Output feedback control of linear multipass processes

An error actuated output feedback controller for a sub-class of linear multipass processes designated as 'differential unit memory' is defined. Further, the design of this controller for closed-loop stability is considered. In particular, a recently developed computationally feasible stability tesits used to present some preliminary work on this problem

Modelling the influence of non-minimum phase zeros on gradient based linear iterative learning control

The subject of this paper is modeling of the influence of non-minimum phase plant dynamics on the performance possible from gradient based norm optimal iterative learning control algorithms. It is established that performance in the presence of right-half plane plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L2 error norm followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over finite trials is apparent convergence to a non-zero error. The source of this slow convergence is identified and a model of this behavior as a (set of) linear constraint(s) is developed. This is shown to provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm are obtained for single-input single-output systems with several right half plane zeroes using Lagrangian techniques and experimental results are given that confirm the practical validity of the analysis

Iterative learning control for constrained linear systems

This paper considers iterative learning control for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms can achieve perfect tracking. The two algorithms differ however in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a "best approximation". The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the e®ectiveness of the proposed methods

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

Stability Assessment Using Contraction Conditions For Unknown Multivariable Feedback Systems

The purpose of this paper is to illustrate, using specific examples, the stability region, the contraction condition region and the monotonic condition region in parameter plane. It is our intention to show that contraction condition region is a substantial part of the complete stability region for high gain (continuous) or for fast sampling (discrete)systems and hence gives considerable insight into the system robustness

Discrete First-Order Models for Multi-variable Process Control

The concept of an mxm invertible continuous first order lag is extended to define an equivalent formulation for multi-variable sampled-data-systems. A large class of proportional plus summation output feedback controllers is constructed. Each controller guarantees the stability of the closed-loop interaction effects if the sampling rate is high enough. The results are extended to show that a multi-variable discrete first order lag, in many cases of practical interest, a quite adequate approximation for the purpose of controller design provided that the plant is minimum-phase and satisfies a contraction-mapping condition. In particular, any discrete model of a minimum phase, continuous, linear, time-invariant plant with CB nonsingular will satisfy the contraction condition provided the sampling rate is high enough

The Numerical Range: A Tool for Robust Stability Studies/

The use of numerical range concepts for assessing robust stability of multi-variable feedback systems is investigated. The characterization of perturbations by their numerical range allows a more detailed description of their gains and phases and allows a robust stability theorem similar in structure to that of Postlethwaite et al with the possibility of arbitrary large perturbations

Modal Decoupling and Dyadic Transfer Function Matrices

Previous results on the feedback control analysis of dyadic transfer function matrices are related to the general concept of modal decoupling and the techniques extended to cope with the case of unbounded or singular D.C. matrices

The Stability of Linear Multi-Pass Processes

The recent contribution by Edwards to the stability analysis of multi-pass processes using the familiar inverse-Nyquist method is discussed using the techniques of functional analysis. It is noted that the modelling procedure suggested by Edwards neglects the finite pass length nature of the processes and takes no account of the initial conditions for each pass. A natural and physically meaningful definition of multi-pass stability is proposed and characterized by conditions on the system operator. Application of the results to a cogging process and a class of linear, time-variant system indicates that previous results are highly pessimistic. The anomaly is explained in terms of a defined notion of stability along the pass