Iterative learning control for LTV systems with applications to an industrial robot

Industrial robots are widely used in industry because of their dexterity, the high manipulation speed and the relatively low price. However, the applicability of these robots is limited by the mediocre accuracy resulting from the low bandwidth of standard industrial controllers. Fortunately, the repeatability of industrial robots is often much better than their tracking accuracy, which can be exploited to improve the accuracy by the application of Iterative Learning Control (ILC). ILC is a control technique that reduces the tracking error along a trajectory that is traced repeatedly by the iterative refinement of a feedforward signal. The tracking accuracy of industrial robots can be improved substantially with ILC by reducing the frequency components of the tracking error beyond the low bandwidth of the standard industrial controller. Below this bandwidth the non-linear dynamics of the robot mechanism are linearised by the controller, but at higher frequencies the closed-loop dynamics depend on the configuration of the robot mechanism. These configuration dependent dynamics can be approximated as linear time-varying (LTV) for small deviations from the repetitive large-scale motion. Therefore, two ILC algorithms for systems with LTV dynamics are developed in this thesis. The norm-optimal ILC algorithm iteratively computes the feedforward that minimises a weighted sum of the norm of the error and the growth of the feedforward. The error is predicted from an LTV dynamic model. The computation of the optimal feedforward is formulated as a finite-time optimal control problem and it is shown that this optimisation problem can be solved using an existing, computationally efficient algorithm. The robust ILC algorithm iteratively computes the feedforward that optimises the reduction of the error for an LTV dynamic model with a given uncertainty. A sufficient condition is derived under which the feedforward reduces the error with a specified fraction for the worst case effect of the uncertainty. This condition takes the finite length of the iteration and the LTV dynamics into account. The computation of the optimal feedforward is formulated as a finitetime dynamic game and the check of the convergence condition is formulated as an anti-causal optimal control problem. It is shown that the dynamic game and the optimal control problem can be solved using existing, computationally efficient algorithms. Convergence analysis shows that the proposed ILC algorithms make the error converge to zero with an adjustable convergence rate if the dynamic model is sufficiently accurate. Increasing the convergence rate reduces the allowable model error. A model error that is too large results in divergence of the tracking error. The allowable model error can be increased by using a robustness filter that removes the components of the feedforward to which the dynamic response is not modelled sufficiently accurate. However, the removed components of the feedforward cannot be used to compensate for the error, which typically results in a non-zero error after convergence. The proposed algorithms are suited for systems with LTV dynamics, they are computationally efficient and they are able to reduce the error monotonically with an adjustable convergence rate. This unique combination of properties makes the algorithms suited for improving the tracking accuracy of industrial robots and other systems with LTV dynamics in practice. The performance of the ILC algorithms is tested experimentally by the application to the industrial St¨aubli RX90 robot. The setpoints for the position of the robot are adjusted with ILC to reduce the tracking error at its end-effector, which is measured with an optical sensor. The experimental results show that the proposed ILC algorithms are able to reduce the measured tracking error substantially, especially if an LTV model of the configuration dependent highfrequency dynamics of the robot is used. The reduction of the tracking error is sufficient for the application of the robot to laser welding of complex trajectories at high speed