Tracking control of nonlinear mechanical systems using Fourier series based learning control

This dissertation describes the development and experimental verification of the Fourier series based learning control schemes for improving the tracking performance of nonlinear mechanical systems with modeling uncertainties. The learning control schemes update the system's input signal to reduce the tracking errors by learning from previous experience executing the same operation. They can be applied to systems with modeling uncertainties, since the design of the learning control algorithm does not require full knowledge about the system model. The modern industries and scientific world placed increasingly high accuracy requirements on automatic machines, such as machine tools, robots and coordinate measuring machines, particularly, those in the optoelectronics and semiconductor industries where positioning and tracking accuracy approach the sub-micron level in high-speed operation. Improving tracking performance is critical for mechanical systems since the demands exceeded the capability of the most conventional mechanisms and controllers. It is a challenging problem, especially in the presence of system uncertainties, which downgrade the system performance even make the system unstable. This dissertation uses Fourier series to describe the system model and proposes new hybrid tracking control schemes for systems (linear or nonlinear) with deterministic uncertainties. The control schemes consist of two parts: a time domain feedback controller and a frequency domain iterative learning controller. The former reduces system variability and suppresses the effect of random disturbances and mismatch of initial condition, so improves robustness of the control system. The later generates the optimal feedforward to compensate the deterministic uncertainties and nonlinearities, hence improves the tracking performance and the stability of the closed-loop system as well. The first learning algorithm is based on the online identified I/O mapping matrix in Fourier space. The second learning control algorithm is an integral control of the Fourier coefficients in Fourier space. Our learning control schemes translate the tracking control problem in time domain to the regulation problem in frequency domain. The regulators modify the Fourier coefficients of the feedforward signal in the way such that the Fourier coefficients of the actual output approach to the corresponding Fourier coefficients of the desired output, or the Fourier coefficients of the tracking error converge to zero. Multi-input multi-output systems are decentralized into a group of single-input single-output subsystems and each subsystem is controlled individually using only the local information of the subsystem. The coupling terms from other subsystems are treated as deterministic uncertainty by the local controller and compensated by the feedforward generated by the learning controller. In this way, the system is decentralized, and linearized along the desired trajectory. The Fourier series based learning control schemes can be applied to a large class of systems. To further increase the applicable range, we also propose a nonlinear learning control scheme, which consists of a nonlinear feedback controller using power series with odd power and the corresponding learning algorithm. The Fourier series based leaning control scheme is superior to the conventional time domain learning control scheme, since it can compensate system time-delay and has data compression function. Their effectiveness is experimentally verified on several electric-mechanical systems. Experimental results show the learning control schemes can significantly increase the tracking accuracy of a large class of systems