Energy saving control for pneumatic servo systems

zyxwvutsrq zyxwvutsrqponm zyxwvutsrqp Proceedings of the 2W3 IEEWASME International Conferenceon Advanced Intelligent Mechatronics (AIM PW3) Energy Saving Control for Pneumatic Servo Systems Khalid k AI-Dakkan Michael Goldfarb Eric J. Barth Dept. of Mechanical Engineering, Vanderbilt University. Nashville, TN, USA [email protected] Dept. of Mechanical Engineering, Vanderbilt University. Nashville, TN, USA [email protected] Dept. of Mechanical Engineering, Vanderbilt University. Nashville, TN, USA [email protected] zyxwvutsrqpo zyxwvut generating power, but need not use the supply when dissipating power. Control approaches related to this notion have been investigated by Quaglia and Gesddi [S, 91, Pu et al. [lo], Wang et al. [Ill, and Arinaga et al. [12]. Specifically, Quaglia and Gestaldi proposed a non-conventional pneumatic cylinder that incorporated multiple cylinder chambers embedded into a single actuator with the intent of recycling the compressed air. Pu et al. describe a pneumatic arrangement that incorporates a standard 4-way spool valve controlled pneumatic servo actuator, with an additional 2-way valve between the two sides of the cylinder. They demonstrated "preliminav results, but since no experimental comparisons were presented, it is unclear what improvements in efficiency were achieved. Wang et al. studied the use of input shaping to choose a command profile for point-to-point motions that would result in energy savings. Finally, Arinaga et al. utilized metering circuits to reduce the aimow requirements for open-loop point-topoint motions. Research focused on energetically efficient closed-loop control of a standard pneumatic servo actuator is conspicuously absent fiom the prior literature. This paper attempts to fill this void by introducing a control methodology that enables significant energetic savings in closedloop control servo aciuation. Abstract Thispaperproposes an energy saving approach io the control ofpneumaiic servo systems. The control meihodology is presenied, followed by experimental results ihai indicate significani energetic savings and esseniially no compromise in tracking performance relative to a purely active approach. Speci$cally, experiments indicaie an energv savings of 10 to 46% (depending on the desired tracking frequency) relaiive to standard 4-way spool valve pneumatic servo actuaior control. The savings are generally higher at lower tracking frequencies, since tracking of higherfrequencies requires more control effori io minimize tracking error, and therefore limits the degree of possible energy swings. zyxwvuts zyxwvuts INTRODUCTION A typical pneumatic servo system, which consists primarily of a proportionally controllable 4-way spool valve and a pneumatic cylinder, is depicted in Figure 1. In this system, the position of the valve spool controls the airflow i&o and out of each side of the cylinder, which in turn results in a pressure differential across the piston and thus imposes a force on the load. In a typical pneumatic servo system, feedbackcontrol is incorporated to command a valve spool motion that will result in a desired motion of the piston load. A considerable amount of work has been conducted in the modeling and feedback control of such systems, including the work by Shearer [l, 2, 31, Mannetje [4], Bobrow and McDonell [5], and Richer and Hurmuzlu [6, 71, among others. Despite the prior work on the control of pneumatic servo systems, relatively little work has focused on the energetic efficiency of such systems. This topic has generally received little attention fiom the research community, presumably because most applications draw energy fiom an essentially limitless reservoir of power. In many applications, however, the supply of power is limited (e.g., in the case of a mobile robot), and in such cases, the energetic efficiency of the controller is significant. Fluid powered systems in particular offer intriguing possibilities with regard to the energetic efficiency of control. Specifically, the 'energetic role of an actuator at any given point in time is either to generate or dissipate power. In a fluid powered system, the energetic role of power dissipation can be provided passively by controlling the resistance to fluid flow. Therefore, ideally, a fluid powered system need only draw fiom the (high pressure) fluid supply when the actuator is 0-7803-7759-1/03/$17.00 0 2003 