AN INVESTIGATION OF HYDRAULIC ACTUATOR PERFORMANCE TRADE-OFFS USING A GENERIC MODEL

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1 AN INVESTIGATION OF HYDRAULIC ACTUATOR PERFORMANCE TRADE-OFFS USING A GENERIC MODEL D. L. Wells, E. K. Iversen, C. C. Davis, S. C. Jacobsen Center for Engineering Design University of Utah Salt Lake City, Utah ABSTRACT This paper investigates the effect of the variation of parameters of system elements on the overall performance of a generic model of a hydraulic actuation system. Specifically, this paper examines the effects on actuator performance of two issues: intrinsic compliance, the physical compliance within the actuator itself; and independent control of the actuator valve areas (e.g., supply and return areas for hydraulic fluid chambers) versus control of actuator valves with fixed area relationships. Increasing intrinsic compliance in the actuator degrades response to controller commands but improves the ability of the actuator to tolerate insults. Independent control of valve areas provides both better response to commands and better rejection of disturbances than control with valves that have fixed area relationships. The performance information provided by the model permits behavior-based design of hydraulic actuation systems. Backaround JNTRODUC TlON A great deal of time has been spent on the design of robots, teleoperation systems, and prosthetics. These projects require actuation systems with specific groups of behavioral characteristics, such as grace, accuracy, strength, and speed. In order to achieve these desired characteristics, the systems need good actuators. However, defining a good actuator and describing how to design a good actuator are difficult problems because actuators are not completely understood [l]. To address this problem, the Center for Engineering Design (CED) at the University of Utah decided to explore the issues involved in the behavior-based design of robot effectors [I]. Some issues brought up by that investigation were: 1) how well external disturbances can be tolerated; 2) how nonlinearities affect actuator performance; 3) how intrinsic qualities can be manipulated to produce desired'behaviors; 4) how additional control possibilities can be used to improve performance; and 5) how hydraulic systems fit into the behavior-based design strategies proposed for systems with electrical motors [I]. Of specific interest is the effect of intrinsic compliance on external disturbance rejection. It has also been suggested that independently controlling valves can improve actuator performance [2-41. Therefore, the effect of this added control flexibility on actuator performance is also sought. The purpose of this research is to develop and use a generic model of a hydraulic actuator to investigate the above issues. A generic model is needed so that the results of the investigation are valid for hydraulic actuation systems in general and not just for specific cases. Also, the model must include elements that have significant effects on actuator performance so that these effects may be analyzed. The model can then be used to quantify trade-offs resulting from these elements in order to permit the development of behavior-based design strategies for hydraulic actuators. In particular, an understanding of the effect on performance of intrinsic compliance, physical compliance within the actuator itself, is sought. Also, this research attempts to show the possible benefits of independently controlling the valve areas in a hydraulic actuator. APPROACH Model of the Actuation Svste m Develoment of a Generic Model: A generic model for a hydraulic actuation system is proposed. The model includes the qualities of interest. It has some elements that account for the intrinsic compliance of the actuator. Also, the model allows for independent control of the valve areas that modulate the flows to and from the actuator. The model also needs to be flexible enough to allow for different load dynamics, structures, and control schemes to be implemented without requiring an entirely new model. A more detailed description of the model, including the dynamic equations, can be found in ~41. The actuator modeled is a one-degree-of-freedom, linear-motion, double-acting actuator. A single actuator with one linear degree of freedom is adequate for the type of information sought. This double-acting actuator model (Fig. 1 and Table 1) consists of a piston-type actuator connected to supply pressures and return reservoirs via control valves. The valves direct fluid flow CH2876-1/90/0000/2168$ IEEE ~

2 M1,Bl CF1 CF2 M2,BZ K1,Al K2, A2 Desired Position Fig. 1. Double-acting hydraulic actuator model Table 1 Double-acting hydraulic actuator model variables PL1 = Load pressure on side one of the piston A1 = Area of accumulator one B1 = Damping of accumulator one Ki = Stiffness of accumulator one Mi = Mass of accumulator one PL~ = Load pressure on side two of the piston A2 = Area of accumulator two B2 = Damping of accumulator two K2 = Stiffness of accumulator two M2 = Mass of accumualator two Psi = Supply pressure side one Ps2 = Supply pressure side two PR~ = Return pressure side one PR~ = Return pressure side two CF1 = Fluid capacitance side one C F = ~ Fluid capacitance side two FL = Load force XL = Load position ML = Load mass BL = Load damping KL = Load stiff ness to and-from fluid chambers on either side of a piston. Also connected to the fluid chambers are fluid accumulators. The accumulators, which represent intrinsic compliance, are modeled as second-order systems with masses, springs, and dampers. In addition to the accumulators, pure fluid capacitances are added to the fluid chambers to represent the compressibility of the fluid. The piston drives a simple, second-order load characterized