The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for perfect signal reconstructability, careful consideration is required when identifying parametric and nonparametric models. In this letter, a comprehensive statistical analysis of estimators under slow sampling is performed. Necessary and sufficient conditions are obtained for unbiased estimates of the frequency response function beyond the Nyquist frequency, and it is shown that consistency of parametric estimators can be achieved even if input frequencies overlap after aliasing. Monte Carlo simulations confirm the theoretical properties.

Iterative learning control (ILC) techniques are capable of improving the tracking performance of control systems that repeatedly perform similar tasks by utilizing data from past iterations. The aim of this paper is to achieve both the task flexibility enabled by ILC with basis functions and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.

Iterative learning control (ILC) yields substantial performance improvement for repetitive motion tasks. While task-flexibility for non-repetitive motion tasks can be achieved with the use of basis functions, this typically comes with a trade-off in performance or design parameters. This study aims to achieve both task-flexibility and high performance with a single time-domain optimization framework. By defining a criterion combining the cost for performance and task-flexibility, an optimal feedforward with task-flexibility of basis function ILC and high performance surpassing standard norm-optimal ILC is obtained. Numerical validation on a two-mass motion system confirm the capabilities of the developed framework.

Iterative learning control yields accurate feedforward input by utilizing experimental data from past iterations. However, typically there exists a tradeoff between task flexibility and tracking performance. This study aims to develop a learning framework with both high task-flexibility and high tracking-performance by integrating rational basis functions with frequency-domain learning. Rational basis functions enable the learning of system zeros, enhancing system representation compared to polynomial basis functions. The developed framework is validated through a two-mass motion system, showing high tracking-performance with high task-flexibility, enhanced by the rational basis functions effectively learning the flexible dynamics.

The requirements for high accuracy and throughput in next-generation data-intensive motion systems lead to situations where position-dependent feedforward is essential. This article aims to develop a framework for interpretable and task-flexible position-dependent feedforward through systematic learning with automated experimental design. A data-driven and interpretable framework is developed by employing Gaussian process (GP) regression, enabling accurate modeling of feedforward parameters as a continuous function of position. The data is efficiently collected and illustrated through an iterative learning control (ILC) algorithm. Moreover, a framework for experimental design in the sense of automatically determining the training positions is presented by exploiting the uncertainty estimates of the GP and the specified first-principles knowledge. Two relevant case studies show the importance and significant performance improvement of the approach for position-dependent snap feedforward for a simplified 1-D wafer stage simulation and experimental application to position-dependent motor force constant compensation in an industrial wirebonder.

Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this letter is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and actuation above the Nyquist frequency of the sensor, such as vision-in-the-loop systems. The developed method assumes smoothness of the frequency response function, which allows to disentangle aliased components through local models over multiple frequency bands. The method identifies fast-sampled models of slowly-sampled systems accurately in a single identification experiment. Finally, an experimental example demonstrates the effectiveness of the technique.

Sampled-data control requires both on-sample and intersample performance in high-precision mechatronic systems. The aim is to design a discrete-time linearly parameterized feedforward controller to improve both on-sample and intersample performance in a multi-modal motion system. The continuous-time performance is considered as state compatibility by a multirate zero-order-hold differentiator. The developed approach enables the linearly parameterized feedforward controller design for sampled-data systems with physically intuitive tuning parameters. The performance improvement is validated by comparing the developed approach with a conventional approach using a backward differentiator for a multi-modal motion system.

Machine learning techniques, including Gaussian processes (GPs), are expected to play a significant role in meeting speed, accuracy, and functionality requirements in future data-intensive mechatronic systems. This paper aims to reveal the potential of GPs for motion control applications. Successful applications of GPs for feedforward and learning control, including the identification and learning for noncausal feedforward, position-dependent snap feedforward, nonlinear feedforward, and GP-based spatial repetitive control, are outlined. Experimental results on various systems, including a desktop printer, wirebonder, and substrate carrier, confirmed that data-based learning using GPs can significantly improve the accuracy of mechatronic systems.