ap-4-12.dvi Acta Polytechnica Vol. 52 No. 4/2012 A Flexible Adjustment and Control System for Hydraulic Machines Daniel Banyai1, Lucian Marcu1 1 Technical University of Cluj-Napoca, Department of Mechanical Engineering, B-dul Muncii, nr. 103–105, Cluj-Napoca, Romania Correspondence to: daniel.banyai@termo.utcluj.ro Abstract Due to the advantages of hydraulic systems with variable displacement, it was necessary to design a control system that can adjust the pressure, flow, power or a combination of these features, that can be easily integrated into the pump body without changing its mechanical construction. The objective of this work was to study the dynamic behavior of this electro-hydraulic control system. To achieve these objectives, first the adjusting system was analyzed by numerical simulations, and then a stand was constructed for testing the performance of these adjustable pumps. It was shown that this control system is superior to existing systems. Keywords: adjustable pump, control system, dynamic behavior. 1 Introduction This paper presents a study of high power drives, namely hydraulic systems, pursuing a high degree of automation, minimum power consumption, adapt- ability to a large range of industrial applications and perturbations. The systems should be flexible. Essential trends in the construction of present- day non-hydraulic machines are toward flexibility and automation. The aim is to increase the level of in- telligence of the machines and their adaptation to possible disturbances. [2] Variable displacement pumps allow easy control of system parameters (pressure, flow, power, or com- binations of these parameters). Their technical char- acteristics make them the best option for most appli- cations, from machine tools to mobile devices. [2] Companies with a tradition in manufacturing pumps and motors with axial piston and variable displacement (Rexroth, Bosch, Vickers, Parker) have been producing this type of machinery for highly au- tomated systems since the 1980, but there is little data in the literature on constructive solutions. The biggest producers of hydraulic machines are opting for mechano-hydraulic control structures that can be used in circuits for regulating pressure, flow and power independently of each other, with each control parameter requiring a different type of con- structive control structure [7]. 2 System description The purpose of this paper is to report on optimiza- tions of the adjustment structure of hydraulic pa- rameters, their control in the system to which be- long, and tests on the assembly pump-adjustment system. Figure 1 presents a schematic diagram for an au- tomatic control system proposed for implementation in a research program [1, 2]. The system contains the following components: 1 – a variable displace- ment pump with axial pistons; 2 – a linear hydraulic motor for changing the angular position of the pis- ton block holder, in order to modify the flow of the pump; 3 – a proportional directional valve that con- trols the position of the linear motor; 4 – pressure sensors; 5 – a diaphragm for measuring the flow rate of the pump; 6 – electronic circuits that calculate the pressure drop on the diaphragm, then determine the flow, and then the hydraulic power generated by the pump is obtained via a signal from a pressure sensor and the signal that represents the flow; 7 – an elec- tronic comparator, designed to find the error between the programmed value and the actual value of the ad- justed parameter (pressure, flow, power); 8 – an elec- tronic controller, used to compensate the errors and give the command signal for the proportional valve; 9 – switches whose state determines the control struc- ture; 10 – a fixed displacement pump, which provides the necessary flow for positioning the hydraulic mo- tor. This flow can be taken from the flow of the ad- justable pump, and in this case the auxiliary pump is no longer required; 11 – a relief valve, which protects the system from exceeding the permissible pressure in the hydraulic components. Thus, without a change in pump construction, this can be integrated into any control circuit for adjustable hydraulic machines, by simply actuating an electrical switch. 