Double duty ratio PWM control method for a novel HSV actuator with low power consumption

Abstract

This paper presents a novel high speed valve (HSV) actuator with low power consumption. The structure design of tapered armature and control method of double duty ratio pulse width modulation (PWM) are proposed in the HSV actuator to improve steady and transient characteristics. The electric-magneto-mechanical model of the HSV actuator is established and investigated by theoretical analysis. Parameters improvement of the HSV actuator is analyzed by the model, and optimized results for a prototype actuator have been obtained. The experimental and simulation curves agree well with the changing trend, and show that the opening time of the HSV actuator is 7.3 ms, the closing time is 20 ms, and power consumption in maintenance stage is 1.35 W, within the stroke of 2.5 mm. Compared with normal driving method, the proposed structure and method have the advantages of opening time reduced by 37%, closing time reduced by 29%, and steady-state power consumption reduced by 93.5%. The proposed structure and method in the HSV actuator are available to meet the driving requirements of both steady and transient performance in fluid control systems better, especially in power shortage or power supply inconvenient engineering.

Keywords

High speed valve double duty ratio pulse width modulation low power consumption

1. Introduction

As a new type of electro-hydraulic control technology, digital hydraulic technology has the advantages of high reliability, high precision, simple and flexible control compared with traditional proportional and servo control technology [1,2]. High speed valve (HSV) is an important actuating element in digital hydraulic control system, and adjusts the pressure or flow timely and accurately with good response index. Compared with the servo valve, HSV has several benefits, including high efficiency, high reliability and robustness [3]. Power consumption of HSV is another key index in areas such as aerospace, deep sea, military industry and other power shortage or power supply inconvenient engineering [4–7]. When HSV works in the environment with high temperature, there exist problems such as null shift and jam in digital hydraulic system. Low power consumption not only saves power energy, but also controls temperature rise of the components, improving the stability and service life of components.

To obtain good steady and transient characteristics, a lot of high performance HSV actuators by intelligent materials, novel structure, and advanced methods have been proposed. For application examples of intelligent materials, piezoelectric stack, giant magnetostrictive material, shape memory alloy and magnetic fluid [8–10] have been adopted in HSV to show faster response and smarter size. But limited by the stability and nonlinearity of intelligent materials, most intelligent materials haven’t been adopted in industry application.

Novel structure and advanced methods for HSV have become more effective to improve steady and transient response characteristics in industry applications. A lot of proposed structures for HSV actuators have been studied. Kong [11] proposed a parallel coil for HSV, and the experimental results showed that the transient performance of the solenoid can be improved greatly. Roemer [12] developed a moving coil actuator, which achieved fast current rise and resulted in a short switching time. Tu [13] developed a rotary valve to achieve high speed and with low power. Xiang [14] proposed a novel ϵ-type solenoid actuator, which reduced the moving mass weight by almost 65% without significant loss of solenoid force, and the response time reduced by 20%. Man [15] proposed a novel high-speed electromagnetic actuator with permanent-magnet shielding. The result shows that the opening time, closing time of actuator are 2.24 ms, 7.28 ms respectively within a stroke of 0.6 mm. Li [16] proposed a HSV actuator with double corner-pole airgaps, which the maximum thrust force is 110N.

Control methods have also been a hot research spot. An accurate control method for the valve can obtain good transient response characteristics. Pulse width modulation (PWM) control is an effective method in recent research. Gabdullin [17] studied the effect of different pulse widths on the heat dissipation of an electromagnetic actuator and showed that power consumption could be reduced by 70%–86% within short pulses of 0.3 ms. Zhou [18] developed a double voltage driving method, which reduced working temperature by 7 °C. Zhong [19] proposed an intelligent pulse-width modulation method, and showed good steady and transient performance, but needed an extra controller and program to get ideal PWM signal.

There have been many related studies on steady and transient characteristics of the HSV actuator. However, it is available to reduce power consumption by advanced control method even if achieving fast response. In this paper, both novel structure design based on tapered armature and PWM control method based on double duty ratio are proposed for the HSV actuator. It takes into account the steady and transient characteristics of response time and power consumption by novel structure and advanced method. This PWM control method is applied to the HSV actuator, and the model of the HSV actuator structure and circuit is established. In addition, a new expression of voltage function is proposed. The HSV actuator in each stage of the voltage and duty ratio can be summarized as a sectional function. Theoretic model is established, and the effects of tapered angle on valve characteristics and pulse width modulation signal with different duty ratios are studied to realize characteristics of both high speed and low power consumption.

