The iterative learning control (ILC) obtains the unknown information from repeated control operations. Meanwhile, the tracking error from previous stages is used as the correction factor for the next control action. Therefore, the ILC controller can make the system tracking error converge to a small region within a limited number of iterations. This study builds a proportional-valve-controlled pneumatic X–Y table system for performing position tracking control experiments. The experiments involve implementing the ILC controllers and comparing the results. The P-type updating law with delay parameters is used for both the x- and y-axes in the repetitive trajectory tracking control. Experimental results demonstrate that the ILC controller can effectively control the system and track the desired circular trajectory at different speeds. The control parameters are varied to investigate their effects on the ILC convergence.
The valve-controlled pneumatic system is a nonlinear system. The linearized models based on complicated procedures are required to apply the classical or modern controller design (McCloy & Martin, 1980; Watton, 1987). Owing to the air compressibility, the pneumatic system is highly nonlinear and temperature sensitive. The system parameters are sensitive to the changes in external load and temperature. Advanced controllers involving complicated computational procedures are frequently required. The modeling and control of a light-weight pneumatic robot system has been studied for the position tracking and end-effector force control (Bobrow & McDonell, 1998). This approach depends completely on the nonlinear dynamic model for the controller design. Meanwhile, the fuzzy and sliding surface control schemes are used for controlling the position of a propositional-valve-controlled pneumatic rodless cylinder (Renn, 2002).
Iterative linear control (ILC) was first proposed by Arimoto, Kawamura, and Miyazaki (1984). The PID-type learning algorithm was proposed to ensure tracking error convergence between the system output and a reference input. Theoretically, under the assumption of the same initial conditions, the tracking error should converge to zero with increasing number of iterations. Different learning control schemes are also provided by Amann, Owen, and Roger (1996), Bien and Xu (1998), Kurek and Zaremba (1993), Moore (1992) and Moore and Xu (2000) for the comparison and improvement of learning speed and control accuracy. The ILC system operates in two dimensions, time and trial number. This complicated two-dimensional (2-D) analysis system has previously been studied by Arimoto et al. (1984), Padieu and Su (1990), and Geng, Lee, Carroll, and Haynes (1991). Some practical implementations of ILC controller have been applied to position control of mechanical systems (Barton, Lewin, & Brown, 2000; Chen & Zeng, 2003).
This study uses a P-type ILC algorithm with time delay parameter to control a pneumatic X–Y table so that it follows the desired circular trajectory. The proportional-valve-controlled pneumatic X–Y table system is established for the position tracking control experiments. The pneumatic cylinders controlled by the proportional valves are sensitive to external loads and essential nonlinear systems. Thus, the constant-gain linear controller, such as PID, cannot track the position reference input accurately. Section 2 discusses the scheme of the P-type ILC controller. Meanwhile, the experimental apparatus used for this research is designed and shown in Section 3. The ILC controllers are implemented in the pneumatic platform to verify the tracking ability of the system given different reference inputs, as shown in Section 4. The experimental results using the traditional PID and ILC controllers are presented to provide a comparison. Finally, the delay time parameter is adjusted to seek to reduce the mean square error of tracking control.
This study investigates the position tracking control of a proportional-valve-controlled pneumatic X–Y table. The experimental platform is built to provide a control study. The PID and the ILC controllers are employed for repetitive trajectory tracking control of the X–Y table. The experimental results show that the traditional PID controller cannot follow the reference trajectory efficiently. Using the ILC controller, the tracking error information from the previous control trial can be used to update the control signal for the current trial to reduce the tracking errors. Through ILC control, the system can follow the repetitive circular reference track following the learning procedure. The delay time parameter d is also discussed here as the parameters of the controller. The parameter can be changed to provide a better learning update. System parameter change can be detected by the learning controller from the increase in tracking errors, which are then reduced by the ILC scheme. The iterative learning control has the advantage of minimal complexity, both in formulation and in computation. Simultaneously, it can maintain repeated trajectory tracking. This characteristic can make ILC scheme attractive to the industry due to its ability of on-line learning in a relatively simple way when compared with other model based methods.