by a mass, spring, and damper. The force and position of the load are fed back to a controller, which uses these values, in addition to the desired force and desired position inputs, to control the valve areas. The supplies and reservoirs are at constant pressures. Also, the servovalves are modeled as first-order low pass systems. This assumption about the servovalves is not unreasonable for modeling many types of servovalves, and, if such valve models are not accurate enough, the models can easily be modified [5-81. Fxoerime qtal Valwtion of the Mod& : Experimental verification of the model is necessary to ensure that the simulation results yield an adequate representation of a real system. The validation is performed as a two-point validation. The responses for two situations are measured. In one situation no accumulators are present in the lines between the valve and the piston. In the other situation accumulators are present. Both situations are simulated using the model, and the model parameters are tuned to give responses that match the actual responses. For a successful validation, the simulated responses must match the actual responses, the model parameters must have reasonable values, and the estimates for the same elements in the two simulations must be approximately the same for both simulations if the elements are the same in both experiments. Pctuat ion Svstem Performance Since the goal is to observe actuator performance, performance needs to be defined. Performance is separated into two different catagories in order to provide information on the actuator's ability to respond to commands and to external disturbances. One type of performance, &-Q: active performance, is the response to commands (a desired position, for example). This performance can be characterized by how quickly the actuator moves as commanded and by how accurately the actuator performs as commanded. In this paper the method for determining active performance is the position response to a step input in position. The quantitative parameter chosen as the measure of active performance is the rise time, defined here as the time taken by the system to go from 10% of the commanded position to 90% of the commanded position. we Perform: Another type of performance, passive performance, is the response to external disturbances (a velocity disturbance at the load, for example). This performance can be characterized by the amount by which the actuator is perturbed from its undisturbed state, and it reflects the ability of a system to absorb or reject disturbances. The method for determining passive performance is the force response to a velocity disturbance at the load. The velocity disturbance follows a sin"2 profile. The quantitative parameter chosen is the maximum force generated at the actuator due to the disturbance. Simulation of the Model The dynamic equations of the model are simulated using the Advanced Continuous Simulation Language (ACSL) 191. The effect of intrinsic compliance on both active and passive performance is the first issue looked at in the simulations. The rise time as a function of intrinsic actuator stiffness (inverse of compliance) is found. and the maximum disturbance force as a function 2169

3 of actuator stiffness is also determined. Then, the effects of independent area control are examined. For independent area control, all of the valve areas opening into the hydraulic cylinder are varied independently. This is achieved by allowing the gains in the control law to vary. In the control law used, the gains are modulated by the ratio between the pressure drop across the supply valve on one side of the piston and the pressure drop across the return valve on the other side (since supply on one side works in concert with return on the other side). This way the flows in one side and out the other remain about the same regardless of load pressures, removing flow limitations due to fixed areas. For comparison with the independent area control, simulations are run in which the supply and return areas are all related by a fixed geometric relationship so that control of one area automatically determines the value of the other areas. Experimental Validation RESULTS The experimental validation tests and simulations were carried out as described above. A 0.1 Hz square wave (effectively a step input) was used as the position command for the system so that the responses measured were effectively step responses. The experimental responses were adjusted by calibration values from [lo]. Figs. 2 and 3 compare the simulated responses to the experimental responses. For both situations in the two-point validation, the simulated responses are close to the actual responses. From these validation results, it can be seen that the model approximates the actual system well. Consequently, the model's predictions can be trusted. 0 I I I I I I I Fig. 2. Validation plot: no accumulator, position response comparison of simulated and actual response ' o Fig. 3. Validation plot: accumulator, position response comparison of simulated and actual response Simulation of the Model Simulations were now performed on the validated model to address the effects on performance of the system elements. The effect of intrinsic compliance on active and passive performance was evaluated. Also, the effects of independent area control were simulated. i nsi i. In general, the position re.$%set to?r'sy/nput in position had the characteristics of a second-order step response. When the intrinsic compliance increased, the rise time increased, and the response was less damped. The force responses to the velocity disturbance had characteristics of a sin**2 profile; the force rose to a maximum and then dropped off. When the intrinsic compliance increased, the maximum force decreased. Refer to [4] for plots of the individual responses. The information about the effect of compliance on performance is detailed in Figs. 4 and 5. The effect of compliance on active performance is shown in Fig. 4. The effect of compliance on passive performance is shown in Fig. 5. The performance parameters are shown as a function of the intrinsic stiffness (stiffness is plotted instead of compliance because the actual model parameter changed in the simulations is the intrinsic stiffness). As the stiffness of the hydraulic actuation system is increased (i.e., the compliance is decreased), the system becomes faster but cannot absorb disturbances as well. IndeDendent Area Cont rol: The results for independent area control (Figs. 6-9) show that independent area control significantly improves actuator performance. The independent area control improves 1170