IEEE Control Approach Standard control systems are generally energetically nonconservative, and as such require supply power in order to dissipate load power [13]. As previously mentioned, however, fluid powered systems offer the ability to dissipate significant power without the use of supply pressure by modulating the flow through cylinder exhaust valves. Specifically, if a standard pneumatic servo actuator shown in Figure 1 is modified by replacing the single 4-way valve with two 3-way valves, as shown in Figure 2, then dissipative forces can be imposed on the load without the use of supply power. The work presented herein takes such an approach by developing two control modes for the actuator configuration shown in Figure 2 - an active mode, which utilizes aimow fiom the air supply, and a passive mode, which utilizes exclusive control of the flow fiom the cylinder to the exhaust. The active mode is pattemed after a standard pneumatic servo system and as such couples the two 3-way valves to effectively behave as a single 4-way valve. The passive mode utilizes each 3-way valve as if it were a 2-way valve modulating the flow resistance between each side of the cylinder and atmosphere. A Switching law 264 zyxwvutsrq zyxwvutsrqpo zyxwvuts zyx zyxwvutsr is developed to switch between active and passive modes of operation based on the current pressure states in the cylinder and the desired actuation force. Experimental results indicate significant energetic savings and essentially no compromise in tracking relative to a purely active approach. The mathematical model for a pneumatic double-acting cylinder driving an external inertia load has been well described in the literature [14, 151. With the assumption that the gas is perfect, the pressure and temperature inside the chamher are homogenous, and kinetic and potential (i.e., gravitational) energy of the fluid are negligible, the rate of change for the pressure inside a pneumatic chamber can be expressed as: where i;ab)is the rate of change in pressure inside chambers a and b, respectively, m,,,, and m,, Figure 1. A standard pneumatic servo actuator driving au inertial load. are the inlet and outlet mass flow rates to/kom chambers a and b, respectively, k is the ratio of specific heats ,R is the universal gas constant, Tis the flnid temperature , Vr4*,is the volume of each cylinder chamber, and is the rate of change in the volume of chambers a and b. The compressible mass flow rate though a valve orifice with effective area A 4 can be described as: to$, zyxwvutsrqp A where C, is the discharge coefficient, P. is the upstream pressure, and C, is a nondimensional coefficient given by, p'oportional spool 3--y valves ineltid load Figure 2. Modification of standard pneumatic x m actuator lor accommodating energy saving control arcbitedure where Pd is the downstream pressure on either side of the valve orifice (dependent on the sign of m ), C, is the critical pressure ratio that divides the flow regimes into unchoked and choked flow, and C, and C, are two constants defined as follows: Modeling the Pneumatic Servo System The load dynamics of the system shown in Figure 2 can be written as: and pneumatic cylinder zyxwvutsrq zyxwvut At? + b i =.,F = P . 4 -&Ab - P & , (7) (1) where M is the payload plus the piston and rod assembly mass, b is the viscous Wction coefficient, and Fw is the force resulting kom the differential cylinder pressure, given by. .,F 2k R(k-I) Bimodal Sliding Mode Control Due to the extensive nonlinearities and the presence of paramehic uncertainty in pneumatic systems, sliding mode control is generally well suited to the control of pneumatic servo actuators. For the system described in the previous section, the plant output, which is the load position x must be differentiated three times to produce the control input, which is the valve areaAdand as such the system is characterized by third order dynamics. Defining a sliding surface as (2) where Pa and Pb are the absolute pressures in chamber o and chamber b, respectively, A,, and Ab are the areas of the two sides of the piston, P,. is the absolute ambient pressure, A, is the rod cross-sectional area. 285 zyxwvuts zyxwvutsr zyxwvu zyxwvuts zyxwvu zyxwvutsrqpo where e is the position error, 1 is a strictly positive constant and n is three. In standard sliding mode control, the controller consists of two components, a (non-robust) equivalent control law (which utilizes model