Force Control of Electro-Hydraulic Servo System Based on Load Velocity Compensation

Shoukun Wang, Hu Liu, Junzheng Wang and Deyang Zhang

(Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China)

Abstract: In an electro-hydraulic servo control system, the force servo system is an important component. However, due to the nonlinear characteristic of hydraulic systems, traditional control methods cannot achieve satisfactory control performances. To deal with this issue, a load velocity compensation algorithm based on the structural invariant principle is proposed in this paper. First, the theoretical analysis of the hydraulic and cylindrical force control system is presented, and the mathematical model of the force control system is established. Then the open-loop frequency response characteristics of the system are analyzed, in which the Bode diagram shows that the bandwidth of the system is obviously expanded after adopting the load velocity compensation algorithm. Finally, a practical hydraulic and cylindrical force servo system is introduced to validate the feasibility of the proposed controller, the experimental results demonstrate that the proposed method can improve the performance of force control and eliminate the influence of load stiffness on the dynamic characteristics of the system through a set of comparative experiments with different elastic loads.

Key words: electro-hydraulic servo control system; force servo control; load velocity compensation; elastic load

Force servo control systems are widely used in various fields of industrial production, such as structural fatigue testing machine, rolling mill tension control system, load simulator and wheel brake device[1]. The advantage of the traditional PID control is that this method is easy to implement, and it has been widely used in the control of hydraulic systems[2]. However, due to the disadvantages such as small stability margin, high-order strong coupling and the existence of interference of the hydraulic servo force control system, the gain of the control parameters is greatly limited. These disadvantages make accurate servo control of the force control system difficult to achieve.

The adaptive control method is equally a research hotspot[3-4], employing adaptation laws to compensate for uncertain parameters. Andrew and other researchers proposed a simplified algorithm, which is based on Lyapunov analysis of adaptive parameters to compensate for the uncertainty of the system parameters[5]; Lizalde combined a neural network based method with the sliding mode control method to design a controller for the electro-hydraulic servo force control system[6]. Yesser proposed a nonlinear system control method based on combination of adaptive control with offset error and sliding mode control[7]. However, the limitations of these methods cannot be ignored, for example, complicated calculation may be required, which cannot meet the real-time requirement in motion control systems. As the conventional PID regulator technology has been widely used in hydraulic systems for its simplicity, clear functionality and easy implementation. In this paper, the electro-hydraulic servo force control system can be controlled by adding the load velocity compensation on the basis of the conventional PID control algorithm[8].

The structure of this paper is organized as follows: in Section 1, the principle of electro-hydraulic servo force control system and the mathematical model of the force control system are introduced; the design of high performance force controller is described in Section 2; Section 3 presents the experiment results; the results are discussed and some conclusions are drawn in Section 4.

1 System Description and System Model

1.1 Structure of the electro-hydraulic force servo system

The typical electro-hydraulic force servo control system schematic diagram is shown in Fig.1.

Fig.2 Structure of electro-hydraulic servo force control system

Fig.1 Electro-hydraulic force servo control system

The hardware of electro-hydraulic force servo control system includes the following parts: hydraulic modules, a controller, a driver and sensor modules[9]. When the force control signal and the feedback signal of force sensor are not equal, the servo amplifier output the bias current to control the electro-hydraulic servo. And the electro-hydraulic servo valve output the values of flow and pressure to promote the hydraulic cylinder. When the feedback signal of the sensor is equal to the input signal, the output force of the hydraulic cylinder is kept at a desired force[10].

1.2 Model of the electro-hydraulic force servo system

1.2.1Open-loop transfer function of the system

According to the classical flow linearity, flow continuity and force balance equation, the block diagram of the symmetric valve control asymmetric cylinder can be obtained. In Fig.2[11], ΔUis the input for the control command,Fis the output force andXis the load displacement.xvis the servo valve spool displacement,Kais the amplifier gain, andKsvis a gain without considering servo valve dynamics.Kqis the servo valve flow gain.Kfis the force sensor gain,A,Vt,Kceare the effective area of the cylinder, the effective volume of the cylinder,the leakage coefficient, respectively.βeis hydraulic bulk modulus,mis the mass of moving parts,Blis load damping coefficient,klis the load elastic coefficient, andαis the effective area ratio of the rod cavity to the rodless cavity.

