<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Comparison of different repetitive control architectures: synthesis and comparison. Application to VSI Converters

Repetitive control is one of the most used control approaches to deal with periodic references/disturbances. It owes its properties to the inclusion of an internal model in the controller that corresponds to a periodic signal generator. However, there exist many different ways to include this internal model. This work presents a description of the different schemes by means of which repetitive control can be implemented. A complete analytic analysis and comparison is performed together with controller synthesis guidance. The voltage source inverter controller experimental results are included to illustrative conceptual developmentsPeer ReviewedPostprint (published version

PI output feedback control of differential linear repetitive processes

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass-to-pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws. These are for the sub-class of so-called differential linear repetitive processes which arise in applications areas such as iterative learning control. They show how a form of proportional-integral (PI) control based only on process outputs can be designed to give stability plus performance and disturbance rejection

Learning and Reacting with Inaccurate Prediction: Applications to Autonomous Excavation

Motivated by autonomous excavation, this work investigates solutions to a class of problem where disturbance prediction is critical to overcoming poor performance of a feedback controller, but where the disturbance prediction is intrinsically inaccurate. Poor feedback controller performance is related to a fundamental control problem: there is only a limited amount of disturbance rejection that feedback compensation can provide. It is known, however, that predictive action can improve the disturbance rejection of a control system beyond the limitations of feedback. While prediction is desirable, the problem in excavation is that disturbance predictions are prone to error due to the variability and complexity of soil-tool interaction forces. This work proposes the use of iterative learning control to map the repetitive components of excavation forces into feedforward commands. Although feedforward action shows useful to improve excavation performance, the non-repetitive nature of soil-tool interaction forces is a source of inaccurate predictions. To explicitly address the use of imperfect predictive compensation, a disturbance observer is used to estimate the prediction error. To quantify inaccuracy in prediction, a feedforward model of excavation disturbances is interpreted as a communication channel that transmits corrupted disturbance previews, for which metrics based on the sensitivity function exist. During field trials the proposed method demonstrated the ability to iteratively achieve a desired dig geometry, independent of the initial feasibility of the excavation passes in relation to actuator saturation. Predictive commands adapted to different soil conditions and passes were repeated autonomously until a pre-specified finish quality of the trench was achieved. Evidence of improvement in disturbance rejection is presented as a comparison of sensitivity functions of systems with and without the use of predictive disturbance compensation

Sparse Iterative Learning Control with Application to a Wafer Stage: Achieving Performance, Resource Efficiency, and Task Flexibility

Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using $\ell_1$ norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.Comment: 12 pages, 14 figure

Intelligent and High-Performance Behavior Design of Autonomous Systems via Learning, Optimization and Control

Nowadays, great societal demands have rapidly boosted the development of autonomous systems that densely interact with humans in many application domains, from manufacturing to transportation and from workplaces to daily lives. The shift from isolated working environments to human-dominated space requires autonomous systems to be empowered to handle not only environmental uncertainties such as external vibrations but also interaction uncertainties arising from human behavior which is in nature probabilistic, causal but not strictly rational, internally hierarchical and socially compliant.This dissertation is concerned with the design of intelligent and high-performance behavior of such autonomous systems, leveraging the strength from control, optimization, learning, and cognitive science. The work consists of two parts. In Part I, the problem of high-level hybrid human-machine behavior design is addressed. The goal is to achieve safe, efficient and human-like interaction with people. A framework based on the theory of mind, utility theories and imitation learning is proposed to efficiently represent and learn the complicated behavior of humans. Built upon that, machine behaviors at three different levels - the perceptual level, the reasoning level, and the action level - are designed via imitation learning, optimization, and online adaptation, allowing the system to interpret, reason and behave as human, particularly when a variety of uncertainties exist. Applications to autonomous driving are considered throughout Part I. Part II is concerned with the design of high-performance low-level individual machine behavior in the presence of model uncertainties and external disturbances. Advanced control laws based on adaptation, iterative learning and the internal structures of uncertainties/disturbances are developed to assure that the high-level interactive behaviors can be reliably executed. Applications on robot manipulators and high-precision motion systems are discussed in this part

Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains

This paper develops a fault-tolerant iterative learning control law for a~class of~linear time-delay differential batch processes with actuator faults using the repetitive process setting. Once the dynamics are expressed in this setting, stability analysis and control law design makes use of the generalized Kalman-Yakubovich-Popov (KYP) lemma in the form of the corresponding linear matrix inequalities (LMIs). In particular, sufficient conditions for the existence of a fault-tolerant control law are developed together with design algorithms for the associated matrices. Under the action of this control law the ILC dynamics have a monotonicity property in terms of an error sequence formed from the difference between the supplied reference trajectory and the outputs produced. An extension to robust control against structured time-varying uncertainties is also developed. Finally, a simulation based case study on the model of a~two-stage chemical reactor with delayed recycle is given to demonstrate the feasibility and effectiveness of the new designs

Vibration suppression in multi-body systems by means of disturbance filter design methods

This paper addresses the problem of interaction in mechanical multi-body systems and shows that subsystem interaction can be considerably minimized while increasing performance if an efficient disturbance model is used. In order to illustrate the advantage of the proposed intelligent disturbance filter, two linear model based techniques are considered: IMC and the model based predictive (MPC) approach. As an illustrative example, multivariable mass-spring-damper and quarter car systems are presented. An adaptation mechanism is introduced to account for linear parameter varying LPV conditions. In this paper we show that, even if the IMC control strategy was not designed for MIMO systems, if a proper filter is used, IMC can successfully deal with disturbance rejection in a multivariable system, and the results obtained are comparable with those obtained by a MIMO predictive control approach. The results suggest that both methods perform equally well, with similar numerical complexity and implementation effort