Iterative learning control: algorithm development and experimental benchmarking

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, known as the trial length. The process is reset prior to the commencement of each execution. The basic idea of ILC is to use information from previously executed trials to update the control input to be applied during the next one. The first experimental facility is a non-minimum phase electro-mechanical system and the other is a gantry robot whose basic task is to pick and place objects on a moving conveyor under synchronization and in a fixed finite time duration that replicates many tasks encountered in the process industries. Novel contributions are made in both the development of new algorithms and, especially, in the analysis of experimental results both of a single algorithm alone and also in the comparison of the relative performance of different algorithms. In the case of non-minimum phase systems, a new algorithm, named Reference Shift ILC (RSILC) is developed that is of a two loop structure. One learning loop addresses the system lag and another tackles the possibility of a large initial plant input commonly encountered when using basic iterative learning control algorithms. After basic algorithm development and simulation studies, experimental results are given to conclude that performance improvement over previously reported algorithms is reasonable. The gantry robot has been previously used to experimentally benchmark a range of simple structure ILC algorithms, such as those based on the ILC versions of the classical proportional plus derivative error actuated controllers, and some state-space based optimal ILC algorithms. Here these results are extended by the first ever detailed experimental study of the performance of stochastic ILC algorithms together with some modifications necessary to their configuration in order to increase performance. The majority of the currently reported ILC algorithms mainly focus on reducing the trial-to-trial error but it is known that this may come at the cost of poor or unacceptable performance along the trial dynamics. Control theory for discrete linear repetitive processes is used to design ILC control laws that enable the control of both trial-to-trial error convergence and along the trial dynamics. These algorithms can be computed using Linear Matrix Inequalities (LMIs) and again the results of experimental implementation on the gantry robot are given. These results are the first ever in this key area and represent a benchmark against which alternatives can be compared. In the concluding chapter, a critical overview of the results presented is given together with areas for both short and medium term further researc

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

Measurements, Models, Systems and Design

531 s.

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Tests certifiés pour la stabilité structurelle de systèmes multidimensionnels

In this paper, we present new computer algebra based methods for testing the structural stability of n-D discrete linear systems (with n >= 2). More precisely, we show that the standard characterization of the structural stability of a multivariate rational transfer function (namely, the denominator of the transfer function does not have solutions in the unit polydisc of \C^n) is equivalent to the fact that a certain system of polynomials does not have real solutions. We then use state-of-the-art computer algebra algorithms to check this last condition, and thus the structural stability of multidimensional systems.Nous présentons dans cet article de nouvelles méthodes, basées sur des techniques de calcul formel, pour tester la stabilité structurelle de systèmes n-D linéaires et discrets (avec n > 2). Plus précisément, nous montrons dans un premier temps que la condition classique de stabilité structurelle d'une fonction de transfert rationnelle multivariée (à savoir que le dénominateur de celle-ci n'a pas de zéros à l'intérieur du polydisque unité de \C^n) est équivalente au fait que des systèmes d'équations polynomiales, obtenus via certaines transformations, n'ont pas de zéros réels. Nous utilisons ensuite des algorithmes de résolutions de systèmes algébriques pour vérifier cette dernière condition et ainsi la stabilité structurelle de systèmes multidimensionnels

NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter estimation

A new control scheme has been presented in this thesis. Based on the NonLinear Geometric Approach, the proposed Active Control System represents a new way to see the reconfigurable controllers for aerospace applications. The presence of the Diagnosis module (providing the estimation of generic signals which, based on the case, can be faults, disturbances or system parameters), mean feature of the depicted Active Control System, is a characteristic shared by three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric Approach (NLGA) has been accurately investigated and than improved to extend its applicability to more complex models. The standard NLGA procedure has been modified to take account of feasible and estimable sets of unknown signals. Furthermore the application of the Singular Perturbations approximation has led to the solution of Detection and Isolation problems in scenarios too complex to be solved by the standard NLGA. Also the estimation process has been improved, where multiple redundant measuremtent are available, by the introduction of a new algorithm, here called "Least Squares - Sliding Mode". It guarantees optimality, in the sense of the least squares, and finite estimation time, in the sense of the sliding mode. The Active Control System concept has been formalized in two controller: a nonlinear backstepping controller and a nonlinear composite controller. Particularly interesting is the integration, in the controller design, of the estimations coming from the Diagnosis module. Stability proofs are provided for both the control schemes. Finally, different applications in aerospace have been provided to show the applicability and the effectiveness of the proposed NLGA-based Active Control System