2. Structure and methodology

2.1. Structure

The proposed HSV actuator is illustrated in Fig. 1, which includes tapered armature, spring, sleeve, coil, yoke iron, and so on. When the coil is energized, the yoke iron attracts the tapered end of the armature, which in turn overcomes the spring force to move the armature. In the end, the armature is in the state of suction with yoke iron, which closes the fluid channel of the HSV. When the coil is not energized, the armature returns to initial position by the action of the spring, which opens the fluid channel of the HSV.

Compared with the traditional valve, the advantage of the HSV actuator shown in Fig. 1 is the proposed structure of tapered armature. Figure 2 shows comparison of different armatures where x is stroke, σ is air gap. The stroke of the traditional armature is equal to the air gap and the stroke of the tapered armature is larger than the air gap, which makes the air gap of the tapered armature smaller within the same stroke. The magnetic flux distribution of the actuator in Fig. 3 shows that tapered armature with a certain angle makes the air gap shorter in normal direction, and the magnetic reluctance of air gap between yoke iron and armature could be reduced. Under the same condition, the smaller magnetic reluctance makes the greater electromagnetic force, resulting in fast response characteristics [20–22]. But the larger tapered angle of armature will also reduce electromagnetic force in axial component. So, the tapered angle of the armature is a vital parameter in the proposed HSV actuator, and a suitable value needs to be considered to improve the response characteristics.

Fig. 1.

Structure of the proposed HSV actuator.

Fig. 2.

Comparison of different armatures.

Fig. 3.

Magnetic flux distribution of the HSV actuator.

Fig. 4.

Double duty ratio PWM waveforms.

2.2. Methodology

The proposed method of double duty ratio PWM is shown in Fig. 4. The working cycle is divided into three stages, which are opening stage, maintenance stage, and closing stage. Different duty ratios driving voltages are applied in different stages to achieve both fast response and low power consumption. The HSV actuator is driven by high duty ratio, low duty ratio, and zero value, when valve is in opening stage, in maintenance stage, and closing stage respectively. In the opening stage, the HSV actuator is driven by a high duty ratio and gets high voltage input. It makes the coil current increase rapidly and fast movement of the armature with transient high power. In the maintenance stage, the HSV actuator is driven by a low duty ratio. It not only generates basic maintain force in opening position, but also achieves less power consumption. The low duty ratio is also available to control the temperature rise, as well as improve the stability of the HSV actuator. In the closing stage, the coil is not energized, and the armature returns to the initial position by spring. So the proposed method is available to meet the control requirements both in transient and steady state.

To achieve a double duty ratio signal, an analog circuit is shown in Fig. 5. Firstly, double voltage signal is synthesized by an external pulse signal that is generated by the monostable trigger circuit, invert proportional operation circuit I, invert proportional operation circuit II, invert input summing circuit and invert proportional operation circuit III. Then, the double voltage signal is compared with the high frequency triangular wave signal through PWM signal modulation circuit, to produce a double duty ratio pulse width modulation signal with different adjustable duty ratios. Finally, the HSV actuator is driven by a signal power amplifier circuit.

Fig. 5.

Circuit for double duty ratio signal.

3. Modeling

The model of the proposed HSV actuator includes three parts, which are circuit submodel, magnetic submodel, and mechanical submodel.

3.1. Circuit submodel

According to Kirchhoff’s voltage law, the differential equation of the circuit system can be obtained. $\begin{eqnarray}\displaystyle u(t)=i(t)\cdot R+\frac{d({\Psi})}{dt}=i(t)\cdot R+N\frac{d{\phi}}{dt} & & \displaystyle\end{eqnarray}$ (1) where u is driving voltage (V), i is coil current (A), R is resistant ( $\Omega$ ), 𝛹 is flux linkage (Wb), N is coil turns, Φ is magnetic flux (Wb). $\begin{eqnarray}\displaystyle u(t)=\left\{\begin{array}{@{}ll@{}}C & \quad t_{1}\leq t\lt t_{2}\\ l(t) & \quad t_{2}\leq t\lt t_{3}\\ 0 & \quad t_{3}\lt t\leq t_{4}\end{array}\right. & & \displaystyle\end{eqnarray}$ (2) where C is high driving voltage value in high duty ratio, l (t) is driving voltage function in low duty ratio.

In a high duty ratio, the duty ratio can be considered to 100%, and driving voltage value could be a high level with short period.

