The Ninth Scandinavian International Conference on Fluid Power, SICFP05, June 1-3, 2005, Linkoping, Sweden

IMPROVEMENT OF A PROPORTIONAL VALVE DYNAMICS BY MEANS OF A PEAK & HOLD TECHNIQUE

Amirante R. *, Bruno S.* Del Vescovo G. *, Ruggeri M.**

* Department of Mechanical and Industrial Engineering POLITECNICO di BARI - Via Re David 200, - 70125 Bari ITALY

g.delvescovo@poliba.it, amirante@poliba.it

** IMAMOTER CNR Institute for Agricultural and Earthmoving Machines Via Canal Bianco 28, 44044 CASSANA (FE) - ITALY

m.ruggeri@imamoter.cnr.it

ABSTRACT

As well known the performance of a closed or open control loop in hydraulic systems depends strongly on the dynamic behaviour of the directional valves. In this work a middle size proportional directional valve has been studied with a particular input Pulse Width Modulation (PWM) signal. The proportional solenoids of the tested valve have been supplied with a variable duty cycle PWM input signal to obtain a desired spool axial position. In particular an initial peak value of the supply current has been realized with a duty cycle value different from the duty cycle needed to obtain the target axial spool position. This technique has been used to improve the dynamics of the valve when the spool position changes from a lower metering section area to a greater one or vice versa. The results obtained by means of an experimental test rig will show the very important improvements that this new technique provides.

KEYWORDS: Proportional Directional Valves, Peak & Hold, PWM

1. INTRODUCTION

In the last few years the functionalities provided by embedded electronic systems have been increased, offering to the designers, involved in mechatronics systems, tools and methods for a new approach to hydraulic systems design. The first applications were cost effective only if equipped with a low cost electronic control unit; in the same way, the new electro-hydraulic applications are equipped with low and middle cost microprocessors based systems, but the most important differences between the old and the present control systems are the electronics performance and the availability of integrated peripherals, that in microcontrollers allow powerful control functions with a typical task control period of less than 1 ms, and programmable peripherals, useful to generate output power PWM signal profiles, in order to control the valve dynamics. Another important characteristic of the microcontrollers is the real time integration between analog signal acquisition and power output management, that allows to acquire the real position or speed of the valve spool in precisely defined time instants during the output profile generation. Merging the electronics features and the experience derived by the engine control systems design, where peak and hold signals are widely used to control diesel and gasoline fuel injectors, a new

approach to the valve control is experimented, applying the peak and hold approach to proportional valves, for which unlike in on/off actuators the desired spool position varies continuously. The main difference results in a variable peak control function profile and in the research of a physical law, needed to relate the peak profile and its duration to the final spool position and to the valve dynamic model. The advantages of the proposed solution are: 1 - a dynamic response of the controlled valve independent from the final spool position, and in particular, a rising time comparable with the data provided by the valve manufacturer yet without overshoot, 2 a better method to control the actuator position: in fact, being the steady state positioning error of the actuator proportional to the integral of the dynamic characteristic, the shortening of the transition between different positions plays a significant role in the reduction of such an error.

2. THE TEST RIG

The tested valve has been inserted in a hydraulic circuit presented in the Fig. 1 and realized in the Fluid Power Laboratory of Polytechnics of Bari.

Fig. 1: The Hydraulic Plant

A tandem gear pump (1) is driven by an asynchronous electric motor (2). An heat exchanger (3) is mounted on the discharge line and keeps the temperature of the oil at a constant value. The oil temperature is measured by a thermocouple (measuring error 0,5 % of the full scale (0-300C)) that regulates the water flow rate by means of a thermostatic valve (6). A constant flow rate is delivered by the pump while a piloted proportional relief valve (4) is used to control the pressure drop across the valve during the test. When the directional control valve (5) is driven, a part of the flow rate delivered by the pump is discharged by the directional valve while the remaining flow rate is discharged by the relief valve. This phase is characterized by an approximately constant pressure drop. The flow rate discharged by the valve increases with the increasing metering section area and this situation lasts until the valve reaches the saturation point that occurs when the flow rate discharged by the valve equals the whole flow rate delivered by the pump; in this case the relief valve, being closed, doesnt set the pressure drop on the valve.