As shown in Fig.2, the open-loop transfer function of the force control system can be expressed as

(1)

Eq.(1) shows that the electro-hydraulic force control system doesn’t only depend on the characteristics of valve drivers, but also depend on the load stiffness and other load characteristics. Then it can be simplified as

(2)

whereωmis the inherent mechanical frequency,ωris the turning frequency,ω0is the natural frequency of the hydraulic spring and the mechanical spring,ξmis the mechanical damping ratio,ξ0is the overall damping ratio of the hydraulics and mechanics,Kv=KaKsvKqA/Kceis the system whole open loop gain.

1.2.2Open-loop frequency characteristics of the system

At this time, a simulation model can be established to get the system frequency response characteristics in Simulink whenKv=30，ωm=90 rad/s，ω0=350 rad/s，ωr=1 rad/s，ξm=0.15，ξ0=0.1.

Eq.(2) indicates that this system is a 0-type system with poor stability. And as shown in Fig.3, the amplitude margin of the open-loop system is at a relatively high level yet with the shear frequencyωc=4.37 Hz. According to the three-bands theory in automatic control principles, the biggerωcin the intermediate frequency band, the faster response speed of the servo hydraulic circuit. Because the shear frequency of the force control system is quite small in this paper, the whole dynamic characteristics are not ideal for control needs.

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1.2.3Pressure characteristics of the servo valve

As the open-loop gainKvincludes the pressure gain of servo valveKp=Kq/Kce. The servo valve pressure characteristic curve obtained by ensuring the load flow is zero (i.e., the servo valves A and B are closed) and applying the sinusoidal current under the rated pressure.

Fig.3 Open-loop frequency characteristics of the system

Fig.4 Current-pressure curves of the servo valve

As shown in Fig.4, the pressure gain of the flow-type servo valve is about 60 MPa/mA, and the controllable interval of the open-loop valve control system is about ±2 mA. If the input current exceeds this interval, the output of the load pressure will reach the saturation. However, the rated current of the servo valve used in this experiment is 40 mA, which means that the working range of the servo valve spool is very narrow. Therefore, the design for control gain should be conservative as to keep the system from instability. As a result, the way that improves the system response by a conventional PID feedback controller is restricted for such a dynamic force control system.

2 Controller Design

Through the frequency characteristic analysis in Fig.3, it is difficult to improve the dynamic response characteristics of the system by using the general correction method. Therefore, the load velocity compensation method is adopted to eliminate the influence of the load dynamic and improve the tracking characteristics of the force tracking system[10].

Fig.5 Block diagram of the force control system corrected by velocity compensation

The simplified open-loop transfer function of the system can be obtained as

(3)

whereω1=2(1+α2)βeKce/Vt.

Fig.6 Open-loop frequency characteristic after velocity compensation

As shown in Fig.6, adopting the velocity compensation in this paper, the crossover frequency of the system is expanded from the original 4.37 Hz to 47.7 Hz, and the overall bandwidth of the system has been greatly improved. As long as the frequency of the electro-hydraulic servo valve is large enough, the shear frequency of the system can be increased by increasing the open-loop gain of the system.

Then when the dynamic force control subsystem is taken into account, the extra velocity compensation represents an extra flow that has to be supplied by the valve, and the extra flow is used to overcome the effect of friction and load movement[8]. Considering the influence of the noise from the force sensor, the differential term may cause the system instability, thus the feedback controller is simplified as a PI instead of the classic PID. Therefore, this paper considers to use the PI controller which is based on the principle of structural invariance to get a great control response. The principle of the whole controller is shown in Fig.7.

As shown in Fig.7, Δfrefis the reference force signal, Δfis the feedback signal of the force sensor,efis the error force,uPIis the control signal of the PI controller,uvcis the control signal of the compensation controller, Δxis the load velocity. A compensator is set up according to the velocity compensation principle and the final servo valve control signal Δuis the sum ofuvcanduPI. Then by designing the parameters of the PI controller and the velocity compensator, a desired force control consequence can be obtained.

Fig.7 Principle of the whole force controller

3 Experiment and Results

3.1 Hardware overview

In order to verify the feasibility and effectiveness of this method, a single hydraulic cylinder servo force control system was built.

