# Linear System Identification and Vibration Control of End-Effector for Industrial Robots
## 3 Linear System Identification
### Linear System Identification Experiment  
System identification generally can be divided into off-line identification and on-line identification. In this paper, this system model structure and system order have been determined and the background is the industrial robot, so we used the off-line identification, as shown in Figure 7.  
This paper mainly studied the low-frequency vibration of the cantilever beam so the experimental platform (illustrated as Figure 8) was built according to the cantilever beam model designed in Section 2. By amplifying the voltage by 30 times, the power amplifier excites the vibration of the cantilever structure. The laser displacement sensor gathers the displacement signal from the displacement acquisition point. In the process of the experiment, different excitation signals were used to excite the system vibration and collect the real-time signals. The order of state space identification is assumed to be 4, and the identification results are presented in Table 2. The accuracy of the identification results is represented by the root mean square value (MSE) of the actual output value and the output value of the identification model. In the process of data acquisition, the laser displacement sensor is set in advance to carry out sliding average filtering  
Figure 8: System identification experimental platform. Figure 7: Structure diagram of off-line identification. with a length of 265 to reduce the influence of measurement noise. Because the output signal of a laser displacement sensor is the absolute value of its measured displacement value, it is necessary for the average and the trend of the output signal before identification. The identified system model is set as a discrete state space model. In the above table it can be seen that the difference of the excitation signal and sampling frequency will have a significant impact on the identification results. In the above experiments, the optimal performance (i.e., minimum MSE) of Gaussian white noise, Pseudo-Random Binary Sequence (shorted as PRBS) sequence and chirp sweep signal are 2.9043, 2.6542 and 14.2563, respectively. The experiment should be repeated many times to avoid the interference of external factors. By comparing the output of actual and the identification space while three different kinds of signals excited the structure at different frequencies, the optimal situation under different excitation signals is selected. The time-domain differential value of the system is obtained by subtracting the actual output displacement of the system and the output displacement of the identification space at the corresponding time, as shown in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Excitation Signal** & **Sampling Frequency (Hz)** & **Root Mean Square Error** \\ \hline white Gaussian noise & 1000 & 33.6493 \\  & 500 & 6.2939 \\  & 200 & 2.9043 \\ PRBS sequence & 1000 & 29.2545 \\  & 500 & 15.7613 \\  & 200 & 2.6542 \\
0–100 Hz Chirp Signal & 1000 & 14.2563 \\
0–200 Hz Chirp Signal & 1000 & 30.4611 \\
0–300 Hz Chirp Signal & 1000 & 26.1471 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of different identification system. Figure 9: Displacement difference between actual output and identification space output. Figure 9 shows that the influence of different excitation signals on the system identification can be directly represented by the time-domain differential curve. The experimental results show that in the whole system identification process, the maximum output displacement differences of Gaussian white noise, PRBS excitation signal and 1-100 Hz are 4.86 mm, 4.92 mm and 19.1 mm, respectively. Although the values of Gaussian white noise. PRBS excitation signal are smaller than that of the chirps signal, the identification results of these two have the similar time-varying identification difference deviation. But the curve of 0-100 Hz Chirps is stable around line 0 and the maximum difference is focused on a very short time.