16 Acta Polytechnica Vol. 52 No. 4/2012 Figure 1: Electro-hydraulic control system for variable displacement machines The mathematical model of the control system studied in this paper is based on differential equa- tions that take into account nonlinear influences such as pressure and leakage flow dependence, saturation of the flow, limiting the pressure, etc., in order to minimize the deviations between the behavior of the real system and the modeled system. The following differential equations are used to model the system [6]: • equations of state (isothermal transformation) for discrete volumes; (a), (b); • equation of continuity; (c), (d); • equations describing the behavior of an ideal proportional electromagnet; (e); • equations describing the behavior of an ideal controller; (f); • mechanical equilibrium equations; (g). The general form of these equations was taken from the specialized literature [3,6], and they were adapted to the model investigated in the paper, resulting in the system of equations described in (1), where the notations have the following meanings: ṗA – temporal derivative of the pressure function, pA, in the large chamber of the linear hydraulic mo- tor; ṗB – temporal derivative of the pressure func- tion, pB, in the small chamber of the linear hy- draulic motor; pA – pressure in the large chamber of the linear hydraulic motor; pB – pressure in the small chamber of the linear hydraulic motor; pT – tank pressure, (pT = 0); pc – pressure between the auxiliary pump and the control valve; ps – load pres- sure; EU – elasticity modulus; VA – volume of oil under pressure pA; VB – volume of oil under pres- sure pB; VT – (dead) volume in the supply circuit of the linear motor, (volume of connecting pipes); QA – flow rate that enters or is discharged from the large chamber of the positioning hydraulic mo- tor; QB – flow rate that enters or is discharged from the small chamber of the positioning hydraulic mo- tor; A – piston area (rodless); xm – linear position of the hydraulic motor; cLG – leakage flow coefficient dependent on speed; cLP – leakage flow coefficient de- pendent on pressure; α – piston surface ratio; αQ – flow rate coefficient; dv – proportional valve diam- eter; xv – linear position of the proportional valve; ρ – oil density; Tv – time constant for the control valve; Kv – gain of the control valve; U – voltage generated by the PID controller; Uref – command voltage (command value for pressure, flow or power); Ur – voltage generated by the sensors; Kp – pro- portional gain, a tuning parameter of the PID con- troller; Td – derivative gain, a tuning parameter of the PID controller; Ti – integral gain, a tuning pa- rameter of the PID controller; mp – linear motor pis- ton mass; Fam – preload force of the spring in the linear motor; km – spring stiffness; c3; c4 – viscous damping coefficient; m – piston and rod of the re- duced mass of the variable pump; ω – angular veloc- ity of the piston holder of the pump; R – placement radius of the pump’s pistons; a – tilting radius of the variable pump; d – diameter of the pump’s pis- tons. ṗA = EU VA + VT · [QA − A · ẋm − cLG · ẋm + cLP · (pA − pB)] (a) ṗB = EU VB + VT · [−QB + α · A · ẋm − cLG · ẋm + cLP · (pA − pBt)] (b) 17 Acta Polytechnica Vol. 52 No. 4/2012 QA = ⎧⎪⎪⎪⎨ ⎪⎪⎪⎩ αQ · dV · π · xV · √ 2 ρ · (pc − pA), xV ≥ 0 αQ · dV · π · xV · √ 2 ρ · (pA − pT ), xV < 0 (c) QB = ⎧⎪⎪⎪⎨ ⎪⎪⎪⎩ αQ · dV · π · xV · √ 2 ρ · (pB − pT ), xV ≥ 0 αQ · dV · π · xV · √ 2 ρ · (pc − pB), xV < 0 (d) (1) Tv · ẋv + xv = Kv · U (e) U = Kp · (Uref − Ur) + Td · (U̇ref − U̇r) + 1 Ti ∫ (Uref − Ur) · dt (f) mp · ẍm = A · pA − α · A · pB + Fam + km · xm − (c3 + c4)ẋm + m · ω2 · R2 a2 · xm − π · d2 · R 4a · ps (g) Figure 2: Pressure control Figure 3: Flow control Figure 4: Power control 3 Numerical research A study of the dynamic behavior of the electro- hydraulic control system for adjustable hydraulic pumps involves the use of concrete values for the physical and geometrical sizes involved in the model. An F316-type axial piston pump with variable dis- placement, made in Romania by UMP, was cho- sen [10]. The mathematical model was simu- lated in the MatLab Simulink programming environ- ment [11]. The PID controller was tuned using the Ziegler-Nichols method [13]: Kp = 0.3; 1/Ti = 10; KD = 0. The behavior of the system was analyzed, e.g. the response to the step command for pressure, flow and power. When adjusting the pressure, the control step represents the input signal corresponding to the vari- ation in load pressure from 0 to 200 bar, (Figure 2). When setting the flow, the control step represent- ing the input signal corresponds to the variation in flow from 0 to 30 l/min, (Figure 3). In the version of power adjustment the step control that represents the input signal corresponds to a change in power from 0 to 5 kW, (Figure 4). Simulations indicated that the system can be con- trolled with the same controller values for any par- ticularly control type. The dynamic behavior of the system is strongly influenced by the proportionality constant, Kp, so that the natural frequency of the system increases with this constant, and the system is damped. The integral constant, Ti, improves the behavior of the steady state, canceling the stationary error. When the value of this constant is increased, it is observed that the damping of the system decreases signifi- cantly, bringing it to the limit of instability. Having a derivative gain, Kd, even at low levels, the damping of the system decreases, bringing it to the limit of instability. 