In a low duty ratio, voltage signal could be expressed as periodic function. Dividing the total time (t ₃–t ₂) into the number of periods. The driving voltage model in every period is shown as: $\begin{eqnarray}\displaystyle l(t)\text{} & =\text{} & \displaystyle l(t+T)\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle T\text{} & =\text{} & \displaystyle \frac{t_{3}-t_{2}}{n}\end{eqnarray}$ (4) $\begin{eqnarray}\displaystyle l(t)\text{} & =\text{} & \displaystyle \left\{\begin{array}{@{}ll@{}}C & \quad 0<T\leq DT\\ 0 & \quad DT<t\leq T\end{array}\right.\end{eqnarray}$ (5) $\begin{eqnarray}\displaystyle D\text{} & =\text{} & \displaystyle \frac{T_{H}}{T}=\frac{T_{H}}{T_{H}+T_{L}}\end{eqnarray}$ (6) where D is duty ratio, T _H is time of high-level signal, T _L is time of low-level signal, T is time of period, n is number of periods.

3.2. Magnetic submodel

Ignoring the displacement current and hysteresis effects, the vector potential function of magnetic field can be derived from Maxwell’s fundamental equation: $\begin{eqnarray}\displaystyle {\nabla}\times \frac{1}{{\mu}}{\nabla}\times \boldsymbol{A}=\boldsymbol{J}_{s}-{\sigma}\frac{\partial \boldsymbol{A}}{\partial t}-{\sigma}{\nabla}\boldsymbol{V } & & \displaystyle\end{eqnarray}$ (7) where J _s is source current density (A/m²), A is magnetic vector potential (Wb/m), $\mu$ is permeability, σ is reluctivity, V is electric potential (V). $\begin{eqnarray}\displaystyle \boldsymbol{J}_{s}=\frac{i}{k} & & \displaystyle\end{eqnarray}$ (8) where k is the cross-sectional area of the coil.

By Eqs (7) and (8), A can be calculated. $\begin{eqnarray}\displaystyle H=\frac{1}{{\mu}}\times B. & & \displaystyle\end{eqnarray}$ (9)

To obtain the electromagnetic force, the system adopts the principle of virtual work. The electromagnetic force on the armature in the direction of the displacement is given by the following relationship: $\begin{eqnarray}\displaystyle F=\frac{dW(s,i)}{ds}|_{i=\text{const}}=\frac{\partial }{\partial s}\left[\int _{V}\left(\int _{0}^{H}B\cdot dH\right)dV\right] & & \displaystyle\end{eqnarray}$ (10) where F is electromagnetic force, s is virtual displacement, H is magnetic field intensity, B is magnetic flux density.

3.3. Mechanical submodel

The governing equitation for the motion of the HSV actuator is $\begin{eqnarray}\displaystyle m\frac{d^{2}s}{dt^{2}}+f\frac{ds}{dt}+k(s+s_{0})=F & & \displaystyle\end{eqnarray}$ (11) where m is quality of armature, f is friction coefficient, k is spring stiffness, s is armature displacement, s ₀ is the spring initial compressed length, F is electromagnetic force.

The model for the actuator is established combining (1), (2), and (3), and can be solved by using time-stepping finite-element method.

3.4. Model and condition

The three-dimensional finite-element model can be analyzed by the software (Ansys Maxwell). The armature, shell, and yoke iron are made of magnetic material, and the spring and sleeve are made of non-magnetic material. When importing the simulation model, only the coil and other magnetic parts are retained. Figure 6 gives boundary and exciting conditions of the model for the HSV actuator. Except the default boundary conditions and the background object’s balloon boundary conditions extend indefinitely along the edge. The field current is specified in the coil winding and voltage is defined by circuit submodel. The circuit submodel is achieved by using the external circuit in Fig. 7 to obtain double duty ratio PWM power input. The circuit diagram consists of the following elements: voltage source, power switch, control signal, reflux diode, coil inductance, coil resistance. The external circuit for control signal of double duty ratio PWM has been introduced in preview teamwork [23]. The three-dimensional grid mesh of the model with the air region is shown in Fig. 8. The maximum mesh size of armature, yoke iron and shell are 0.6 mm, the other parts are 1 mm. Finally, set the motion conditions and simulation step length.

Fig. 6.

Boundary and exciting conditions of the model.

Fig. 7.

Circuit submodel.

Fig. 8.

Finite element model of the HSV actuator.

