally, the third cost function is generated by analyzing the pressure in the lift side of the boom cylinder In order to capture only the oscillation content in the signal, the following operation is done to the measurement signal under consideration ∫|𝑧(𝑡) − 𝑧̅| 𝑑𝑡 (16) 525 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 In (18), z(t) represents the measured pressure in the boom cylinder, the acceleration of the cab, or the acceleration of the boom The average value of the signal z̅ is subtracted, and then the absolute value of the result is integrated over a given length of time This process is shown graphically in Fig One important consideration for this time-based objective function is that it depends on the length of the time window in consideration That is to say, a signal with a constant oscillation content will have a different objective function value when evaluated using two time windows of different length Another factor is that the units of this objective function are [signal units·seconds] To correct for these aspects, the objective function is often normalized by dividing it by the length of the time window When using this normalization, this objective function formulation is roughly equivalent to the root mean square value of the offset signal By using this objective function, the ES algorithm is able to automatically tune the proportional and derivative gains of the controller to minimize vibrations at a given operating condition It can also be used to objectively compare the performance of different control schemes applied to the system Step 2: Compute area 6 4 Monitored Quantity [-] Monitored Quantity [-] Step 1: Subtract offset and take absolute value -2 -4 -6 -2 -4 -6 10 Time [s] 2 Time [s] x 10 10 x 10 Fig Time-based objective function generation (original signal shown in blue) Simulation Results The simulations presented in this section have two main objectives First, they should make it possible to assess the performance of a given vibration reduction scheme by comparing the vibration of the system with reduced vibration to that of the system without vibration reduction Second, they should demonstrate the capability of the ES algorithm to determine the correct controller gains to minimize machine vibrations For all of these tests, a time constant of 80 ms was used to represent the stroking and de-stroking dynamics of the pump Table Performance of simulated oscillation reduction strategies Cost fcn reduction [%] Test condition PRC Label Road Profile Load [kg] Angle [°] Cab accel TC1 15km/h, flat 66 16.1 TC2 15km/h, flat 5500 66 5.8 TC3 15km/h, flat 11,000 66 14.6 ARCp Boom accel ARCa Cab accel Boom accel Cab accel 68.2 10.7 25.8 27.3 44.0 0.0 17.0 5.6 64.2 0.0 6.7 8.1 TC4 35km/h, flat 66 12.9 70.5 24.8 56.0 39.7 TC5 15km/h, uneven 66 15.2 68.2 13.7 46.0 24.0 TC6 15km/h, uneven 5500 66 12.4 61.7 2.6 47.4 9.7 TC7 15km/h, uneven 11,000 66 24.0 0.0 0.0 0.0 526 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 A range of operating conditions is needed in order to test system performance under various setups The three primary factors in the test setup are: road surface profile, speed of travel, and mass of material in the bucket Depending on how uneven or smooth the road surface is, it could have a significant impact on the vibrations of the system Therefore, two different road profiles, “flat” and “uneven,” were used Both have at least some amount of irregularity in their height profiles, but they are much more pronounced in the “uneven” surface profile The machine’s speed could also have an impact on the amount of energy input into the system (which can be translated into vibration), so two different travel speeds were chosen: 15 and 35 km/h Finally, the mass being carried by the bucket of the wheel loader affects the machine motion and it also has a large impact on the force generated by the motion of the implement (which is used to cancel vibrations in both passive and active setups) Therefore, simulations were run with bucket loads of 0, 5500, and 11,000 kg The first system which must be simulated is the passive ride control On the real-world machine, this system is designed in such a way as to minimize the vibrations at a singular operating condition Therefore, in the simulation, the PRC parameters were optimized for a single case (35 km/h, flat, kg load), which has been indicated with boldface font in Table below Consequently, the PRC could potentially perform better for the other test conditions Performance results for each test condition are given by two different numbers Both of these are given in terms of the percent reduction in the indicated cost function value when compared to a test at the same operating condition with no vibration reduction strategy applied It can be seen from the results in Table that in simulation the passive ride control is capable of significantly reducing the oscillations at both the cab and the boom of the machine The most significant reductions, however are seen in the boom acceleration This makes sense intuitively, as the PRC (and also the ARC schemes) affects the boom motion directly, while the cab motion is only an indirect response to the boom motion Furthermore, the mass of the chassis is much greater than that of the implement, so the boom motion is not capable of making an extreme impact on the motion of the chassis (and hence the cab) Table also shows the same performance results for the pressure- and acceleration-based active ride control systems For each test condition, the controller parameters were tuned using the extremum-seeking algorithm in order to reduce the cab accelerations as much as possible This means that each case is tested under its optimal conditions OF reduction (Cab accel.) [%] Vibration Control Comparison 45 40 35 30 25 20 15 10 PRC TC1 ARCp TC2 ARCa TC3 TC4 TC5 TC6 TC7 Fig Comparison of vibration-reduction schemes It can be seen that the ARCp scheme is also capable of reducing machine vibrations in some cases In fact, for Test Conditions 1, 4, and 5, the results are more or less comparable to the passive ride control case, and in Condition the ARCp actually outperforms the PRC Test condition is the worst case for all three schemes It is far from the PRC design point, but perhaps with continued work the ARC can improve