Repetitive movements are very common in industry applications. Among the widely accepted methodologies for repetitive movement problems, the iterative learning control is a very good choice for it requires little prior knowledge of the system. Among a variety of learning control scheme designs, Tang, Cai, and Huang proposed a Fourier series based iterative learning control. The philosophy of this controller is that tracking control problems in the time domain can be treated as regulating problems by transforming the time domain system dynamics into the frequency domain. The controller has proven to be very attractive....[ Read more ]

Repetitive movements are very common in industry applications. Among the widely accepted methodologies for repetitive movement problems, the iterative learning control is a very good choice for it requires little prior knowledge of the system. Among a variety of learning control scheme designs, Tang, Cai, and Huang proposed a Fourier series based iterative learning control. The philosophy of this controller is that tracking control problems in the time domain can be treated as regulating problems by transforming the time domain system dynamics into the frequency domain. The controller has proven to be very attractive.

In this dissertation, we first improved the Fourier series based controller in two aspects. A mapping matrix is introduced to model system input-output relation history. Unlike the controller by Tang, Cai and Huang, the input increment of a group of harmonics can be generated as a whole directly from the matrix and the tracking error in the previous trial. Thus, the coupling effects of the grouped harmonics, which contain non-linearity information, are considered. Trajectory tracking experiments conducted on a belt driven positioning table indicated that our method was more effective. In addition, a learning scheme based on a piecewise segment approximation method has been proposed as a partial solution to the bandwidth limit problem. Unlike the Fourier series that use constant-weight harmonics, piece-wise constant-weight harmonics were employed to approximate a time domain signal in our method. Therefore, our approximation method contains more local information of the higher frequency harmonics. As a result, the effect due to the bandwidth was reduced and the performance of the closed-loop system was improved. We believe that this method can also be extended to a class of systems with low frequency bandwidth.

Second, we extended the application of the Fourier series based learning controller to the minimum-time (MT) control problem. The proposed MT controller consists of a trajectory planner and the iterative learning controller. The trajectory planner handles geometrical constraints and generates a trajectory that is feasible in kinematics. The learning controller learns the planned trajectory so that it satisfies the optimization constraints.