4 ~~ Fig. 4. Rise time vs. accumulator stiffness lo Y Fig. 5. Maximum disturbance force vs. accumulator stiffness. I Fig. 7. Independent control test: active performance, independent area control. both active and passive performance; it decreases rise time and decreases the maximum force caused by the disturbance. The system with independent area control has the ability to adjust the ratio of area gains and, thereby, to react to various load pressures in order to improve performance. On the other hand, when the area gains are fixed, the system is set to work best at specific load pressures. Deviations from these load pressures compromise the performance of the fixed systems. 0' Time (Sec) 0.5 Fig. 6. independent control test: active performance, fixed area reference. Fig. 8. Independent control test: passive performance, fixed area reference. 2171

5 0 Fig. 9. Independent control test: passive performance, independent area control. The responses predicted by the model are close to the experimental responses. This is true for both parts of the two-point validation. Therefore, the model accurately reflects the actual system. However, the model has some limitations. For example, it does not include the effects of hysteresis, and it assumes a firstorder response for the valves. If hysteresis effects had been included in the model and if the valves had been modeled as second-order systems, the fit between the experimental responses and the simulated responses would have been even better. However, the fit between the experimental responses and the simulated responses is good even though hysteresis and the higher-order models are not incorporated. Also, without those added complexities, the model is simpler and more generic. The interpretation of the effects of compliance is, as a result, easier. The model is simple but accurate enough to give valuable insight into the performance of hydraulic actuation systems. It is evident that the introduction of intrinsic compliance to an actuation system has a profound effect on the performance of the system; this has been known for years. What is interesting is the quantification of the performance trade-offs resulting from the introduction of intrinsic compliance. This information adds to the framework for behavior-based design of actuators [l, 41. As shown, an increase in intrinsic compliance decreases active performance and increases passive performance. How does intrinsic compliance achieve these performance effects? Compliance between the valves and the actuator piston essentially adds another place for hydraulic fluid to flow. Therefore, when the system is disturbed, the fluid is not trapped. Consequently, the relatively incompressible fluid is not compressed, and large disturbance forces are not created. However, since the fluid has more places to 'flow, not all of its energy is directed to useful actuation. Consequently, the system will not be able to move as quickly, and active performance suffers. The compliance effectively increases the load on the system. The introduction of this intrinsic compliance to an actuator system involves the introduction of trade-offs into the design process. If the goal of the system is rapid movement at all costs, then compliance is not a good thing. However, it is often desired that a robotic system reject disturbances well. For example, reduction of the degenerative loads seen by the actuation system may be desired so that the parts will last longer. Another reason may be that the system needs to display a more graceful response to disturbances, avoiding stiff, stereotypical robotic behavior. Whatever the reason, there exists a basic trade-off: speed for disturbance rejection. The intrinsic compliance necessary for a given application can be determined from the effects of the compliance on performance. For a given application, constraints on actuator performance, such as speed required and maximum disturbance force generated, can be translated into an intrinsic compliance to be designed into the system. Using curves that show the performance as a function of compliance (Figs. 4, 5), the designer can determine the compliances that will produce the necessary speed. From these compliances, the designer can then determine which compliance will also produce the best disturbance rejection. Using this process, the designer may determine an optimum compliance that produces the maximum speed and adequately rejects disturbances or that produces the maximum disturbance rejection and maintains appropriate speeds. The compliance resulting from this process will vary depending upon the relative dominance of the active performance constraint and the passive performance constraint. Another situation involving trade-offs occurs when considering independent area control. Independent area control improves both active and passive performance. However, its effect on stability is unknown, although it does not appear