4 Experimental research In order to achieve the objectives of our study, a stand was designed and constructed that was capable of testing the performance of adjustable pumps work- ing under pressure control, flow, power, or a combi- nation of these features. The overall picture and a schematic representation of the experimental plant is presented in Figure 5. 18 Acta Polytechnica Vol. 52 No. 4/2012 Figure 5: The stand The main sub-assemblies of the plant are: 1. the pump, with an electro-hydraulic adjustment system; 2 [8]. the hydraulic energy source for control supply; 3. a specific sensor; 4 [5, 12]. the electricity supply and control system for the proportional distributor, the sensors and the distributor to simulate the load; 5 [4]. the acquisition and control hardware system; 6 [9]. The command and control interface; 7. the load simulator. After tuning the controller, the following con- stants were determined that offer good dynamic be- havior for the system regardless of the chosen con- trol type: Kp = 0.35; 1/Ti = 12; KD = 0, val- ues very close to those obtained in the simulations, which validates the mathematical model. An impor- tant objective of the research was to study the behav- ior of the PID controller with various control struc- tures. The dynamic behavior of the control struc- ture was investigated by recording the signal step re- sponse, which gives the command for pressure, flow and power. Figures 6 to 8 present in graphical form the data for the set of tests carried out on the stand for the three major types of control. Figure 6: System response to a pressure command of 80 bar, and 20 bar Figure 7: System response to a flow command of 28 bar and 12 lpm Figure 8: System response to a power command of 3 kW and 0.1 kW 19 Acta Polytechnica Vol. 52 No. 4/2012 The dynamical behavior of the system is evalu- ated from the time diagrams (simulated and real di- agrams), taking into account the following: • Stability: The model and the real system are well damped. • Rapidity: Response Time: 0.2 seconds for the model and 0.4 seconds for the real system, dif- ference is caused by the uncertainty factors that are approximated in the mathematical model. • Precision: Stationary error below 2 %. The control system has satisfactory behavioral skills for any adjustment structure. 5 Conclusions An analysis of the results indicates that that there are no significant differences between the mathemat- ical model and the real system, so the model can be used for developing new hydraulic machines equipped with this kind of command and control system, which offers the following advantages: Reduced complexity for the circuit construction of the control; it does not involve the use of special expensive equipment; the mechanical structure of the pump is not affected when another hydraulic parameter needs to be con- trolled; the control scheme is integrated with the pi- loting and tracking mechanism into a compact small- size system. It has been shown that, unlike when using con- ventional techniques, the three important hydraulic parameters can be adjusted with the same pump, the same controller and only two pressure sensors by sim- ple electrical switching. Axial piston machines with variable displacement and an electro-hydraulic control system allow com- plete automation, compatible with the operating cy- clograms of complex equipment, by interfacing with a PLC or a process computer. References [1] Banyai, D., Vaida, L.: Electro-hydraulic control system for variable displacement machines, 12th International Conference on Automation in Pro- duction Planning and Manufacturing, p. 50–58, Zilina, Slovakia, 2011. [2] Banyai, D.: New methods in synthesis of hy- draulic machines with variable displacement and electro-hydraulic adjustment, PhD Thesis, Tech- nical University of Cluj-Napoca, Romania, 2011. [3] He, Q. H., Hao, P., Zhang, D., Zhang, H. T.: Modeling and Control of Hydraulic Excavator’s Arm, Journal of Central South University of Technology, Vol. 13, No. 4, 2006, p. 422–427. [4] Năşcuţiu, L., Banyai, D., Marcu, I. 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