Author details

are subtracted and trimmed to 16 bits to avoid any saturation in further computations. In Figure 7, this signal is labeled as ERR, which serves as the input to the Digital\_PID\_Controller. A circular trajectory is consideredin order to evaluate the controller performance. The center of the circumference with a radius of 50 mm is located at (110.0, 0.0, 70.0) being the Z-coordinate constant through the whole movement, i.e., the entire movement is carried out only in the X-Y plane. First, the interpolation process generates each point along the circumference. This point is used to solve the inverse kinematics. Thus, the resulting angle set is converted to encoder counts and written to the setpoint registers of each servo controller. The sampling time for the genera-

Figure 8 shows the response of each servo controller to the generated path. It can be clearly seen that the first and the third joints closely follow the reference trajectory, whereas the second joint shows a larger variation from the commanded trajectory. This could be due to the influence of nonlinear dynamics of the servo motor or due to the gravity force. However, the Cartesian position of the robot remains very close to the commanded trajectory as can be seen

The endeavor of this chapter is how to deal with theoretical and practical issues regarding the control systems. The readers who are not familiar with motion control systems can get a basic knowledge into reconfigurable logic circuit-based digital design. Generally, it is necessary to combine classroom and practical concepts; for that reasons, these sections are not only aimed for the students or professors but also for professionals who want to obtain a basic under-

tion of each point is chosen as Ts ¼ 0:001 s.

in Figure 9.

80 Field - Programmable Gate Array

5. Conclusions

Figure 9. Cartesian response of the system.

standing about the closed-loop control design.

Miguel Angel Martínez Prado, Juvenal Rodríguez Reséndiz\*, Diana Carolina Toledo Pérez, Carlos Miguel Torres Hernández and Gilberto Herrera Ruiz

\*Address all correspondence to: juvenal@uaq.edu.mx

Facultad de Ingeniería, Universidad Autónoma de Querétaro, Cerro de las Campanas SN, Col. Las Campanas, Querétaro, Qro, México
