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DOI: 10.1007/s00170-003-1973-7 ORIGINAL ARTICLE Advanced Manufacturing Technology (2004) J.-C. Renn C. Tsai Development of an unconventional electro-hydraulic proportional valve with fuzzy-logic controller for hydraulic presses Received: 23 May 2003 / Accepted: 22 September 2003 / Published online: 20 February 2004 Springer-Verlag London Limited 2004 Abstract In this study, an unconventional electro-hydraulic pro- portional flow control valve based on a switching solenoid and a fuzzy-logic controller is proposed for application to hydraulic presses. The main purpose of this study is the attempt to de- velop an electro-hydraulic proportional flow control valve with lowest cost. Since the switching solenoid possesses quite non- linear force/stroke characteristics, it is basically not suitable for the development of hydraulic proportional valves. Therefore, the fuzzy-logic controller is employed to linearize the force/stroke characteristics. The basic idea is the utilization of the numer- ically estimated pseudo-force as the feedback signal. Finally, this newly developed electro-hydraulic proportional flow control valve is installed in a hydraulic press. Experimental results show that the control of the ram velocity of the press cylinder using the proposed electro-hydraulic proportional flow control valve is quite successful. Keywords Fuzzy-logic controller Hydraulic press Linearization Proportional valve Solenoid actuator 1 Introduction Presses are perhaps the most commonly used machine tools for metal forming 1. According to different types of actua- tion, they can be classified as mechanical and hydraulic presses. Some distinct advantages of hydraulic presses over mechani- cal ones are the simpler design and construction, the linearly variable output press force and ram velocity of the press cylin- der, the ready adjustment of the ram position and the more ef- fective protection from overload. Figure 1 shows two typical circuits of hydraulic presses 1. The first (Fig. 1a) represents a pump-controlled system, in which a complex variable-dis- placement pump is used to control the output volumetric flow J.-C. Renn C. Tsai (a117) Department of Mechanical Engineering, National Yunlin University of Sci- ence and Technology, 123, University Road, Sec. 3, Touliu, Yunlin, Taiwan 640, R.O. China Fax: +886-5-5312062 rate in a manner that is proportional to an applied electrical sig- nal. Consequently, the ram velocity of the press cylinder can also be linearly controlled. Besides, a pressure-relief valve is employed in the circuit to control the output press force of the press cylinder. In the second hydraulic circuit (Fig. 1b), how- ever, a simple fixed-displacement pump is utilized. The control of the volumetric flow rate and the ram velocity of the press cylinder is achieved by an electro-hydraulic proportional flow control valve. Therefore, this hydraulic circuit basically repre- sents a valve-controlled system. In addition, it may also be found that a pressure-relief valve and an accumulator are installed in this circuit. The former is employed to control the output press force of the press cylinder, and the latter is charged with high- pressure oil at the beginning and then serves as an auxiliary power source. Thus, the hydraulic pressure required to produce a corresponding output press force is maintained constant and, consequently, a smooth control of the ram velocity of the press cylinder can be obtained. Generally speaking, the price of a variable-displacement pump is much higher than that of a conventional fixed-displace- ment pump. Besides, the response speed of a pump-controlled system is much lower than that of a valve-controlled sys- tem 2. Nowadays, therefore, the latter design is still pre- ferred though the former possesses the advantage of energy saving. On the other hand, the valve-controlled hydraulic cir- cuit shown in Fig. 1b requires an electro-hydraulic proportional flow control valve, which is the most important but expen- sive component in the circuit. Figure 2 shows the schematic structure of the valve. It can be observed that such a valve consists of two parts. One is the proportional valve body, in which the proportional solenoid is utilized to regulate the opening area of the valve orifice. The other is the pressure compensator, which maintains a constant pressure drop across the valve orifice in case of possible variations of external loads. Figure 3 shows the structures and characteristics of two com- monly used solenoid actuators 2. The first is the switching solenoid, which is widely applied to the design of traditional hydraulic directional control valves. The second is the propor- Fig.1. Two typical circuits of hy- draulic presses tional solenoid, which is the standard component for the de- velopment of electro-hydraulic proportional valves. As shown in Fig. 3, the switching solenoid and the proportional solenoid have quite different force/stroke characteristics, though they possess almost the same structure. In detail, the former pos- sesses a highly nonlinear behavior regarding the force/stroke characteristic; the static force/stroke characteristic of the lat- ter, however, is quite linear. Such a linear force/stroke rela- tion of the proportional solenoid is the key requirement for the design of electro-hydraulic proportional valves. For example, the valve spool, which is subjected to a constant force in the linear working range, reaches a definite position in the valve body according to Hookes law. This definite position of the spool signifies a definite opening area of the valve orifice. Fur- thermore, it is also observed from Fig. 3 that the relation be- tween the output force and the input current is quite linear. Consequently, the opening area of the valve orifice is contin- uously variable