Iterative Learning Control design for uncertain and time-windowed systems

Iterative Learning Control (ILC) is a control strategy capable of dramatically increasing the performance of systems that perform batch repetitive tasks. This performance improvement is achieved by iteratively updating the command signal, using measured error data from previous trials, i.e., by learning from past experience. This thesis deals with ILC for time-windowed and uncertain systems. With the term "time-windowed systems", we mean systems in which actuation and measurement time intervals differ. With "uncertain systems", we refer to systems whose behavior is represented by incomplete or inaccurate models. To study the ILC design issues for time-windowed systems, we consider the task of residual vibration suppression in point-to-point motion problems. In this application, time windows are used to modify the original system to comply with the task. With the properties of the time-windowed system resulting in nonconverging behavior of the original ILC controlled system, we introduce a novel ILC design framework in which convergence can be achieved. Additionally, this framework reveals new design freedom in ILC for point-to-point motion problems, which is unknown in "standard" ILC. Theoretical results concerning the problem formulation and control design for these systems are supported by experimental results on a SISO and MIMO flexible structure. The analysis and design results of ILC for time-windowed systems are subsequently extended to the whole class of linear systems whose input and output are filtered with basis functions (which include time windows). Analysis and design theory of ILC for this class of systems reveals how different ILC objectives can be reached by design of separate parts of the ILC controller. Our research on ILC for uncertain systems is divided into two parts. In the first part, we formulate an approach to analyze the robustness properties of existing ILC controllers, using well developed µ theory. To exemplify our findings, we analyze the robustness properties of linear quadratic (LQ) norm optimal ILC controllers. Moreover, we show that the approach is applicable to the class of linear trial invariant ILC controlled systems with basis functions. In the second part, we present a finite time interval robust ILC control strategy that is robust against model uncertainty as given by an additive uncertainty model. For that, we exploit H1 control theory, however, modified such that the controller is not restricted to be causal and operates on a finite time interval. Furthermore, we optimize the robust controller so as to optimize performance while remaining robustly monotonically convergent. By means of experiments on a SISO flexible system, we show that this control strategy can indeed outperform LQ norm optimal ILC and causal robust ILC control strategies

Reduced-Order Reference Models for Adaptive Control of Space Structures

In addition to serving as a brief overview of aspects relevant to reduced-order modeling (in particular balanced-state and modal techniques) as applied to structural finite element models, this work produced tools for visualizing the relationship between the modes of a model and the states of its balanced representation. Specifically, error contour and mean error plots were developed that provide a designer with frequency response information absent from a typical analysis of a balanced model via its Hankel singular values. The plots were then used to analyze the controllability and observability aspects of finite element models of an illustrative system from a modal perspective -- this aided in the identification of computational artifacts in the models and helped predict points at which to halt the truncation of balanced states. Balanced reduced-order reference models of the illustrative system were implemented as part of a direct adaptive control algorithm to observe the effectiveness of the models. It was learned that the truncation point selected by observing the mean error plot produced the most satisfactory results overall -- the model closely approximated the dominant modes of the system and eliminated the computational artifacts. The problem of improving the performance of the system was also considered. The truncated balanced model was recast in modal form so that its damping could be increased, and the settling time decreased by about eighty percent

Structural Damage Identification from Limited Measurement Data

The research focused on the development of a new method to identify damaged structural elements from a large flexible space structure on-orbit, using limited measured modal data. Limited measured modal data is loosely defined as measured data containing only a few modal frequencies and less than 10% of the total structural degrees-of-freedom. This effort was decomposed into four specific tasks. The first is the identification of partial modal properties from measured data of the nominal space structure. Second, the finite element model must be adjusted to match the measured nominal partial data. The third task is an analysis of the extent to which structural damage can be localized to individual structural elements using the measured data. In conjunction with this task is the determination of where to best place the limited number of sensors on the structure. Lastly, the identification of structural damage must be performed using the limited measured modal data from a damaged space structure. Identification of the modal parameters was accomplished using the Eigensystem Realization Algorithm, a time domain based method, adopted for use with averaged measured frequency response functions. Model tuning was performed using the Automated Structural Optimization Software package, adapted for model tuning. The method minimizes a cost function based on the mismatch between the measured and analytical eigenstructure. The minimization is solved using the eigenvalue and eigen-vector sensitivities at each iteration step. The determination of prioritized sensor locations and damage localization is performed using the eigenvalue and eigenvector sensitivities