4. Parameters improvements based on modeling

According to simulation model, many parameters such as tapered angle of armature, driving voltage, frequency, duty ratio have a greater impact on the performance. Effects of those variable parameters on steady and transient characteristics of the HSV actuator are introduced as follows.

4.1. Tapered angle

Figures 9(a) and 9(b) give electromagnetic force curves and current curves of the HSV actuator under different tapered angles on armature. It shows that the biggest electromagnetic force is 28N by 20° tapered angle on armature and the smallest electromagnetic force is 21N by 30° tapered angle. But their maximum current is almost the same. Figure 9(c) gives position curves, which shows under the same condition of constant voltage driving method, the relationship between opening time and tapered angle is non-monotonic. In opening stage, as the tapered angle increases, the opening time in the stroke of 2.5 mm decreases first, then increases. For example, the HSV actuator with 20° tapered angle can finish the stroke in a short time of 7 ms, which is less than both tapered angles of 10° and 30°. This is due to variable electromagnetic force in axial components under difference tapered angles. In closing stage, as the tapered angle increases, the closing time decreases. There is an appropriate tapered angle of about 20° to make the desired response characteristic, so the proposed tapered armature is available to improve the response characteristic compared to normal flat end of armature.

Fig. 9.

Transient characteristics under different tapered angles.

4.2. Driving voltage value C

According to Section 3, the value of voltage is an important parameter that affects response time and power consumption. The voltage under common control method can be designed from the circuit model or the winding resistance and the inductance directly. In this double ratio control method, the higher voltage can get a faster response time, but it can also get higher power consumption. Simulation analysis are carried out to optimize the voltage and obtain performance. Figure 10(a) gives current response curves under different driving voltages. In opening stage, the current increases first, then decreases and then increases. When the current drops to the inflection point, it is basically the time for the valve to fully open, which can be concluded from position response curves in Fig. 10(b). This is because armature moves in the magnetic field to produce the induced electromotive force, whose direction is opposite to the excitation direction, thus reducing the current. When the armature stops moving, the current returns to its maximum value then remains stable. In opening stage, as the driving voltage increases, the current curve has a higher slope, and the HSV actuator requires less opening time. In closing stage, the current and position curves have similar descending process and closing time. In the normal driving method, higher voltage such as 36V could be designed to achieve less opening time as well as higher response speed, but it will takes more power consumption in maintenance stage, resulting in higher temperature rise. So it’s better to limit effect of high driving voltage C only in opening stage by proposed method of double duty ratio PWM.

Fig. 10.

Transient characteristics under different voltage.

4.3. PWM frequency 1/T in low duty ratio period

Figure 11 gives current curves under different frequencies. In opening stage and closing stage, current curves are similar. But in maintenance stage, as the PWM frequency in low duty ratio period increases, the fluctuation of holding current can be reduced, which is conducive to keep the HSV actuator on holding position. When the frequency 1/T is higher than 2 kHz, the HSV actuator can meet the requirements of signal stability basically.

Fig. 11.

Transient characteristics under different frequencies.

4.4. Low duty ratio value D

Figure 12(a) gives time curves under different duty ratios. In maintenance stage, as the lower duty ratio increases, the holding current would increase. So a smaller value of low duty ratio is helpful to reduce the power consumption of the HSV actuator in the maintenance stage. But too small value would lead to failure in maintenance stage. When low duty ratio value is set to 5%, current curve will fall to zero before the coil is not energized, which can’t keep the HSV actuator in opening and maintenance stage. Figure 12(b) gives position curves under different duty ratios. In maintenance stage, only the curve of 5% duty ratio start falling ahead of closing stage (20 ms). Figure 13 gives electromagnetic force curve under different duty ratios and spring force curve in maintenance stage. If the HSV actuator can keep working, the electromagnetic force needs bigger than spring force. The spring force is 3.5N when armature is absorbed completely. When the double ratio is about 15%, the electromagnetic force is same as spring force. So, when duty ratio is bigger than 15%, the HSV actuator can work normally. On basis of working stability in maintenance stage, the value of low duty ratio D as small as possible is helpful to reduce power consumption. Considering the friction force, gravity, and other factors, it is more appropriate to select 20% duty ratio.

Based on analysis of the above key parameters, the following parameters are selected to design the prototype. The other parameters are also analyzed, which are omitted in this paper. Parameters of the prototype are shown in Table 1.

Fig. 12.

Transient characteristics under different duty ratio.

Fig. 13.

Force characteristics under different duty ratio.