and is proportional to the input current. This is exactly the basic function of electro-hydraulic proportional valves. The prerequisite to utilize the low-cost switching solenoid instead of the high-cost proportional solenoid is the lineariza- tion of its force/stroke characteristics. Previous reports 35 concerning the linearization of the force/stroke curves of switching solenoids can be found in the 1990s. However, only the linear proportionalintegral controller was employed in these papers. The results of the force linearization were also not fully satisfactory. In this paper, therefore, a nonlinear fuzzy-logic controller together with a closed-loop force-control scheme are proposed to linearize the force/stroke character- istics. Moreover, instead of the installation of an expensive force sensor, this closed-loop force-control scheme utilizes the numerically estimated pseudo-force as the feedback sig- nal to minimize the cost of implementation. In the following, the experimental test device for solenoid actuators is firstly outlined. Fig.2. The schematic struc- ture of the proportional flow control valve Fig.3. The structure and characteristics of the switch- ing solenoid and the propor- tional solenoid 2 Experimental test device The static test device for solenoid actuators is shown in Fig. 4. An open-loop-controlled micro-stepping motor (American Pre- cision Industries, CMD-260) is utilized to control the plunger position of the tested solenoid. In detail, the angular displace- ment of the micro-stepping motor is proportional to the number of pulses of the square-wave signal sent to the driver. The direc- tion of rotation can be easily controlled by sending a Hi (5 V) or Lo (0 V) signal to one input port of the driver. In addition, a ball screw is attached to the rotor, which transforms the angular motion into a rectilinear movement. Besides, this test device pro- vides a position sensor (RDP-LVDT-D2/200) as well as a load cell (BAB-10M) for the measurement of the position and the out- put force of the plunger. In the practical application, however, the load cell is not necessary and a low-cost potentiometer is used to measure the plunger position. To measure the coil excitation current, a series resistor of 10 is used in the electric circuit. To produce the linearly con- trollable input current as well, a voltage-to-current transducer (i.e. amplifier) is employed. Finally, the control of the unit as well as the acquisition and processing of the measured data are all integrated in a Pentium-III-based software controller. Fig- ure 5 shows the measured nonlinear force/stroke characteristics of the tested switching solenoid, which is originally developed for NG02 hydraulic directional valves. In the following sections, two procedures involved in the linearization of the force/stroke characteristics of the switch- ing solenoid are described. The first is the estimation of the pseudo-force signal and the second is the introduction of a fuzzy- logic controller for the closed-loop force control of the switching solenoid. Fig.4. The static test device for solenoids Fig.5. The measured nonlinear force/stroke characteristics of the tested switching solenoid 3 Estimation of the pseudo-force feedback signal Let the pseudo-force, F p , be a function of the plunger position, x m , and the coil current signal, i m ; thus, F p (x m ,i m ) = A(x m )i m + B(x m ). (1) From the experimental results shown in Fig. 6, Table 1 can be established, in which three parameters are involved, the plunger position, the output force of the plunger and the coil current. By a curve-fitting technique, the best-fit polynomials A(x m ) and Fig.6. Experimental results of the graphical relation between the three pa- rameters B(x m ) with minimum order are found to be A(x m ) =1.8211x 4 m 54.3739x 3 m +247.4310 x 2 m 395.0201x m +287.5556 (2) and B(x m ) = 26.7396x 4 m 106.8007x 3 m +143.9303x 2 m 67.1442x m 10.9445. (3) The family curves of the measured actual force and the simu- lation pseudo-force by curve fitting are shown in Fig. 7. The maximal deviation is only about 2 N. Since the position of the plunger, x m , and the coil current, i m , are easily measured and usually known, the output pseudo-force, F p , can be numerically derived from Eqs. 13. Fig.7. Comparisons between the experimentally measured actual force and the estimated pseudo-force by curve fitting Table 1. Functional relation between the polynomials and the plunger stroke x m 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 A 220 160 130 106 82 70 60 60 40 B 20 19.3333 19.6667 17.5 14 12.6667 12 14 7 4 Design of the fuzzy-logic controller Unlike the conventional controller, there are three procedures involved in the implementation of a fuzzy-logic controller, fuzzi- fication of the input, fuzzy inference based on knowledge and defuzzification of the rule-based control signal. (a) Fuzzification In this study, the two input signals to the fuzzy controller are the force error signal, e(k), and its change signal,e(k): e(k) = F d F p , (4) e(k) = e(k)e(k 1). (5) Here F d : desired force signal, F p : estimated pseudo-force signal. Figure 8 shows the fuzzy membership function for the two input signals to determine the degree of input. (b) Inference The inference process consists of a set of rules driven by the linguistic values of the error and the error change signal. Table 2 shows the definition of the rules. (c) Defuzzification The defuzzification is to transform the control signal into an exact control output. In the defuzzification, the method of Fig.8. Fuzzy membership function for two input signals Table 2. Definition of the control rules e(k) NB NM NS ZE PS PM PB PB ZE PS PM PB NB NM NS PM NS ZE PS PM PB NB NM PS NM NS ZE PS PM PB NB e(k) ZE NB NM NS ZE PS PM PB ZS PB NB NM NS ZE PS PM NM PM PB NB NM NS ZE PS NB PS PM PB NB NM NS ZE