Moreover, two pressure transducers (1% error of the full scale, measuring range 0-200 bar) have been mounted near the ports P and A of the proportional valve in order to measure the pressure drop on the metering section during the spool movement. The proportional valve has an integrated spool position sensor LVDT (Linear Variable Displacement Transducer) in order to measure the axial spool movement. One of the coil acting on the spool of the valve, is piloted by a signal produced by means of a high-dynamics voltage supplier (7) that amplifies the analog signal produced by an acquisition card. In fact the voltage amplifier is piloted by an analog signal provided by a general purpose National Instrument Acquisition Card and a flexible LabVIEW code has been properly realized to change the parameters of the output signal. In this way it is possible to change all the signal parameters, in particular:

- the frequency of the PWM - the amplitude of the maximum voltage - the duty cycle of the PWM - the frequency and the amplitude of an additional dither

Moreover it is possible to break a single PWM signal in different phases characterized by different duty cycle values.

Polarization phase (PWM) Peak & Hold phase (PWM) Hold phase (PWM)

Fig.2 : An example of the average voltage signal deriving from the PWM signals produced by the voltage supplier in three consequent different phases

The Fig.2 shows an example of three consequent phases; the upper diagram shows the average voltage signal deriving from the PWM voltage signals produced by the voltage supplier. In the Fig.3 the command front panel realized in LabView has been reported. The signal is constituted by :

- A polarization phase - A Peak phase - A Hold phase

Fig.3 : The LabVIEW Control Panel

The realized LabVIEW code is very flexible and easy to use and, moreover, with reference to the Fig. 3, allows the setting of the following parameters:

- PWM signal frequency - The frequency and the amplitude of the dither - The duty cycle and the duration of the polarization phase - The duty cycle and the duration (number of waves) of the Peak phase - The duty cycle and the duration (number of waves) of the Hold phase

In this way it is possible to simulate in a flexible way the output signal of the power device of a commercial electronic driver. Moreover, a strategy based upon a buffered acquisition, allows the contemporary acquisition of the following signals during the movement of the spool:

- the spool position (LVDT) - the pressure upstream of the valve, pP - the pressure downstream of the valve, pA - the PWM voltage signal provided by the high dynamics voltage supplier - the current running through the coil

3. A THEORETICAL APPROACH

In this section, the dynamics law of the spool will be illustrated from a theoretical point of view. The forces acting on the spool can be divided into 6 components: - the magnetic force - the viscous forces that the oil flow acts on the spool

- the mechanical viscous friction - the spring centring force - the flow forces in unsteady conditions - the inertial force It must be considered that the tested proportional valve has a parabolic opening law i.e. the opening surface area increases in a quadratic way with the increasing axial spool movement. In order to derive the dynamics law of the spool, two subsequent phases must be distinguished. Indicating with Q the flow rate discharged by the valve during the opening, a first phase must be considered when:

Q

where B is the magnetic flux density that is a function of the magnetic field H according to the magnetic behaviour of the material, while H is related to the absorbed current by means of the relation:

IlnH =

(8)

where n is the number of turns, l the magnetic path length and I is the current. When the valve reaches the saturation point the flow force is related to the pump flow rate according to the following equation because the flow rate across the valve is constant:

=

AtgQF flow

12 (9)

The general dynamics law becomes:

20 )())(( xf

xxKxcxmtIF ++++= &&& (10)

Where all the constant terms are included in f. Generally the proportional valve is inserted into a hydraulic circuit that avoids the saturation of the flow rate and keeps the pressure drop at a constant value. In this way the second phase is absent. In the examples that will be presented in this work both the two phases are present because a pressure drop is enforced on the valve in the first phase but there is the possibility that in certain situation the saturation point is reached. We can consider anyway that its reasonable that the peak of the magnetic force doesnt extend its effects beyond the saturation point. From a general point of view, it can be considered that the effects due to the flow forces must be negligible if compared to the effects of the spring. In fact the flow forces change with the pressure conditions so determining a different axial position at the same absorbed current value. In this case, all the flow force terms in the equations 5 and 10 can be neglected so reducing the spool dynamics law to a 2nd order mechanical system that can be more easily solved by means of analytical or numerical methods. Moreover this law is valid during the whole spool movement without the discontinuity caused by the saturation point. The last observation has not been confirmed in the experimental tests so the future of research activity will face the study of a valve with a better behaviour, although at the same time a study dealing with the correlation between the flow force behaviour during the axial spool movement and the level of the advantageous effects deriving from a Peak & Hold technique can be considered very interesting from a fluid dynamic and theoretical point of view.

4.THE EXPERIMENTAL RESULTS

In this section the obtained experimental results will be presented. Figures 4 and 5 show respectively the experimental profile of the spool position, with superimposed the plot of the average value of PWM voltage signal, and the profile of the absorbed current.

