#### Abstract

The stronger impact load will appear in the initial phase when the large electric cylinder is tested in the hardware-in-loop simulation. In this paper, the mathematical model is built based on AMESim, and then the reason of the impact load is investigated through analyzing the changing tendency of parameters in the simulation results. The inhibition methods of impact load are presented according to the structural invariability principle and applied to the actual system. The final experimental result indicates that the impact load is inhibited, which provides a good experimental condition for the electric cylinder and promotes the study of large load simulator.

#### 3. Modeling and Simulation Based on AMESim

The test bed is a synthetic system consisting of mechanism, hydraumatic, measurement and control, which can be divided into position servo system and load simulation servo system. Firstly we, respectively, build mathematic model for the servo system based on AMESim. Then the parameters are set and adjusted to keep consistency between experiment and simulation curve. Finally, we get the mathematic model of the test bed through combining two servo systems. This model will be applied to analyze the reason of the impact load and design controller.

##### 3.1. Modeling and Simulation of the Position Servo System

Position servo system is to control the position of electric cylinder without load. The electric cylinder is composed of servo motor, gear reducer, screw, and piston rod and its transmission model is shown in Figure 3 . Equation (1) shows the mathematic model of the position servo system and the block diagram is shown in Figure 4. The main parameters are shown in Table 1. When the position instruction is 100 mm and the load instruction (Fm) is 0 t, the experiment and simulation response curves are shown in Figure 5. It indicates the correctness of this model. Consider where is the position instruction; is the rotate speed instruction of servo motor, is the input voltage of the armature winding; is the current of the armature winding; is the resistance of the armature winding; is the electromagnetic torque coefficient; is the voltage coefficient; is the electromagnetic torque of the motor shaft; is the output moment of motor; is the output moment of electric cylinder; is the moment of inertia of the motor shaft; is the viscous friction coefficient of the motor shaft; is the output speed of servo motor; is the position response; is the moment of inertia of the drive system; is the viscous friction coefficient of the drive system; is the transmission ratio; is the screw lead; is the mechanical transmission efficiency; is the quality of the piston rod; is the viscous friction coefficient of the piston rod; is the loading force.

##### 3.2. Modeling and Simulation of the Load Simulation Servo System

Load simulation servo system is to control the output force of 100 t hydraulic servo cylinder when the output of the piston rod is in the fixed constraint. The load simulation servo system is composed of oil sources, overflow valve, servo valve, and 100 t hydraulic servo cylinder. The model is shown in Figure 6 which is built through adding hydraulic components in the library [20, 21]. When the load instruction is 30 t, the experiment and simulation response curves are shown in Figure 7. The result indicates that the load response is particularly fast and stable.

##### 3.3. Modeling and Simulation of the Load Simulator

Figure 8 shows the model of the load simulator through combining position servo system with load simulation system. Figure 9 shows the load responses curves when the position instruction is set to 100 mm and load instruction is set to 30 t. The result indicates that the model can reflect real system.

#### 4. Reason of the Impact Load

Figure 10 is the schematic diagram of the load simulator. The control current of the servo valve is ±40 mA. When the 30 t electric cylinder extends its piston rod along the movement direction and 100 t hydraulic servo cylinder provides 30 t load, the output of control current in the servo controller is shown in Figure 11. The control current is −40 mA in the initial stages of loading and servo valve core moves left in order to provide 30 t load. P gets connected to A and B gets connected to T at this moment. The pressure of 100 t servo cylinder’s rodless cavity is raised. Since 30 t electric cylinder extends its piston rod along the movement direction, the piston of 100 t servo cylinder is forced to move left. The oil of A cannot be discharged by P, which makes the pressure of the rodless cavity rise in 100 t servo cylinder. The rod cavity will lead to negative pressure as B cannot suck oil by T. Therefore, the differential pressure between rodless cavity and rod cavity is expanding rapidly and the 40 t impact load appears in the initial stage. Then, the control current becomes positive value and servo valve core moves right to make P get connected to B and A get connected to T. The pressure of rodless cavity is kept by differential pressure between A and T, which can provide 30 t load. The instant rise and fall of control current will also produce impact load in the process of experiment because the servo valve works in the high pressure and large flow. Therefore, the changing rate of control current should not be too high.

#### 5. Inhibition Methods of Impact Load

The impact load can seriously destroy the dynamic loading precision and even may damage the mechanical structure of electric cylinder, so we must adopt methods to suppress it. This paper presents some simple control algorithms based on structure invariance principle which is not only easily translated into computer language to be applied in the high precision real-time control system,but also can suppress the impact load.

##### 5.2. Feedforward Compensation Based on Speed

The loading force is disturbed when 30 t electric cylinder starts to move. The feedforward compensation based on speed can improve dynamic tracking ability and restrain interference [22, 23]. The speed of 30 t electric cylinder multiplying by a scale factor will be a part of the control current of the servo valve. The new model of the load simulator is shown in Figure 15. When we apply these two methods into control program of the real system, the load response in the experiment is shown in Figure 16. It can be seen that when 100 t servo cylinder and 30 t electric cylinder start to be controlled, a small impact load still exists. Therefore, we adopt a control method of incremental PID control algorithm.

##### 5.3. Incremental PID Control Algorithm

The instant rise and fall of control current will also produce impact load in the process of experiment because the servo valve responds fast and works in the environment of high pressure and large flow. Therefore, the rate of control current should not be too high. The output of the incremental PID is which can be achieved by the following: where , , and are parameters of the PID algorithm, is the difference between expected and sampling value, and is the control period.

In order to improve the anti-interference ability of the system, we should not keep zero.   is bigger and , are both zero in the first control cycle and is very small, which makes the value of very big. Therefore, we should make in the first control cycle and utilize adaptable value in the other control cycles.

When we adopt the above control methods, the load response of the load simulator in the experiment is shown in Figure 17. It can be seen from Figures 2 and 17 that the impact load is suppressed in the process of dynamic loading.

#### 6. Conclusion

The impact load of the large load simulator in the initial stage is caused by the contradiction in the direction of movement between servo valve and 100 t servo cylinder. The experiment result indicates that the combined application of delay control, feedforward compensation based on speed, and incremental PID control algorithm based on structural invariability principle not only improves the load environment, but also suppresses the impact load, which is favorable for the application and generalization of the large load simulator.

#### Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.