information to enforce the condition i = 0), and a switching component, which robustly enforces the condition < 0 , where V is the Lyapunov function. When the two 3-way valves are coupled so as to emulate a single 4-way spool valve, one valve will connect one chamber to supply with a given effective area, while the other valve will connect the other chamber to atmosphere with the same effective area. Thus the valve commands are essentially equal in amplitude and opposite in sign. As such, two possibilities exist for the equivalent control term, one corresponding to the charging of chamber a and discharging of b, and one corresponding to the charging of chamber b and discharging of a. Utilizing the definition of s given in Equation (8) and the system model given by Equations (l-7), the resulting equivalent control components for these two cases are of the form: the valve connected to chamber a is closed. Following kom the sliding surface as defined by Equation (8), the equivalent control laws describing the exhausting modes of operation are given by: Miry) - 2 1 U-., = =- U_. =A,. = &I -21 (?-:,)-A (X-X,)-L ' ( i - i , ) ) + i ( - - P- )I+' bAf v. m(A.V;.P-)) P,P,A, v, '(i.t,))+k(P."'".P v. r. where u . ~ ,and ~ uq,4 are the equivalent control laws for the case of purely passive dynamics (i.e., exhausting chambers a and b, respectively). zyxwvutsr The complete control law is formed by adding a robustness component to the equivalent control law, such that the total control effort is given by: where K,,Kz,K,and K, are strictly positive gains and @I,'%, and @, defme boundary layer thicknesses. ActlvelPassIve Mode Switching Switching between active and passive control is achieved based on the equivalent control outputs of the previously described control laws. The models upon which the equivalent control laws are based were derived such that positive control commands uq.3 and uq,, indicate that solutions exist that will provide actuator control with purely passive means. Negative passive mode control commands uq,) and uq,4 indicate that a negative area would be required to achieve the desired motion, and thus indicate that passive solutions do not exist, and as such, active control is necessary to track the desired input. The controller therefore must choose either ueslor u ~ ,whichever ~ , is positive. As previously mentioned, when the system is in t h first mode MI (uq,p.,is selected) or second mode MZ(uq,2 is selected), the valve commands are essentially equal in amplitude and opposite in sign. Specifically, a positive uq,, indicates that chamber U must be charged and chamber b discharged, (MI = 1 and M(2,3f)= 0), and a positive uq.l indicates the opposite, (M2= 1 and M(l,3.4)= 0). However, in passive modes (i.e. M, or one chamber polt will he closed &ile the other chamber is being discharged. In particular, a positive uq,3 indicates that chamber a can be discharged while chamber b is being closed (i.e. M, = 1 and +,zn = 0 ) and uq, indicates the opposite (i.e. & = 1, and = 0). The system remains in M3 or until the positive U+ or zyxwvutsrqpo zy zyxwvutsrq where is ue9,,the equivalent control law when chamber a is being charged i n d chamber b is-being discharged and ueb2 is the equivalent control law when chamber b is being charged and chamber a is being discharged. The four functiOh.7 f l p , ,pa),% P i , P b ) , %Pa,pm), and % P b . P a m ) are as follows: [%Pm . I ...................................... (choked) (10) .~~ *ere a-and p represent the subscript of P in the Y functions in which .asymbolizes the subscript of the upstream pressure and p symbolizes the subscript of the downstream pressure. . w), When the two control valves can operate independently (i.e., when they need not emulate a single 4-way valve), two additional conpol modes are allowed. One is to discharge chknber a while the valve connected to chamber b is closed, and the other mode is to discharge chamher b while 286 zyxwvutsrqponmlk zyxwvuts reaches the maximum valve opening, otherwise the system will be in MI or M,. U+ ness component gains were selected as K,, = 6.5 mm’ (0.01 in’) and K3* = 3.25 mm2 (0.005 in’), and h was chosen to be 75 s-’. zyxwvu zyxwvut zyxwvutsr zyxwvutsr Experimental Setup A schematic for the system setup is illustrated in Figure 2. The double acting cylinder pimba 314-DXP) used in the experiment has a stroke length of 10.2 cm (4.0 in), inner diameter of 5.1 cm (2.0 in), and piston rod diameter