Fig. 4: Average voltage and spool position without peak (experimental results)

Fig. 5: Current profile without peak (experimental results)

From the diagram of Fig. 4 it can be argued that in the tested valve the time needed to reach the axial position corresponding to about 50% of the whole axial spool travel is approximately 200 ms. The profile of the spool position shows an over dampened behaviour of the spool while the profile of the current shows a 1st order system behaviour that is typical of the electric behaviour of the coil, while an initial polarization current is visible in the first part of the diagram. The polarization current is determined by the initial phase of the PWM voltage signal with a 2% duty cycle value corresponding to about 80 mA. The polarization current is a feature used in industrial application, in order to reduce the time needed to generate the field necessary to move the valve spool till the desired position from the unexcited position. Applying a low potential to the valve coil, an equilibrium position is reached, where the force does not produce a spool movement, but the additional current required to start the spool movement is lower, reducing yet the global valve response time. The current profile is related to the equation:

dtdiLRiV += (11)

where R is the coil resistance, V is the potential applied to the inductor, L is the inductance of the valve coil, i is the current, and t is the time.

In the hypothesis of closure of the switch starting from the 0=i condition, the equation solution is:

=

t

RL

eRVi 1 (12)

that lead to a saturation value of RVi = . A numerical simulation, reported in the Fig. 6, shows this

law.

Fig. 6 Current behavior at the closure of switch (simulation results)

Infact, in order to understand the electronic control functionality and the electrical power provided by the power stage of the test bench, a typical valve control signal behavior has been simulated, by means of the MULTISIM 7 code, an electronic circuit simulator capable to perform analog/digital circuit simulation. In the Fig. 7 the electric circuit model with the PWM signal generator is shown. This circuit has been used to simulate the behavior of the electrical power supply circuit when the PWM technique is applied.

Fig. 7: Electric circuit with PWM signal generator

In the Fig. 8a and 8b, the current profiles of the previous circuit during an increasing or decreasing PWM duty cycle are shown. In these figures it is possible to notice the effects of the Power MOS transistor switching on the current in the valve coil inductance. For example, considering the current

behaviour in the increasing PWM duty cycle condition (Fig. 8a), it can be observed that for every switching two different phases are present: in the first phase (active duty cycle phase) the current increases while in the second phase the current decreases (passive duty cycle phase). Thus, the negative effect of the second phase is that the time to reach the current steady value increases if compared to the case of a constant control value (100% of PWM duty cycle). Similarly, during the valve opening transient, where an intermediate PWM duty cycle value is superimposed starting from a lower value, the coil discharge phase, during the passive PWM duty cycle phase, generates a current decrement in the inductance that lead to a major current rising time and then to a longer valve opening transient.

Fig. 8a: Current profile during an increasing PWM duty cycle phase (simulation results)

Fig. 8b: Current profile during a decreasing PWM duty cycle phase (simulation results)

The Equ. 12 and the last observations explain also that, if a small valve spool displacement is needed ( i.e. a small force) a small current must be provided, with a low potential generated by a small PWM duty cycle; in the last case the time to reach the desired current value can be reduced increasing the initial voltage value as shown in the Figures 10 and 11 and it is easy to foresee that the improvements introduced by the Peak & Hold technique will be more evident at the lower axial spool position.

Fig. 9: Current profiles with and without peak (experimental results)

Fig. 10: Average voltage with and without peak (experimental results)

Fig. 11: Spool positions with and without peak (experimental results)

In the Figures 9, 10 and 11, the results corresponding to a Peak & Hold technique are presented. In particular it can be noticed that after the first polarization phase, a PWM signal with 100% duty cycle value has been used and then the same duty cycle value of the example in the Figures 4 and 5 has been supplied. From the current profile (Fig.9) it can be argued the sudden increase of the current in the first phase of the opening corresponding to the peak PWM voltage signal; this is due to the absence of the passive duty cycle phases. In the diagram of the Fig. 11 the previous spool displacement profile has been superimposed to the new profile in order to evaluate the improvement provided by the P&H technique. The spool reaches the target axial position in approximately 25 ms reducing the positioning time to 1/8 of the previous case. It must be considered that the number of waves that constitutes the peak voltage signal must be opportunely calibrated in order to stop the spool movement at the desired position. The following two figures show, respectively the two cases of an underestimated and overestimated Peak time length. The diagrams put in evidence that in the first case the benefits deriving from the peak are less evident than the previous test while in the second case an overshoot of the axial position is evident.