Fig.8 Experimental platform

As shown in Fig.8, the force sensor is installed at the end of the hydraulic cylinder rod. In order to verify the control effect of this algorithm on the elastic load, a spring (spring stiffness is 22 N/mm) is put into the iron tube and a hard object is placed on the left side of the iron tube. The hydraulic cylinder used in this experiment is designed by the lab independently. It adopts an asymmetric cylinder structure and a built-in high precision resistive displacement sensor. The servo valve adopts the electro-hydraulic servo valve FF101-16. The servo valve control cylinder system is convenient to install. The main parameters and performance indicators are shown in Tab.1.

Tab.1 Main parameters of the servo system

3.2 Experimental results

In order to compare the control effects between this method and the traditional PI method, the response curves are experimentally measured under the given step and sinusoidal signal.

Fig.9 Step signal response for different PI controller parameters

Fig.9 shows that the step response curves with different PI controller parameters. Since there is a dead zone characteristic of the servo valve, the given signal value are set to 1 000 N and the initial value are set to 300 N. If the controller parameters are smaller, the response speed is slow; if the controller parameters are larger, it leads the system into oscillation. Although the final steady-state error can reach a small value in the response curves under the control of PI controller, the response speed of the system has reached its limit. In order to solve this problem, the load velocity compensation algorithm is proposed in this paper to accelerate the response and reduce the overshoot. Since the velocity sensor is not used in the test system, the velocity signal is obtained by differentiating the displacement. Generally, because the signal of the sensor has large noise, the tracking differentiator is used in this paper. By setting suitable parameters, the smoother velocity signal can be obtained by differentiating the displacement signal[12].

The coefficients set in this paper are based on the theoretical value calculated in Section 2, and the compensation effect of different coefficients is analyzed by a large amount of experimental data. Finally, the range of velocity compensation coefficient is obtained.

Fig.10 illustrates the load force curves under different methods, and Fig.11 shows the load velocity obtained by the tracking differentiator. As shown in Fig.10 and Fig.11, since the velocity of the load suddenly increases to nearly 30mm/s at the start of the movement, the response speed with the load velocity compensation is faster than that of the PI controller with the same proportional coefficient and integral coefficient.

Fig.10 Step signal response of velocity compensation

Fig.12 shows the tracking behavior of the given sinusoidal signal when the PI controller is used. The amplitude of the given force is 500 N and the frequency is only 0.25 Hz. It is obvious that the tracking effect of the sinusoidal force signal is poor when the PI control is used. If the gain of the controller is smaller, the large phase lag and amplitude attenuation will be generated. On the contrary, if the gain of the controller is larger, it will produce jitter and other unstable phenomena. These phenomena verify the difficulty of the force servo control system.

Fig.11 Load velocity

Fig.12 Sinusoidal response for PI controller

Fig.13 Sinusoidal response for velocity compensation

As shown in Fig.13, the sinusoidal signals are set with the amplitude of 500 N, frequency of 0.5 Hz and 1.0 Hz respectively. It can be found that the output force tracking deviation with the velocity compensation is smaller than that of the PI controller, and the phase lag is improved obviously both in low frequency and in high frequency. Although the lag is 30° at 1 Hz, the results of the force servo control system basically meet the control requirements.

In order to show that this algorithm can improve the effect of load stiffness on the dynamic response, springs with different stiffness are chosen. In this paper, spring stiffness of 22 N/mm and 38 N/mm are selected to verify the step response.

As shown in Fig.14, the response time of the two kinds of elastic loads is about 0.5 s when the step signal is 1 000 N. With the velocity compensation, it can overcome the influence of the different load stiffness, and finally can improve the response speed of the force tracking system. Fig.15 illustrates the load velocity curves of the different loads. It can be seen that the velocity of the larger stiffness load is smaller. If the PI controller is used, due to the large controller parameters, the overshoot of the step response may be too large. However, when the load velocity compensation is used, the smaller PI controller parameters can be select to reduce the overshoot.

Fig.14 Step response of different elastic loads

Fig.15 Load velocity of different elastic loads

However, this algorithm also has some limitations. When the stiffness of the elastic load is great, because the displacement deformation is very small, the corresponding velocity will be very small, then the velocity compensation will be meaningless.

4 Conclusion

In this paper, a force controller with the velocity compenstation algorithm is designed to improve the tracking accuracy of output force trajectory. Firstly, the mathematical model of the hydraulic and cylinderical force control system is gestablished in the frequency domain, and the system bandwidth is obviously expanded through the proposed controller. Then experimental results demonstrate that the velocity compensation method can improve the tracking performance. Finally, the experiments of different stiffness show that this algorithm can improve the influence of load stiffness for the force control system.