center of gravity is used: y = n summationtext i=1 W i B i n summationtext i=1 W i , (6) where y: the output of the fuzzy controller, W i : the degree of firing of the ith rule, B i : the centroid of the consequent fuzzy subset of the ith rule. The output actuating signal of the fuzzy controller, u(k),is defined as u(k) = u(k 1)+u(k). (7) Figure 9 shows the output membership function for the actu- ating signal change, u(k). Fig.9. Output membership function for the actuating signal change Fig.10. Block diagram of the force-control scheme using pseudo-force as feedback signal 5 Experimental results of force linearization by pseudo-force feedback Figure 10 shows the block diagram of the force-control scheme using the estimated pseudo-force as its feedback signal. The corresponding experimental results of the force linearization using the fuzzy-logic controller are shown in Fig. 11. In the range of plunger positions 0.15 mm x m 0.95 mm, the ex- perimentally measured force signals are almost straight and horizontal lines, which signify the successful linearization of the force/stroke characteristics. In the same range, more- over, the estimated pseudo-force also agrees very well with the experimental one. This further proves the validity of the model described by Eqs. 13. However, it is also observed that the measured force signals in the range of plunger pos- itions 0 mm x m 0.15 mm are not properly linearized. This is chiefly because of the obvious difficulties of compensating the highly nonlinear and almost vertical force/stroke curves in this range, as shown in Fig. 5. Table 3 shows the compar- isons of the technical data between the conventional propor- tional solenoid and the new proportional switching solenoid. Because the output flow rate through the valve orifice with a con- stant pressure drop is proportional to the plunger stroke 2 and the linear working stroke of the new proportional switch- ing solenoid is shorter, the available flow rate through the Fig.11. Experimental results of the force linearization using the fuzzy-logic controller Table 3. Comparisons between the two proportional solenoid actuators Conventional New proportional proportional switching solenoid solenoid Type (Magnet-Schultz (Seven Ocean GRF045) NG02) Linear working stroke 3 mm 0.8mm Linear maximal output force 65 N 25 N Maximal excitation current 0.81 A 0.45 A newly developed proportional flow control valve is expected to be smaller. Nevertheless, a low-cost proportional flow con- trol valve using the new proportional switching solenoid instead of the conventional proportional solenoid has been successfully developed. 6 Installation in a hydraulic press and experimental results A valve-controlled hydraulic press is used in the laboratory to verify the performance of the proposed unconventional propor- tional flow control valve. The piston diameter and the maximal stroke of the ram are 350 mm and 250 mm, respectively. The maximal ram velocity is 300 mm/min, corresponding to a vol- umetric flow rate of 30 l/min. The output press force reaches 2000 kN if the supply hydraulic pressure is set to be 210 bar. To measure the ram velocity, a linear potentiometer is firstly utilized to acquire the signal of the ram position. Then, the ram velocity is numerically obtained by v m (k) = x m (k)x m (k 1) T s , (8) where v m : measured ram velocity, T s : sampling time. Figure 12 shows the experimental step responses of the ram velocity to three different force inputs. Because the pressure compensator maintains a constant pressure drop across the valve orifice, the output flow rate is proportional to the stroke of the solenoids plunger. It is thus observed that the ram velocity is controllable in a manner that is proportional to the desired in- put force and the performances are satisfactory. This proves the feasibility of the attempt to develop a low-cost unconventional proportional flow control valve. On the other hand, however, the maximal ram velocity corresponding to the maximal desired input force of 25 N reaches only 96 mm/min, which is approxi- mately 1/3 of the original one. Fig.12. Experimental step responses of the ram velocity to three different force settings 7 Conclusion In this paper, a new proportional switching solenoid has been successfully developed and applied to the design of an uncon- ventional proportional flow control valve for hydraulic presses. Three conclusions may be drawn from this research. Both attempts to use the numerically estimated pseudo-force as the feedback signal and to linearize the force/stroke relation of the switching solenoid by a fuzzy-logic controller were suc- cessful. The newly developed unconventional proportional flow con- trol valve for hydraulic presses possesses a remarkable advantage of lower cost, because the price of a switching solenoid is only about 10% of that of a proportional solenoid. The available flow rate through the newly developed propor- tional valve is smaller than that through the original one. This may be regarded as the cost of linearization. Such a defect, how- ever, may be easily overcome by choosing a switching solenoid having a larger output force for the linearization, like the switch- ing solenoid for NG03 hydraulic valves. Acknowledgement The financial support of the National Science Council under Grant No. NSC 91-2213-E-224-006 is greatly appreciated. References 1. Weck M (1991) Werkzeugmachinen Fertigungssysteme, vol 1. VDI Ver- lag, Dsseldorf, Germany 2. Backe W (1993) Steuerungs- und Schaltungstechnik II, Umdruck zur Vorlesung. RWTH Aachen, Germany 3. Cheung NC, Lim KW, Rahman MF (1993) Modeling a linear and limited travel solenoid. Proc IEEE IECON93 3:15671572 4. Rahman MF, Cheung NC, Lim KW (1995) Position estimation in solenoid actuators. Proc IEEE Trans Ind Appl 1:476483 5. 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