of 1.6 cm (0.62 in). Two four-way proportional valves (Positionex SW-360) are attached to the chambers with two ports of each valve blocked to make the valves function as three-way valves. A mass load of IO kg (a brass block connected to the end of the piston rod) slides on a track with linear bearings (Thompson lCB08FAOLlO). Three pressure transducers (Omega PX202-2OOGV) are attached to the pressure supply tank and each cylinder chamber, respectively, and a linear potentiometer (Midori LP-IOOF) with 10 cm (3.94 in) maximum travel measures the linear position of the inertial load. Control is provided by a Pentium 4 computer with an A/D card (NI PCI-6031E), which drives the two proportional valves via a pair of KEPCO bipolar ~,,,, power supply/amplifiers. .The control inputs, u ~ ~ . ~ ,represent the valve effective areas, A , In the experiment, bowever, the control command is the spool displacement. The effective area is therefore transformed to spool displacement using the inverse of the following relation, Experimental Results Experiments were conducted to compare the tracking performance and average required mass flow rate of the proposed bimodal control with the performance and average required mass flow rate of a standard 4-way valve controller. Average mass flow rate was found by charging the 5gallon pressure supply tank to about 7 atmospheres (90 psig) before Nnning each experiment and measuring the tank pressure as the experiment was performed. Assuming the air in the supply tank to he an ideal gas undergoing an isothermal process, the mass in the supply tank is proportional to the tank pressure. Tracking experiments were conducted for sinusoidal frequencies of 0.25 Hz through 1.5 Hz and square wave. The experimental results of tracking performance for 0.25 Hz sinusoidal command signal are shown in Figures 3 and 4 for bimodal control and standard active control, respectively. Both systems showed similar tracking performance. The control input signal of bimodal control shows reduction (magnitude and period) in valves opening to supply and increase in valves opening (mapitude and period) to exhaust in comparison with standard active control, which ideally has the same valve opening to supply and exhaust. In bimodal control system, a significant amount of switching between passive and active mode occurs when A3 or A, reaches the maximum valve opening (0.01 14 in’) causing it to switch to A2 or A,. The results of where, r, is the radius of the total effective orifice area, the control inputs are depicted in Figures 5 and 6 for biwhich is 0.0735 cm’ (0.01 14 in2),x, is the valve spool dismodal control and standard active control, respectively. placement, and 6 is the variable of integration. A polynoThe bimodal control causes the system to run at a lowmial fit to the fifth order was used as an approximation to pressure level compared to standard active control that m s the inverse of (14), yielding the following general form, close to the supply pressure level. The result of pressure x, = U , A ~ + ~ , A ; + ~ , A ~ + ~ , A ~ + ‘(14) ~ A ~ + Uvariation ~ in bimodal control and standard active control is shown in Figure 7. The responses to 1.25 Hz sinusoidal where as,or, 03, 02, (11, and a0 are constants. In addition, a command signal and square signal of the two control sysdead zone is utilized to compensate for the inaccuracy in tems are illustrated in Figures 8 through 11. The average adjusting the spool zero position and the difference in energy savings for different commad signals/frequencies thickness between the spool and the orifice diameter. Model are listed in Table 1. Experiment shows a reduction in enparameters for the experiment are C =, 8;C, = 0.528; V, = ergy savings as the desired frequency increases, since the 18 cm3 (0.8 in3) (initial volume in chamber a);V., = 18 cm3 controller requires a higher level of control effort to track (0.8 in3) (initial volume of chamber b); T=298 K, R = 287 the higher frequencies. m’/(s’.K) (444850 in’/s’/K) ; L = 10.2 cm (4 in) (total stroke); r = 2.54 cm (1 in) (cylinder inner radius); C, = 0.8 (area ratio); b = 13.1 Kgh (0.9 slugls) (estimated viscous Conclusion fiiction coefficient). These parameters were obtained via This paper presents an activelpassive controller that takes experiment when possible, and through calculation when advantage of the ability of a fluid to passively dissipate experimental measurement was not possible. In order to power to reduce the power consumption of a pneumatic provide a fair comparison between the standard active conservo system by as much as 46%, with little to no sacrifice trol (4-way valve) and bimodal (two 3-way valves) controlin !racking performance. The maximum energy saving for ler, the sliding mode control gains were the same for the the system tested occurs at a frequency of 0.5 Hz, which is active modes in both control laws. Specifically, the thicksomewhere in between the fiiction domination of very low ness of the boundary layers was selected to be @,.’ = 43.2 d s ’ (1700 ids2), ‘.b3,4= 12.7 d s ’ (500 ids’), the robust- zyxwvutsrqp zyxwvutsr zyxwvutsr zyxwvutsrqp zyxwvutsr 207 zy zyxwv frequencies and the more significant control effort required to track higher kequencies. Figure 6. Experimental results of the control input for 0.25Hz using Standard Active Control (red is valve A, black is valve B). zyxwvu Figure 7. Experimental results of pressures variation using Bimodal control and Standard Active control for 0.25& @Lackis chamber A pressure, gray is chamber B pressure). Figure 3. Experimental results of Bimodal Control tracking performance for 0.25Hz (black is actual position, gray is desired position). zyxwvu zyxwvutsrqponmlkjihgfed zyxwvutsrqponmlkjihgfedcb I 0 1 2 1 . 1 1 1 . *..a s 2 a I nm.. & c. '0 12 31 ,I Figure 8. Experimental results of Bimodal Control tracking performance for 1.25Hz (black is the actual signal, gray is desired trajectory,). Figure 4. Experimental results of Standard Active Control tracking performance for 0.25Hz (black is actual position, gray is desired position). L D I 8 . . 2 , . . , ' r h.. .. , l I . F m r e 9. Experimental results of Standard Active Control tracking performance for 1.25Hz (black is the actual signal, gray is desired trajectory). nw. * Figure 5. Experimental results ofthe control input for 0.25Hz using Bimodal Control @lackis valve A, gray is valve B). , 288 zyxwvutsr zyxwvutsrq zyxwvutsrqponmlkjihgfedcbaZY Richer, E. and Hmuzlu, Y., “A High Performance Pneumatic Force Actuator System: Part I-Nonlinear Mathematical Model” ASME Jownal of Dynarmc Systems, Measurement, and Control, vol. 122, no. 3, pp. 416425,2000. Figure 10. Experimental results of Bimodal Control tracking performance for unity step (black is the actual signal, gray is desired trajectory,). .U - I( Richer, E. and H m u z l u , Y., “A High Performance Pneumatic Force Actuator System: Part 11-Nonlinear Control Design” ASME J o d of Dynamic Systems, Measurement, and Control, vol. 122, no. 3, pp. 426434,2000. zyxwvu Quaglia, G. and Gastaldi, L., “The Design of Pneumatic Actuator with Low Energy Commptiou,” The 4th Triennial International Symposium on Fluid Control, Fluid Measurement, and Visualization, pp. 10611066,1994. Figure 11. Experimental results of Standard Active Control tracking performance for unity step (black is the actual signal, gray is desired trajectory). Quaglia, G . and Gastaldi, L., “Model and Dynamic of Energy Saving Pneumatic Actuator,” The 4th Scandinavian International Conference on Fluid Power, vol. 1,481492,1995. zyxwvutsrqp Frequency % Saving (W 0.25 30 0.5 46 0.75 42 1 27 16 14 IO 1.25 1.5 unity step Pu, J., Wang, J. H., Moore, P. R., and Wong, C. B., “A New Strategy for Closed-loop Control of ServoPneumatic Systems with Improved Energy Efficiency and System Response,” The Fifth Scandinavian International Conference on Fluid Power, pp. 339-352, 1997. Wang, J., Wang, J-D., Liau, V., “Energy Efficient Optimal Control of Pneumatic Actuator Systems,” Systems Science,Vol. 26,3, pp. 109-123,2000, Arinaga, T., Kawakami, Y., Terashima, Y., and Kawai, S., “Approach for Energy-Saving of Pneumatic Systems,” Proceedings of the 1st FPNI-PhD Symposium, pp. 49-56,2000. 1131 Seth, B., and Flowers, W.C., “Generalized Actuator Concept for the Study of the Efficiency of Energetic Systems,” ASME Joumal of Dynamic Systems, Measurement, and Control, vol. 112, no. 2, pp. 233238,1990. zyxwvutsrqp Table 1. Average Energy Saving achieved when using Bi- modal Control References Shearer, J. L., “Study of Pneumatic Processes in the Continuous Control of Motion with Compresses Air I,” Transactions of the ASME, vol. 78, pp. 233-242, 1956. Shearer, J. L., “Study of Pnenmatic Processes in the Continuous Control of Motion with Compresses Air II,” Transactions of the ASME, vol. 78, pp. 243-249, 1956. Shearer, J. 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