Modeling and Simulation of Valve-controlled Cylinder System Based on Bond Graph

AMESim is a high performance modeling, simulation and dynamic analysis software. Based on the bond graph theory and the principle of hydraulic control, a simulation model of valve-controlled cylinder system is established by using AMESim software. By changing different factors of the hydraulic system and setting different target wave curves, the system effects with different conditions are discussed and the simulation results provide a theoretical guidance for modeling optimization.


Introduction
For the research on dynamic characteristics of the electro-hydraulic servo system, the most frequently used way is the Transfer Function method, but it is used only when applied for linear system.Themajority of the electro-hydraulic servo systems have nonlinear, time-varying characteristics and lack of the accurate mathematical model, the system must do a linearization processing when using traditional transfer function method, it is inconvenient to study the dynamic characteristics.It has some limitations.At the opposite, after a long period of development and improvement (Norman & Mark, 2005), the bond graph theory (Paynter, 1959) based on the Principle of Conservation of Energy is becoming more and more useful on the analysis of the electro-hydraulic servo system (Shin & Sheu, 1991).

The Bond Graph Modeling of Valve-controlled Cylinder
Based on the rules of hydraulic element and the basic concept of power bond graph, combined with the causal relationship of power bond, integrated with the analysis of power flow of the hydraulic system, and taken into full account the typical nonlinear factor of the system (Wang et al., 2007), a bond graph model for the control system is built, as is shown in Figure 1.And a force closed-loop control (Wang, 2004)

Analysis of the Cylinder System and Simulation Results
The output signal is simulated by AMESim on computer when the input signal is a sine wave which its frequency is 10 Hz, the mutation occurs when the hydraulic cylinder reaching the limit position or inverting and the hydraulic cylinder jittered, as is shown in Figure 4.The force mutation might beinduced by position disturbance of the hydraulic motor and the compressibility of the hydraulic oil, and the gap of the joints may also be the causation.Be familiar with the output force, there are obvious peaks for the pressure and the flow rate of the two hydraulic cylinder vessels, as is shown in Figures 5 and 6.In theory, a sudden change of flow quantity may lead to pressure mutation, it is common and complex.When the input signal is a 2 Hz sine wave, the simulation results show that as the hydraulic cylinder reaches the limit position, the ripple is apparently displayed in the force signal and it has big overshoot, as shown in Figure 7.As in the third cycle, the amplitude of peak signal becomes smaller than it has before, but there still exist jitter.
The results indicate that the amplitude of the tracking curve attenuates seriously and the tracking performance changes to be worse.It shows that the system has good performance with the advantages of stable performance and small system error with little jitter, as is shown in Figure 8.The reasons for this are the limit to interior mechanism and dead zone can lead to response curve mutations when the hydraulic cylinder gets to the limit position.In order to improve the system, the control parameter should be adjusted, at the same time system optimization method is established on the basis of the facts.
Figure 8. Force tracking curve of hydraulic cylinder In the hydraulic system, pipes are used to connect the hydraulic source, control mechanism and executor module.The installation location, structure dimension, material, mechanical properties of the pipeline and the physical properties of the brake fluid all have a significant effect on the dynamic performance of the system.
Figure 9 shows the impact of different piping length as the inner diameter is 10 mm and the wall thickness is 2 mm.By comparison with simulation curve, it can be found that the longer the length of the pipeline is, the more seriously the hysteresis will be and the system requires more time to be stable.For the length of the pipe is 4 m, it will lead to a long time lag problem (Liu & Hu, 2008).
Figure 9. Pressure impact curve of different piping length (1.l=0.8 m, 2.l=2 m, 3.l=4 m) Do the same operation as before, Figure 10 shows the impact of different inner diameter of 8 mm, 12 mm and 16 mm as the pipeline is 4 meters long and wall thickness is 2 mm.In the picture, it can be found that the pressure pulsation changes from high to low and then changes to be high.For the pipe of 8 mm, the pipeline is long and thin and the damping of the pipe is large, so the system has a small peak flow.But for the pipe of 16mm, the diameter fits the system and it has an effect on reducing the pressure shock.It can be found that there is a lag for different length of the pipe.And Figure 11 shows the pressure impact of different wall thickness of the pipe.Besides the geometric parameter of the pipe, the pipe of different material also affects the system.For this situation, suppose that the pipe is a flexible pipe (Guo et al., 2006) as the modulus of elasticity (E=10MPa) and the pipe is a rigid pipe (E=2.06×10 5 MPa). Figure 12 is the simulation curve of different material.The figure shows the fluid flows steady as the pipe is a flexible pipe. Figure 12.Pressure impact curve of different piping material (1.E=10 MPa, 2. E=2.06×10 5 MPa)

Conclusion
This paper studies the Valve-controlled Cylinder system and builds a bond graph model.By simulating on computer, it discusses the hydraulic pressure impact and flow pulsation on the system of different factors, such as length, inner diameter, wall thickness and material of the pipeline.Through the analysis of the simulation results, it can be found: (1) The length, inner diameter and wall thickness of the pipe all have effect on the peak of the pressure pulsation.The inner diameter has a significant effect on the system in the three factors, the inner diameter should best fit the system, the wall thickness also have a faint effect on the impact.
(2) In the hydraulic cylinder system, the pipeline of the system will cause significant hysteresis phenomena if it is too long and the other two factors have relatively less effect.So in the case of a certain length of the pipe, control strategy should be considered in order to compensate for the effect of the hysteresis problem.
(3) The pressure impact on system is different for different kinds of material.The flexible pipe can partially absorb the pressure shock in the pipeline so the system has a steady pressure.At the opposite, the impact of the rigid pipe will directly affect the actuator and this will cause pressure shock on the system.
(4) Although the pressure impact is unavoidable, pressure peak can be reduced by optimize the characters of the system, and it also can shorten the stabilization time.
All these results provide a theoretical guidance in model optimizationand have a guiding significance on the process design and improvement.
bond graph model for Valve-controlled Cylinder is built based on basic equation bond graph model.It is shown in Figure 2.

Figure 1 .
Figure 1.Bond graph model for control system 4 simulation model is built, as shown in Figure3.The hydraulic system with electro-hydraulic servo-controlled valve is a typical passive torque servo system(Tanaka et al., 2006), it consists of simulative load system and the carried objects.Thedouble action piston type hydraulic cylinder is executive component of the system and gear rack simulates the steering gear in the model.Rotation angle signals and torque signals of the gear are set as the target signal,the tensionand piston position are measured by sensors as the hydraulic cylinder makes the reciprocating motion.Then they are compared with the setting values.The controller takes the signal asinput and controls flow rate by adjusting the opening size of the servo valveafter the position error is amplified by preamplifier.To optimize system performance with targeted strategy(Yamada & Shimizu, 2007), the paper will study on several important parameters and the influences onthe system.

Figure 3 .
Figure 3. AMESim Model of Valve-controlled Cylinder system

Figure 4 .
Figure 4. Force curve of piston rod

Figure 7 .
Figure 7. Output signal of force curve