# Analysis of a Novel Automatic Control Approach for the Free Forging Hammer
## 5 Case Study and Discussion
### Experiments  
Three sets of comparative experiments are described in this section, for which the trajectory references were set as 0.3 m, \(0.06\sin(0.5\uppi\mathrm{t})+0.3\) m, and \(0.08\sin(\uppi\mathrm{t})+0.3\) m, respectively. The first command aimed to illustrate the dynamic performance of the proposed system under a unit step response, the second command was set to evaluate the performance of a normal-level motion trajectory (constant forging process), and the third one tried to verify its performance for a fast motion trajectory (fast forging process). To evaluate the effectiveness of the proposed free forging system, the following three controllers were tested and compared:  
1. TC: This is the traditional controller (TC) without any other adjustment during the control process, in which the position of the main cylinder is adjusted by the given pass or an operating handle;
2. PID: This is the Proportional-Integral-Derivative controller. The key parameters \(k_{p}\), \(k_{i}\), and \(k_{d}\) are tuned by trial and error methods and set as 100, 200, and \(-5\), respectively;  
Figure 14: Experimental platform of 8 MN program-controlled free forging hammer. As shown in Figure 15, the three controllers have different overshoots under the trigger of the step signal, where TC is the largest and Fuzzy-PID is the smallest. Since there is no preprocessing with the steady-state error and response speed in TC, the performance of TC is worse than the other two controllers. By comparing the performance indices of the three controllers, although the \(I_{mean}\) of TC is the smallest, the forging hammer system with TC has a poor anti-interference ability and large fluctuations of up to 9 mm, having a great influence on the machining accuracy. Due to combining the reference signal and the feedback signal, PID possesses a certain robustness for dealing with the interference items and some uncertainties to some extent, thereby reducing the steady-state error and improving the response speed of the hydraulic system. However, PID is worse than Fuzzy-PID in \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indices** & \(I_{mean}\) & \(I_{max}\) & \(I_{sd}\) & \(I_{co}\) \\ \hline TC & 19.79 & 70.81 & 26.74 & 1.52 \\ PID & 11.23 & 38.47 & 12.20 & 1.50 \\ Fuzzy-PID & 9.18 & 16.93 & 8.09 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Indices for the second set of experiments. Figure 17: Experiments of fast-level trajectory motions (Fast Forging). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indices** & \(I_{mean}\) & \(I_{max}\) & \(I_{sd}\) & \(I_{co}\) \\ \hline TC & 7.56 & 87.56 & 32.49 & 1.75 \\ PID & 21.48 & 59.70 & 20.53 & 1.73 \\ Fuzzy-PID & 14.63 & 22.98 & 14.10 & 1.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Indices for the third set of experiments. terms of all indices. Namely, the proposed fuzzy-PID achieves the best control performance. By online self-tuning of the PID parameters according to the deviation between the reference and the real-time measured data, \(I_{mean}\) and \(I_{sd}\) were significantly reduced compared with PID. The mean tracking error and the maximum tracking error was reduced to less than 2.59 and 6.42 mm with less control efforts compared with PID controller, respectively. To further test the dynamic performance and the steady-state performance of the proposed free-forging hammer system, the hammerhead was moved along a sinusoidal trajectory. Figure 16 gives the tracking results of tracking \(0.06\sin(0.5\pi\mathrm{t})+0.3\) with the three controllers compared and their performance indices are presented in Table 4. Compared with Fuzzy-PID, TC and PID produced large overshoots in each stroke, and the hammerhead fluctuated greatly during the downward stroke, leading to a tracking error of up to 70 mm and a low machining accuracy. However, things were significantly improved after adding fuzzy control, and as a result, the maximum overshoot of fuzzy-PID was only 1.6 mm.