Douglas A. Bristow

A survey of iterative learning control

This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

A High Precision Motion Control System With Application to Microscale Robotic Deposition

Decreasing the minimum feature size of solid free-form (SFF) fabrication techniques requires advancements in both the SFF process and the actuating hardware. Microscale robotic deposition (mu-RD) is an ink-deposition SFF process where recent advances in ink design coupled with a high-precision motion system can lead to the fabrication of parts with microscale-sized features. This paper presents a control algorithm that combines nonlinearity compensation and a learning feedforward approach to achieve high-precision tracking with a standard, off-the-shelf motion system. The off-the-shelf motion system is affected by several nonlinear disturbances that severely inhibit the accuracy of linear models for small motions. Iterative learning control (ILC) is used in an inverse identification procedure to obtain accurate maps of the disturbances. These maps are used in the controller to yield a linear system after nonlinearity cancellation. As a further improvement, ILC is used to increase accuracy in tracking the repetitive portion of specific part trajectories. The combined approach yields extremely low contour tracking errors and is used to fabricate two types of periodic parts demonstrating high aspect ratios and spanning elements. Although high-precision tracking can also be achieved with an expensive, customized system, the off-the-shelf system combined with the control technique presented here provides a more cost-effective solution. The proposed control technique is effective for improving performance of repeatable, but uncertain nonlinear systems

Monotonic Convergence of Iterative Learning Control for Uncertain Systems Using a Time-Varying Filter

Time-varying Q-filtering in iterative learning control (ILC) has demonstrated potential performance benefits over time-invariant Q-filtering. In this paper, LTV Q-filtering of ILC is considered for uncertain systems. Sufficient conditions for stability and the important monotonic convergence property are developed for the uncertain system. A class of LTV Q-filters that has particular benefit for rapid motion trajectories is presented, and monotonic convergence conditions are developed. The developed conditions highlight a relationship that the bandwidth can be increased locally and decreased elsewhere to localize high performance at specific times. These conditions are also iteration-length invariant and allow for significant design freedom after analysis enabling online modification of the LTV Q-filter.

A manufacturing system for microscale robotic deposition

This paper presents initial results in the development of a fabrication system capable of producing prototype parts with feature sizes on both the meso- and micro-scale using a technique known as robocasting. A dual-stage design is proposed, but the work presented here focuses on individual control of the first or coarse stage. This stage suffers from several known position-dependent disturbances, and a technique for identifying and compensating for them through an inverse-mapping is presented. A loop-shaped feedback controller and iterative learning feedforward controller are designed. Experimental results show the controller to be extremely effective in tracking repeated trajectories. In many cases contour error is on the order of the feedback resolution.

Weighting matrix design for robust monotonic convergence in Norm Optimal iterative learning control

In this paper we examine the robustness of norm optimal ILC with quadratic cost criterion for discrete-time, linear time-invariant, single-input single-output systems. A bounded multiplicative uncertainty model is used to describe the uncertain system and a sufficient condition for robust monotonic convergence is developed. We find that, for sufficiently large uncertainty, the performance weighting can not be selected arbitrarily large, and thus overall performance is limited. To maximize available performance, a time-frequency design methodology is presented to shape the weighting matrix based on the initial tracking error. The design is applied to a nanopositioning system and simulation results are presented.

A Numerical Method for Determining Monotonicity and Convergence Rate in Iterative Learning Control

In iterative learning control (ILC), a lifted system representation is often used for design and analysis to determine the convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large N×N matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N2) and is typically limited to short iteration lengths because of computational memory constraints. As an alternative approach, the implicitly restarted Arnoldi/Lanczos method (IRLM) can be used to calculate the ILC convergence rate with calculations of O(N). In this article, we show that the convergence rate calculation using IRLM can be performed using dynamic simulations rather than matrices, thereby eliminating the need for large matrix construction. In addition to faster computation, IRLM enables the calculation of the ILC convergence rate for long iteration lengths. To illustrate generality, this method is presented for multi-input multi-output, linear time-varying discrete-time systems.

Monotonic convergence of iterative learning control for uncertain systems using a time-varying Q-filter

Time-varying Q-filtering in iterative learning control (ILC) has demonstrated potential performance benefits over time-invariant Q-filtering. In this paper, LTV Q-filtering of ILC is considered for uncertain systems. Sufficient conditions for stability and the important monotonic convergence property are developed for the uncertain system. A class of LTV Q-filters that has particular benefit for rapid motion trajectories is presented, and monotonic convergence conditions are developed. The developed conditions highlight a relationship that the bandwidth can be increased locally and decreased elsewhere to localize high performance at specific times. These conditions are also iteration-length invariant and allow for significant design freedom after analysis enabling online modification of the LTV Q-filter.

Combined H ∞ -feedback and eterative learning control design with application to nanopositioning systems

This paper presents a coordinated design framework for precision motion control (PMC) systems. In particular, the focus is on the design of feedback and feedforward controllers operating on systems that repeatedly perform the same tasks. The repetitive nature of the tasks suggests the use of Iterative Learning Control (ILC). However, in addition to the repeatability of the desired trajectory, the class of systems under study examines the effect of non-repeating disturbances and possible reset errors. The rejection of uncertain, but bounded, disturbances suggests the use of H infin design. The non-repeating disturbances and reset errors necessitate coordination of the feedback and feedforward designs. The assumption that the disturbances have a particular frequency distribution affords a frequency domain separation between the two controller degrees of freedom. Experimental results are given on a piezo-driven nanopositioning device demonstrating the benefits to the presented approach.

Optimizing Learning Convergence Speed and Converged Error for Precision Motion Control

This brief paper considers iterative learning control (ILC) for precision motion control (PMC) applications. This work develops a methodology to design a low pass filter, called the Q-filter, that is used to limit the bandwidth of the ILC to prevent the propagation of high frequencies in the learning. A time-varying bandwidth Q-filter is considered because PMC reference trajectories can exhibit rapid changes in acceleration that may require high bandwidth for short periods of time. Time-frequency analysis of the initial error signal is used to generate a shape function for the bandwidth profile. Key parameters of the bandwidth profile are numerically optimized to obtain the best tradeoff in converged error and convergence speed. Simulation and experimental results for a permanent-magnet linear motor are included. Results show that the optimal time-varying Q-filter bandwidth provides faster convergence to lower error than the optimal time-invariant bandwidth.

Iterative learning control of bead morphology in Laser Metal Deposition processes

Laser Metal Deposition (LMD) is a layer-based manufacturing process in which a laser and powdered metal are used to create a molten bead that is then traced along a path to create functional parts. The properties of the structure, including shape and material microstructure, are the result of complex interactions between the laser, the powder, the part substrate and other factors. Thus, a control algorithm is needed to accurately produce the designed part. However, feedback control of the process can create phase lag in the resulting control structure, which in turn can create dimensional instability. Additionally, the LMD process has been shown to change with part height or layer number. Taking these issues into account, a feed-forward, adaptive-type controller that changes with each fabricated layer, should be used. This paper first presents a dynamic model for the LMD process that incorporates the dependency of the process on part height. Then, an optimal Iterative Learning Process Control algorithm is presented to regulate the melt pool morphology of a deposited part using layer number as the iteration axis. A simulation study on the LMD process using the designed process controller shows that it is able to achieve good tracking performance.