Decoupling and iterative approaches to the control of discrete linear repetitive processes

This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model

LMIs - A fundamental tool in analysis and controller design for discrete linear repetitive processes

Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite durations. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes.published_or_final_versio

A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint

Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties

ased on the proportional-integral-derivative (PID) control structure widely used in engineering applications, a robust indirect-type iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties. An important merit is that the proposed ILC design is independent of the PID tuning that aims primarily to hold robust stability of the closed-loop system, owing to the fact that the ILC updating law is implemented through adjusting the setpoint of the closed-loop PID control structure plus a feedforward control to the plant input from batch to batch. According to the robust H infinity control objective, a robust discrete-time PID tuning algorithm is given in terms of the plant state-space model description to accommodate for time-varying process uncertainties. For the batchwise direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory. Only measured output errors of current and previous cycles are used to implement the proposed ILC scheme for the convenience of practical application. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method

Stabilization of positive switched systems with time-varying delays under asynchronous switching

This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods

Relationships between digital signal processing and control and estimation theory

Bibliography: leaves 83-97.NASA Grant NGL-22-009-124 and NSF Grant GK-41647.Alan S. Willsky

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

Positive L1 observer design for positive Switched systems

Published version of an article in the journal: Circuits, Systems, and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s00034-013-9737-6This paper investigates the problem of L1 observer design for positive switched systems. Firstly, a new kind of positive L1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive L1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the L1 -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Measurements, Models, Systems and Design

531 s.