Multivariable norm optimal iterative learning control with auxiliary optimization

The paper describes a substantial extension of Norm Optimal Iterative Learning Control (NOILC) that permits tracking of a class of finite dimensional reference signals whilst simultaneously converging to the solution of a constrained quadratic optimization problem. The theory is presented in a general functional analytical framework using operators between chosen real Hilbert spaces. This is applied to solve problems in continuous time where tracking is only required at selected intermediate points of the time interval but, simultaneously, the solution is required to minimize a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. Applications to the discrete time case, including the case of multi-rate sampling, are also summarized. The algorithms are motivated by practical need and provide a methodology for reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear whilst maintaining the desired tracking accuracy necessary for task completion. Solutions in terms of NOILC methodologies involving both feedforward and feedback components offer the possibilities of greater robustness than purely feedforward actions. Robustness of the feedforward implementation is discussed and the work is illustrated by experimental results from a robotic manipulator

Multivariable Iterative Learning Control Design Procedures: from Decentralized to Centralized, Illustrated on an Industrial Printer

Iterative Learning Control (ILC) enables high control performance through learning from measured data, using only limited model knowledge in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this paper is to develop a range of approaches for multivariable ILC, where specific attention is given to addressing interaction. The proposed methods either address the interaction in the nominal model, or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-off between modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that fits the modeling budget and control requirements. This trade-off is demonstrated in a case study on an industrial flatbed printer

An Innovative MIMO Iterative Learning Control Approach for the Position Control of a Hydraulic Press

To improve the performance of hydraulic press position control and eliminate the need to manually define control signals, this paper proposes a multi-input-multi-output (MIMO) Iterative Learning Control (ILC) algorithm. The MIMO ILC algorithm design is based on the inversion of the known low frequency dynamics of the hydraulic press, whereas the unknown and uncertain high frequency dynamics are discarded due to their low influence in the learning transient. Moreover, for the MIMO ILC convergence condition, a graphical method is proposed, in which the ILC learning filter eigenvalues are analyzed. This method allows studying the stability and convergence rate of the algorithm intuitively. Theoretical analysis and results prove that with the MIMO ILC algorithm the position control is automated and that high precision in the position tracking is gained. A comparison with other model inverse ILC approaches is carried out and it is shown that the proposed MIMO ILC algorithm outperforms the existing algorithms, reducing the number of iterations required to converge while guaranteeing system stability. Furthermore, experimental results in a hydraulic test rig are presented and compared to those obtained with a conventional PI controllerThis work was supported in part by the Department of Development and Infrastructures of the Government of the Basque Country via Industrial Doctorate Program BIKAINTEK under Grant 20-AF-W2-2018-00015

Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc

Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

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