Motion stabilization in the presence of friction and backlash: a hybrid system approach

In this paper a hybrid system approach is considered to deal with backlash and friction induced nonlinearities in mechanical control systems. To describe the low velocity frictional behaviour a linearized friction model is proposed. The novelty of this study is that based on the introduced friction model, the stability theorems developed for hybrid systems can directly be applied for controller design of mechanical systems in the presence of Stribeck friction and backlash. During the controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. Simulation measurements were performed to confirm the theoretical results

H∞ control for networked systems with random communication delays

Copyright [2006] 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 note is concerned with a new controller design problem for networked systems with random communication delays. Two kinds of random delays are simultaneously considered: i) from the controller to the plant, and ii) from the sensor to the controller, via a limited bandwidth communication channel. The random delays are modeled as a linear function of the stochastic variable satisfying Bernoulli random binary distribution. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H∞ disturbance attenuation level. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality (LMI) approach. An illustrative example is provided to show the applicability of the proposed method

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

On general systems with network-enhanced complexities

In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties

Establishing a framework for the effective design of resilient supply chains with inherent non-linearities

Purpose of this paper: Previous control theory research on supply chain dynamics has predominantly taken a linear perspective of the real world, whereas nonlinearities have usually been studied via a simulation approach. Nonlinearities can naturally occur in supply chains through the existence of physical and economic constraints, for example, capacity limitations. Since the ability to flex capacity is an important aspect of supply chain resilience, there is a need to rigorously study such nonlinearities. Hence, the purpose of this paper is to propose a framework for the dynamic design of supply chains so that they are resilient to nonlinear system structures

Flight control systems properties and problems, volume 1

This volume contains a delineation of fundamental and mechanization-specific flight control characteristics and problems gleaned from many sources and spanning a period of over two decades. It is organized to present and discuss first some fundamental, generic problems of closed-loop flight control systems involving numerator characteristics (quadratic dipoles, non-minimum phase roots, and intentionally introduced zeros). Next the principal elements of the largely mechanical primary flight control system are reviewed with particular emphasis on the influence of nonlinearities. The characteristics and problems of augmentation (damping, stability, and feel) system mechanizations are then dealt with. The particular idiosyncracies of automatic control actuation and command augmentation schemes are stressed, because they constitute the major interfaces with the primary flight control system and an often highly variable vehicle response

Triangular signal stabilization of nonlinear systems

Many nonlinear systems display self-sustained oscillations which are often undesirable. The stabilizing effect of a high frequency input signal on an oscillating system with one nonlinearity is determined by the characteristics of the nonlinear element in the system, the linear portion of the system and the amplitude of the signal. This investigation has been concerned with the effect of a triangular wave stabilizing signal on these self oscillations. The equivalent gains for several common nonlinearities are derived. The pseudo describing function introduced by Oldenburger and Boyer for sinusoidal stabilization has been extended to the triangular wave case, and it is shown that the pseudo describing function for an odd nonlinearity is real. The pseudo describing function is used in an analysis similar to describing function analysis in order to predict the existence and amplitude of the self oscillation of a triangular wave stabilized, closed loop, nonlinear system. The experimental results are in close agreement with the predictions of the theory --Abstract, page ii

Design of Control Systems with Multiple Backlash Nonlinearities Subject to Inputs Restricted in Magnitude and Slope

This paper develops a computational method for designing a control system that is an interconnection of transfer functions and multiple decoupled backlash nonlinearities where each backlash is modelled as an uncertain band containing multi-valued functions. The design objective is to ensure that the system outputs and the nonlinearity inputs always stay within their prescribed bounds in the presence of all inputs whose magnitude and whose slope are bounded by respective numbers. By using a known technique, each backlash is decomposed as a linear gain and a bounded disturbance. Essentially, the original design problem is replaced by a surrogate design problem that is related to a linear system and thereby can readily be solved by tools available in previous work. Moreover, as a result of using the convolution algebra A, the method developed here is applicable to rational and nonrational transfer functions. To illustrate the usefulness of the method, linear decentralized controllers are designed for a binary distillation column where valve stiction characteristics are taken into account

Flatness-based Deformation Control of an Euler-Bernoulli Beam with In-domain Actuation

This paper addresses the problem of deformation control of an Euler-Bernoulli beam with in-domain actuation. The proposed control scheme consists in first relating the system model described by an inhomogeneous partial differential equation to a target system under a standard boundary control form. Then, a combination of closed-loop feedback control and flatness-based motion planning is used for stabilizing the closed-loop system around reference trajectories. The validity of the proposed method is assessed through well-posedness and stability analysis of the considered systems. The performance of the developed control scheme is demonstrated through numerical simulations of a representative micro-beam.Comment: Preprint of an original research wor