A Norm Optimal Approach to Time-Varying ILC With Application to a Multi-Axis Robotic Testbed

Abstract

In this paper, we focus on improving performance and robustness in precision motion control (PMC) of multi-axis systems through the use of iterative learning control (ILC). A norm optimal ILC framework is used to design optimal learning filters based on design objectives. This paper contains two key contributions. The first half of this paper presents the norm optimal framework, including the introduction of an additional degree of design flexibility via time-varying weighting matrices. This addition enables the controller to take trajectory, position-dependent dynamics, and time-varying stochastic disturbances into consideration when designing the optimal learning controller. Explicit guidelines and analysis requirements for weighting matrix design are provided. The second half of this paper seeks to demonstrate the use of these guidelines. Using the design details provided in the paper, norm optimal learning controllers using time-invariant and time-varying weighting matrices are designed for comparison through simulation on a model of a multi-axis robotic testbed.Index Terms-Design methodology, learning control systems, multiple-input-multiple-output (MIMO) systems, time-varying systems.

Robust optimal iterative learning control with model uncertainty

“…W ≈ 0, the updated weights are approximately equal to the given Q and R. In addition, as an effect of the convergence of the robust ILC, i.e. u j+1 → u j as j → ∞, the solution of λ in (18) shows that λ j+1 → +∞. Thus Q j+1 converges to Q , while R j+1 increases eventually to a very large value in the trial domain.…”

“…Even though some works have already discussed the importance of weight matrices in convergence analysis and converged performance of norm-optimal ILC [15], [18], they only consider fixed weights for all trials. Here, we will demonstrate the change of weights trial-by-trial in order to achieve robustness, which also provides more insight into the effects of weights on robustness and convergence speed of norm-optimal ILC with model uncertainty.…”

A Data-Driven Constrained Norm-Optimal Iterative Learning Control Framework for LTI Systems

“…when a perfect model is known. In case of model-plant mismatch, increasing the weight W u on the input effort can guarantee robust monotonic convergence for a given additive uncertainty [9], [14]. This comes down to trading off nominal performance, represented by the asymptotic tracking error, for robustness to system uncertainty.…”

Precision coordination and motion control of multiple systems via iterative learning control

“…In [2,51], a novel ILC control design which enables the control designer to focus on contour tracking was introduced. [2] presented a frequency based combined CCILC and ILC control scheme.…”