Fig. 12a: example of under-estimated peak time duration (experimental results)

Fig. 12b: example of overestimated peak time duration (experimental results)

The last spool behaviour must be avoided because an overshoot in spool position turns into an overshoot of the flow rate discharged to the actuator and this can result in an overspeed of the controlled actuator, which can be harmful especially in case of fluid metering, for example in the position control of a crane arm. From this example it can be argued the need to calibrate an opportune value of the peak time length. In fact, a simple law needed to establish a correlation between the target position of the spool and the optimal value of the peak time length has been found. The Fig. 13 shows the profile of the optimal number of waves of the peak to obtain the target final position that is proportional to the final duty cycle value. It can be noticed that the law is approximately linear and this profile can be easily implemented in an electronic driver, that is able to interpolate the optimal value of peak time length at different final spool positions.

Fig. 13: Profile of the optimal number of waves in the peak phase at different final duty cycle values

After the characterization of the peak time length other two types of experimental tests have been realized, considering the movement of the spool from a previous intermediate axial position to a greater or lower one. In the first case it is obvious that the optimal peak time length must be resized opportunely because the second peak time length must be reduced when the spool moves from an intermediate position and not from the rest position.

Fig. 14a: profile of the average voltage signal with and without an intermediate peak (experimental results)

Fig.14b: profile of the spool position with and without an intermediate peak (experimental results)

In the second case an intermediate phase of 0% duty cycle value to decrease the time needed to reach the final position has been used. The improvements introduced by this technique are evident in both cases.

Fig. 15a: profile of the average voltage signal with and without an intermediate 0% duty cycle voltage signal (experimental results)

Fig.15b: profile of the spool position with and without an intermediate 0% duty cycle voltage signal (experimental results)

5.CONCLUSIONS

In this work the experimental results dealing with the application of a P&H technique to proportional directional control valves have been reported. This technique shows important improvements on the valve dynamics, reducing the opening time to 1/8 of the time deriving from the application of a normal PWM signal. Moreover, a generic law between the optimal peak time duration and the desired final spool position has been found. This law is approximately linear and for this reason it can be considered very simple to be implemented by an embedded electronic driver. Using this law, the target pressure value (proportional relief valve) or the target spool position (proportional directional control valve) can be reached avoiding harmful overshoots. It must be stressed that the P&H technique can provide significant improvements in high quality hydraulic components and not only in low quality components with low dynamics behaviour.

Moreover, a section of the paper shows the general dynamics law of the spool, and indicates the need to estimate correctly the flow force profile in the two phases (before and after the saturation point) when they are not negligible if compared to the spring and inertial forces. The correlation between the advantageous effects of the peak current and the dynamics of the spool will be investigated in the future and contemporarily the design of the embedded electronic driver (patent pending) that implements the P&H technique will be faced.

References

[1]. Merrit, H. E., 1967 Hydraulic Control systems, John Wiley & sons

[2]. M.Borghi, M.Milani, R. Paoluzzi, 1998 Transient flow force estimation on the pilot stage of a hydraulic valve; Proceedings of the ASME-IMECE FPST Fluid Power SYSTEMS & Tech, Vol.5 pp.157-162

[3]. G. Del Vescovo, A. Lippolis, 2003, CFD analysis of flow forces on spool valves, Proceedings of the 1st International Conference on Computational Methods In Fluid Power Technology, Melbourne November 26-28 2003

[4]. K. Krishnaswamy, P.Y .Li, 2002 On Using Unstable Electrohydraulic valves for control; Journal of dynamic systems, Measurement and control, March 2002 Vol.124

[5]. G. Del Vescovo, A. Lippolis, 2002, Flow forces analysis on a four way valve, Proceedings of 2nd FPN PhD International Symposium, Modena, July 3-6 2002

[6]. Vergil Muraru, Cornelia Muraru, Theoretical and experimental research of the Proportional Solenoids for Electrohydraulic Control Systems 2nd International FPNI Ph.D. Symposium on Fluid Power, Modena (ITALY) - 3/6 July, 2002

[7]. Pohl, M. Sethson, P. Krus, J.O. Palmberg, Modelling and simulation of a fast 2/2 switching valve Fifth International Conference on Fluid Power Transmission and Control (ICFP 2001) April 3-5, 2001 Hangzhou, China

[8]. Winkler Bernd ,2004 Development of a fast low-cost Switching Valve for Big flow rates Proceedings of 3rdN PhD International Symposium, Terrassa (Barcellona), July 2004