to affect it much. Also, in order to use independent area control, it may be necessary to switch the types of valves being used (e.g., using cartridge valves instead of using spool valves [2, 41). The characteristics of the valves needed to employ independent area control may be different from those of the original valves. If the valves needed for independent area control have bad characteristics, the benefits may be offset. Therefore, the trade-offs involved in independent area control must also be considered when designing a system for a desired behavior. The degree of benefit derived from the independent area control scheme used in the simulations varies depending upon the state of the system. Since the four areas of the normal valves have fixed relationships, the normal valves are best suited to a specific system state; whereas, independent area control adjusts to the state 2172

6 of the system in order to improve performance. However, as the state of the system approaches the best-suited state for the normal valves, the performance of the independent-area-control system approaches that of the normal valves at that state, and the benefits of the independent control decrease. Independent area control also has the drawback of increased system complexity. Independent area control requires four valves, each with its own electronics, to achieve the four independent areas. Also, the control law used in the simulations for independent area control is more complex. These limitations and drawbacks come with the benefits and possibilities of independent area control. CONCLUSIONS The generic hydraulic actuator model permits insight into the physics and mechanics of the system. Although it is possible to fit the experimental data more precisely with, for instance, a tenth-order regression onto a set of basis functions, the insight and the generic nature of the model would be lost, and only a mathematical model of a specific system would remain. The model developed enables documentation of the effects of parameters such as intrinsic compliance, masses, and damping. Also, system concepts such as independent area control can be tested. The data show that intrinsic compliance improves passive performance and degrades active performance. Moreover, independently controlling the valve areas of a hydraulic actuator yields better active and passive performance than controlling the actuator when the valve has fixed area relationships. Intrinsic compliance and independent area control add more trade-offs to the design of actuation systems. The actuator model can be used to examine these tradeoffs and to design hydraulic actuation systems with desired behaviors. For example, the designer can determine parameter values, such as the values of intrinsic compliances, that an actuator needs in order to obtain a desired performance from a system with a given controller, load, and structure. Similarly, if a specific system already exists (i.e. the load, actuator, and structure are given), the designer can test various control schemes to determine which scheme will result in the best performance. In fact, this was done with the concept of independent area control. FUTURE DIRECT10 NS There are many new avenues to explore with this model. The concept of independent area control can be investigated in more detail. The effect of independent area control on system stability can be checked. Also, other independent area control schemes can be explored. For example, if a disturbance were to cause the pressure in the actuator to pass a specific limit, all of the valves can be opened completely in order to minimize the effects of the disturbance. Independent area control can also be used to make the actuator feel more compliant [4] Another interesting concept is the idea of smart accumulators (i.e., smart compliance). Smart accumulators are accumulators which become stiff when the actuator is trying to move accurately and which become compliant when a disturbance insults the actuator [4]. Consequently, the actuator can respond to commands quickly and accurately, receiving the active performance benefit of systems with low compliance. When the system is disturbed, though, the compliance of the smart accumulator would increase. The system would then be able to reject the disturbance. Smart accumulators would, therefore, benefit from both good active performance and good passive performance. ACKNOWLEDGMENTS This material is based upon work supported under a National Science Foundation Graduate Fellowship. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation. The author would also like to acknowledge the support of the Naval Ocean Systems Center of the Office of Naval Research. [l] REFERENCES Jacobsen, Stephen C., Craig C. Smith, Klaus B. Biggers, and [2] Korane, Kenneth J Cartridge valves: Precise control in a compact package. ',24 October, (31. Robecs, Brian J Poppet valves for directional control., - 11 August [4] Wells, David Leighton An analytical and experimental investigation of the effect of intrinsic compliance on hydraulic actuator performance. Master's thesis, University of Utah. [5] Neal, T. P Performance estimation for electrohydraulic control systems. Technical Bulletin #126. East Aurora, NY: MOOG Inc. Controls Division. [6] Thayer, William J Specification standards for electrohydraulic flow control servovalves. Technical Bulletin #117. East Aurora, NY: MOOG Inc. Controls Division Transfer functions for MOOG servovalves. Technical Bulletin #103. East Aurora, NY: MOOG Inc. Controls Division. [8] Watton, J The dynamic performance of an electrohydraulic servovalve/motor system with transmission line effects. the ASMF (March): [91 Reference, Mitchell and Gauthier Assoaates. Concord, Mass., [lo] Center for Engineering Design, NOSC - H P W I I. 2173