the system behavior even in this condition Finally, the same seven tests were simulated for the acceleration-based active ride control scheme, using the cab acceleration as the feedback signal Again, the controller parameters were optimized for each test condition, which Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 should be possible on the real-world system For this case, only the cab acceleration cost function is considered, since that is the specific vibration content this controller seeks to attenuate.Once again, the simulation shows that the active ride control scheme is capable of reducing machine vibrations for almost every condition In most cases, this setup is capable of performing at least as well as both of the other oscillation reduction schemes Having generated the performance evaluations for each of the vibration-reduction setups, the three of them are compared in Fig This plot considers only the cab acceleration, as that is the only fair comparison for the ARCa structure using cab acceleration feedback All three seem well-suited for attenuating machine oscillations, but it appears that, at least in simulation, certain strategies perform better than others For instance, in Test Condition 4, both the ARCa and the ARCp seem to outperform the PRC case, with ARCa performing times as well as PRC At any rate, the simulation results indicate that the active control structures, especially the scheme using acceleration feedback, are suitable replacements for the passive scheme on the reference machine Conclusions This paper summarizes the research done toward the development of an active control structure for vibration reduction in mobile hydraulic construction equipment A representative system simulation was constructed which can give a good indication of the real-world system performance This simulation included the rigid body machine dynamics as well as a simplified tire model It was also capable of replicating the performance of the current passive vibration control mechanism installed on the reference machine In the interest of replacing this passive structure with an active electrohydraulic control scheme, a suitable control structure was designed for the system This active control setup is more economical than the passive control, because it does not require additional hardware to be added to the machine The active control scheme utilizes the boom position and either the boom lift cylinder hydraulic pressure or the acceleration of the cab or boom as feedback signals to generate a control output The feedback signal is run through a proportional-derivative controller, which uses a gain scheduler to populate the proportional and derivative gains based on the current operating condition For this research, the extremum-seeking algorithm was employed to find the optimal gain values for each operating condition Finally, the various vibration attenuation strategies were compared to determine their relative performances In order to compare them in a numerical fashion, an objective function was determined using a time-domain signal (e.g pressure or acceleration) This objective function was then used to compare the different strategies side-byside From this analysis, it was shown that the active vibration strategies are capable of attenuating machine oscillations in simulation, and they are likely appropriate substitutes for the currently-employed passive control system One of the primary future works for this research is to verify these simulation results with experimental testing It should also be mentioned that the cost benefits mentioned in this paper assume the availability of the necessary electrohydraulic components In some cases, therefore, an additional initial investment may be required before seeing cost benefits References [1] M.K Palmer, V.A Simkus, C.P Beaudin, B.A Vogt, Ride Control System, US005733095, 1998 [2] Bosch Rexroth, Bosch RSM2-25 Stabilizing Module Documentation, (n.d.) https://md.boschrexroth.com/modules/BRMV2PDFDownloadinternet.dll/RE64618_200405.pdf?db=brmv2&lvid=54395&mvid=12026&clid=20&sid=4C91FA7EF1A61CDF7561C6021E432F07.borextc&sch=M&id=12026,20,54395 (accessed March 30, 2016) [3] R Gianoglio, F Salvatore, J Weber, Method and Device for Damping the Displacement of Construction Machines, US20070299589, 2007 [4] C Williamson, S Lee, M Ivantysynova, Active Vibration Damping for an Off-Road Vehicle with Displacement Controlled Actuators, International Journal of Fluid Power 10 (2009) 5–16 doi:10.1080/14399776.2009.10780984 [5] R Rahmfeld, M Ivantysynova, An Overview about Active Oscillation Damping of Mobile Machine Structure, International Journal of Fluid Power (2004) 5–24 doi:10.1080/14399776.2004.10781188 [6] K.B Ariyur, M Krstić, Real-Time Optimization by Extremum-Seeking Control, John Wiley & Sons, Inc., Hoboken, NJ, 2003 [7] R Rajamani, Vehicle Dynamics and Control, 2nd ed., Springer, New York, 2012 [8] P Krus, J.-O Palmberg, Damping of Mobile Systems in Machines with High Inertia Loads, Proceedings of the JFPS International Symposium on Fluid Power 1989 (1989) 63–70 doi:10.5739/isfp.1989.63 527 528 Addison Alexander et al / Procedia Engineering 176 (2017) 514 – 528 [9] D Cristofori, Advanced Control Strategies for Mobile Hydraulic Applications, Doctoral thesis, Purdue University, 2013 [10] D Cristofori, A Vacca, K Ariyur, A Novel Pressure-Feedback Based Adaptive Control Method to Damp Instabilities in Hydraulic Machines, SAE International Journal of Commercial Vehicles (2012) 586–596 doi:10.4271/2012-01-2035 [11] G.F Ritelli, A Vacca, Experimental-Auto-Tuning Method for Active Vibration Damping Controller: The Case Study of a Hydraulic Crane, 9th IFK 2014 (2014) ... Machine For the purposes of determining the performance of the active vibration damping method used in this paper, a reference machine was needed which could be a representative case for describing... circuitry [1,2] Passive damping is typically effective in cancelling vibrations, but only in a very limited range of operating conditions Furthermore, by modifying the hydraulic circuit, the response... “passive” vibration damping These designs take advantage of the behavior of hydraulic systems, often incorporating specialized components or adding capacitive and/or resistive elements into the existing