An energy based formalism for state estimation and motion control

This work presents an energy based state estimation formalism for a class of dynamical systems with inaccessible/unknown outputs and systems at which sensor utilization is costly, impractical or measurements can not be taken. The physical interactions among most of the dynamical subsystems represented mathematically in terms of Dirac structures allow power exchange through the power ports of these subsystems. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. The feedback-like information is utilized in realizing state observers for this class of dynamical systems. Necessary and sufficient conditions for observability are studied. In addition, estimation error asymptotic convergence stability of the proposed energy based state variable observer is proved for systems with linear and nonlinear dynamics. Robustness of the asymptotic convergence stability is analyzed over a range of parameter deviations, model uncertainties and unknown initial conditions. The proposed energy based state estimation formalism allows realization of the motion and force control from measurements taken from a single subsystem within the entire dynamical system. This in turn allows measurements to be taken from this single subsystem, whereas the rest of the dynamical system is kept free from measurements. Experiments are conducted on dynamical systems with single input and multiple inaccessible outputs in order to verify the validity of the proposed energy based state estimation and control formalism

Model reduction by moment matching with preservation of global stability for a class of nonlinear models

Model reduction by time-domain moment matching naturally extends to nonlinear models, where the notion of moments has a local nature stemming from the center manifold theorem. In this paper, the notion of moments of nonlinear models is extended to the global case and is, subsequently, utilized for model order reduction of convergent Lur'e-type nonlinear models. This model order reduction approach preserves the Lur'e-type model structure, inherits the frequency-response function interpretation of moment matching, preserves the convergence property, and allows formulating a posteriori error bound. By the grace of the preservation of the convergence property, the reduced-order Lur'e-type model can be reliably used for generalized excitation signals without exhibiting instability issues. In a case study, the reduced-order model accurately matches the moment of the full-order Lur'e-type model and accurately describes the steady-state model response under input variations.</p

Model reduction by moment matching with preservation of global stability for a class of nonlinear models

Model reduction by time-domain moment matching naturally extends to nonlinear models, where the notion of moments has a local nature stemming from the center manifold theorem. In this paper, the notion of moments of nonlinear models is extended to the global case and is, subsequently, utilized for model order reduction of convergent Lur'e-type nonlinear models. This model order reduction approach preserves the Lur'e-type model structure, inherits the frequency-response function interpretation of moment matching, preserves the convergence property, and allows formulating a posteriori error bound. By the grace of the preservation of the convergence property, the reduced-order Lur'e-type model can be reliably used for generalized excitation signals without exhibiting instability issues. In a case study, the reduced-order model accurately matches the moment of the full-order Lur'e-type model and accurately describes the steady-state model response under input variations.</p

Precise tip positioning of a flexible manipulator using resonant control

A single-link flexible manipulator is fabricated to represent a typical flexible robotic arm. This flexible manipulator is modeled as an SIMO system with the motor torque as the input and the hub angle and the tip position as the outputs. The two transfer functions are identified using a frequency-domain system identification method, and the resonant modes are determined. A feedback loop around the hub angle response with a resonant controller is designed to damp the resonant modes. A high-gain integral controller is also implemented to achieve zero steady-state error in the tip position response. Experiments are performed to demonstrate the effectiveness of the proposed control scheme

Mechanical and control-oriented design of a monolithic piezoelectric microgripper using a new topological optimisation method.

International audienceThis paper presents a new method developed for the optimal design of piezoactive compliant micromechanisms. It is based on a flexible building block method, called FlexIn, which uses an evolutionary approach, to optimize a truss-like planar structure made of passive and active building blocks, made of piezoelectric material. An electromechanical approach, based on a mixed finite element formulation, is used to establish the model of the active piezoelectric blocks. From the first design step, in addition to conventional mechanical criteria, innovative control-based metrics can be considered in the optimization procedure to fit the open-loop frequency response of the synthetized mechanisms. In particular, these criteria have been drawn here to optimize modal controllability and observability of the system, which is particularly interesting when considering control of flexible structures. Then, a planar monolithic compliant micro-actuator has been synthetized using FlexIn and prototyped. Finally, simulations and experimental tests of the FlexIn optimally synthetized device demonstrate the interests of the proposed optimization method for the design of micro-actuators, microrobots, and more generally for adaptronic structures