# Ground Simulation Tests in Two-Dimensional Dynamic Acceleration Environment
## 4 Synchronous Loading of 2-D Dynamic AE
### Control of Servo Tracking System for Angular Position of Unit Being Tested  
Because of the elastic deformation of the transmission mechanism, the servo system of the axial angular position of the unit being tested is a very complicated high-order system. The servo motor drives the turntable through the conveyor belt, which negatively affects the dynamic response characteristics of the system. To suppress the interference caused by load changes, measures are required to form fully closed-loop control. In addition, control strategies and system rigidity both needs to be improved.  
Feed-forward control is an open-loop control strategy for a certain disturbance parameter. It can make use of the characteristics of the object to improve the response speed of the system. However, it does not compensate for other disturbances. This problem can be solved by a closed-loop system using a compound control strategy with a combination of feed-forward and feedback control. The compound control strategy can not only reduce the dynamic influence of the disturbance on the controlled parameters by feed-forward control, but also reduce the steady error of the system by feedback control. Many researchers have studied the application of the compound control strategy based on feed-forward compensation in the position servo control system. To compensate for system nonlinearity, [PERSON] et al. [18] applied feed-forward PID tracking controls to the design of an electro-hydraulic system. [PERSON] et al. [19] used a feed-forward PID compound controller to design a vision-based closed-loop laser solid freeform fabrication system.  
As shown in Figure 12, the position compound controller uses a control strategy with speed/acceleration feed-forward compensation and integral separation PID. The speed/acceleration feed-forward compensation makes the controlled signals of the system insensitive to external disturbances and changes in the internal parameters of the system. The speed feed-forward controller can reduce the tracking error caused by damping. The acceleration feed-forward controller can reduce or eliminate the tracking error caused by the system inertia, thus improving the disturbance-rejection performance of the system. The parameters of the feed-forward PID controller includes a proportional coefficient (K\({}_{\text{P}}\)), derivative coefficient (K\({}_{\text{d}}\)), integral coefficient (K\({}_{\text{i}}\)), velocity feed-forward coefficient (K\({}_{\text{v}\text{f}}\)), acceleration feed-forward coefficient (K\({}_{\text{a}\text{f}}\)), and integral separation coefficient K\({}_{\text{l}}\). When the error is less than the set value, K\({}_{\text{l}}\) = 1 and the integral loop nodes take effect; otherwise, K\({}_{\text{l}}\) = 0 and the integral loop nodes do not take effect, the position error is no longer integrated, and the integral saturation is suppressed.  
Consistent with Figure 12, the feed-forward compound PID control rules can be expressed as follows:  
\[\left\{\begin{array}{l}u_{1(t)}=K_{eff}{}^{d\varphi_{(t)}}/{dt}+K_{aff}{}^{d \varphi_{(t)}}/{dt}\\ u_{2(t)}=e_{(t)}+\int K_{\text{l}}K_{\text{l}}\varepsilon_{(t)}d(t)\\ u_{3(t)}=K_{d}{}^{d\varphi_{(t)}}/{dt}\\ u_{(t)}=K_{p}(u_{1(t)}+u_{2(t)}-u_{3(t)})\end{array}\right., \tag{15}\]  
where u\({}_{\text{l}(t)}\) is the feed-forward output of the velocity and acceleration, u\({}_{\text{2}(t)}\) is the output of the position loop, u\({}_{\text{3}(t)}\) is the output of the velocity loop, u\({}_{\text{(t)}}\) is the output of the PID controller, cp\({}_{\text{(t)}}\) is the set position, v\({}_{\text{(t)}}\) is the actual angular speed of the servo motor, and e\({}_{\text{(t)}}\) is the error of the set position from the actual position.