Dynamics and Control of Smart Structures for Space Applications

Smart materials are one of the key emerging technologies for a variety of space systems ranging in their applications from instrumentation to structural design. The underlying principle of smart materials is that they are materials that can change their properties based on an input, typically a voltage or current. When these materials are incorporated into structures, they create smart structures. This work is concerned with the dynamics and control of three smart structures: a membrane structure with shape memory alloys for control of the membrane surface flatness, a flexible manipulator with a collocated piezoelectric sensor/actuator pair for active vibration control, and a piezoelectric nanopositioner for control of instrumentation. Shape memory alloys are used to control the surface flatness of a prototype membrane structure. As these actuators exhibit a hysteretic nonlinearity, they need their own controller to operate as required. The membrane structures surface flatness is then controlled by the shape memory alloys, and two techniques are developed: genetic algorithm and proportional-integral controllers. This would represent the removal of one of the main obstacles preventing the use of membrane structures in space for high precision applications, such as a C-band synthetic aperture radar antenna. Next, an adaptive positive position feedback law is developed for control of a structure with a collocated piezoelectric sensor/actuator pair, with unknown natural frequencies. This control law is then combined with the input shaping technique for slew maneuvers of a single-link flexible manipulator. As an alternative to the adaptive positive position feedback law, genetic algorithms are investigated as both system identification techniques and as a tool for optimal controller design in vibration suppression. These controllers are all verified through both simulation and experiments. The third area of investigation is on the nonlinear dynamics and control of piezoelectric actuators for nanopositioning applications. A state feedback integral plus double integral synchronization controller is designed to allow the piezoelectrics to form the basis of an ultra-precise 2-D Fabry-Perot interferometer as the gap spacing of the device could be controlled at the nanometer level. Next, an output feedback linear integral control law is examined explicitly for the piezoelectric actuators with its nonlinear behaviour modeled as an input nonlinearity to a linear system. Conditions for asymptotic stability are established and then the analysis is extended to the derivation of an output feedback integral synchronization controller that guarantees global asymptotic stability under input nonlinearities. Experiments are then performed to validate the analysis. In this work, the dynamics and control of these smart structures are addressed in the context of their three applications. The main objective of this work is to develop effective and reliable control strategies for smart structures that broaden their applicability to space systems

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities

Copyright [2001] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper investigates the robust reliable control problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, state time-delay, parameter uncertainties, possible actuator failures and unknown nonlinear disturbances, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback memoryless controllers such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains stochastically exponentially stable in mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the desired robust reliable exponential stability despite possible actuator failures, which are in terms of the solutions to algebraic Riccati inequalities. An illustrative example is exploited to demonstrate the applicability of the proposed design approac

Global stabilization of a Korteweg-de Vries equation with saturating distributed control

This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. Two different types of saturated controls are considered. The well-posedness is proven applying a Banach fixed point theorem, using some estimates of this equation and some properties of the saturation function. The proof of the asymptotic stability of the closed-loop system is separated in two cases: i) when the control acts on all the domain, a Lyapunov function together with a sector condition describing the saturating input is used to conclude on the stability, ii) when the control is localized, we argue by contradiction. Some numerical simulations illustrate the stability of the closed-loop nonlinear partial differential equation. 1. Introduction. In recent decades, a great effort has been made to take into account input saturations in control designs (see e.g [39], [15] or more recently [17]). In most applications, actuators are limited due to some physical constraints and the control input has to be bounded. Neglecting the amplitude actuator limitation can be source of undesirable and catastrophic behaviors for the closed-loop system. The standard method to analyze the stability with such nonlinear controls follows a two steps design. First the design is carried out without taking into account the saturation. In a second step, a nonlinear analysis of the closed-loop system is made when adding the saturation. In this way, we often get local stabilization results. Tackling this particular nonlinearity in the case of finite dimensional systems is already a difficult problem. However, nowadays, numerous techniques are available (see e.g. [39, 41, 37]) and such systems can be analyzed with an appropriate Lyapunov function and a sector condition of the saturation map, as introduced in [39]. In the literature, there are few papers studying this topic in the infinite dimensional case. Among them, we can cite [18], [29], where a wave equation equipped with a saturated distributed actuator is studied, and [12], where a coupled PDE/ODE system modeling a switched power converter with a transmission line is considered. Due to some restrictions on the system, a saturated feedback has to be designed in the latter paper. There exist also some papers using the nonlinear semigroup theory and focusing on abstract systems ([20],[34],[36]). Let us note that in [36], [34] and [20], the study of a priori bounded controller is tackled using abstract nonlinear theory. To be more specific, for bounded ([36],[34]) and unbounded ([34]) control operators, some conditions are derived to deduce, from the asymptotic stability of an infinite-dimensional linear system in abstract form, the asymptotic stability when closing the loop with saturating controller. These articles use the nonlinear semigroup theory (see e.g. [24] or [1]). The Korteweg-de Vries equation (KdV for short)Comment: arXiv admin note: text overlap with arXiv:1609.0144

An Unknown Input Multi-Observer Approach for Estimation, Attack Isolation, and Control of LTI Systems under Actuator Attacks

We address the problem of state estimation, attack isolation, and control for discrete-time Linear Time Invariant (LTI) systems under (potentially unbounded) actuator false data injection attacks. Using a bank of Unknown Input Observers (UIOs), each observer leading to an exponentially stable estimation error in the attack-free case, we propose an estimator that provides exponential estimates of the system state and the attack signals when a sufficiently small number of actuators are attacked. We use these estimates to control the system and isolate actuator attacks. Simulations results are presented to illustrate the performance of the results

Space Structures: Issues in Dynamics and Control

A selective technical overview is presented on the vibration and control of large space structures, the analysis, design, and construction of which will require major technical contributions from the civil/structural, mechanical, and extended engineering communities. The immediacy of the U.S. space station makes the particular emphasis placed on large space structures and their control appropriate. The space station is but one part of the space program, and includes the lunar base, which the space station is to service. This paper attempts to summarize some of the key technical issues and hence provide a starting point for further involvement. The first half of this paper provides an introduction and overview of large space structures and their dynamics; the latter half discusses structural control, including control‐system design and nonlinearities. A crucial aspect of the large space structures problem is that dynamics and control must be considered simultaneously; the problems cannot be addressed individually and coupled as an afterthought