Table 1

Parameters of the HSV actuator

Parameters	Value
Resistance of coil (Ω)	15
Coil turns (tr)	800
Stroke (mm)	2.5
Mass of armature (kg)	0.006
Tapered angle of armature	20°
Spring coefficient (N/mm)	0.5
Driving voltage (V)	36
Frequency (kHz)	2
Low duty ratio (%)	20
High duty ratio (%)	100

5. Experimental validation

5.1. Testing system

Figure 14 gives a HSV actuator characteristics testing system. The signal generator generates a control signal input to the driving circuit that provides excitation for the HSV actuator. Current and displacement of armature can be measured by the sampling resistance on the driving circuit and the laser displacement sensor. The value is finally recorded and displayed by Labview system. In maintenance stage, electrical energy is converted to copper resistance loss. The power consumption can be obtained from the measured current value through the Eq. (12). $\begin{eqnarray}\displaystyle P=i^{2}R. & & \displaystyle\end{eqnarray}$ (12)

The analysis shows that the higher driving voltage applied to the HSV actuator can get a shorter response time. But the power consumption will increase with the higher voltage. In order to make a better comparison, 18 V constant voltage and 36 V double ratio voltage are selected as an example for the experiment.

Fig. 14.

HSV actuator characteristics testing system.

Fig. 15.

Experimental results.

5.2. Experiment results

Figure 15 gives the HSV actuator experimental results under two control driving methods (double duty ratio control method and constant voltage) within the 2.5 mm stroke. When driven by 18V constant voltage, the power consumption is smaller than other simulation voltage. The opening time of the HSV actuator is about 11.6 ms, the closing time is about 28 ms, and power consumption in maintenance stage is about 21 W. When driven by 36 V double duty ratio control method, the opening time is about 7.3 ms, the closing time is about 20 ms, and power consumption in maintenance stage is about 1.35 W. In the PWM switching process, power amplifier tubes generate electrical losses only in the saturation and cut-off stages. In the HSV actuator loss, the electrical losses caused by power amplifier tubes are supposed to be a lesser part, which is ignored in this paper. Compared with constant voltage driving method, the current by proposed method increases significantly faster in opening stage and drops to a lower value in maintenance stage. The changing trend of the experimental curves is in accordance with the simulation curves in last section, except slight distinction in amplitude and time delay caused mainly by actual mechanical impact and friction hysteresis. The experimental results show that the proposed method has the advantages of opening time reduced by 37%, closing time reduced by 29%, and steady-state power consumption reduced by 93.5%, compared with normal driving method. Therefore, it can be concluded that high voltage is required for driving during the opening stage, which can reduce the opening time. But in the maintenance stage, it is not necessary to keep constant voltage which will increases the power consumption of the HSV actuator. In addition, when entering the closing stage, due to the continuous energization in the maintenance stage, the closing time will also increases. This is because the continuous energization makes the coil current larger, and increases current weakening time after the voltage is off, resulting in an increase in the release delay time of closing the valve. So, double duty ratio control method satisfies the working requirements of the HSV actuator, which can optimize the dynamic characteristics and reduce the power consumption effectively.

6. Conclusion

A HSV actuator with low power consumption is presented based on both novel structure design of tapered armature and PWM control method of double duty ratio. The Effects of tapered armature and control method on steady and transient characteristics of the HSV actuator are studied by theoretic model and experimental test. The changing trends of the experimental and simulation results agree well, except slight distinction in amplitude and time delay caused mainly by actual mechanical impact and friction hysteresis. On the one hand, the proposed tapered armature for the HSV actuator is available to improve the transient characteristic compared with normal flat end of armature. On the another hand, driven by proposed control method, the opening time of the HSV actuator is about 7.3 ms, the closing time is about 20 ms, and power consumption in maintenance stage is about 1.35 W. The results show that the proposed method has the advantages of opening time reduced by 37%, closing time reduced by 29%, and steady-state power consumption reduced by 93.5%, compared with constant voltage driving method. Besides, the proposed method only needs single voltage power supply, which is effective to apply in industry than double voltage driving method introduced in previous work. Therefore, the proposed structure and method in the HSV actuator are available to reduce the power consumption when keeping high response speed characteristics, and meet the driving requirements of both steady and transient performance in fluid control systems better, especially in power shortage or power supply inconvenient engineering.

Footnotes

Acknowledgements

The authors gratefully acknowledge the support of key R&D Program Projects in Zhejiang, China (2019C02019).

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