Positive trigonometric polynomials for strong stability of difference equations

We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial, assessing strong stability amounts to deciding positive definiteness of a multivariate trigonometric polynomial matrix. This latter problem is addressed with a converging hierarchy of linear matrix inequalities (LMIs). Numerical experiments indicate that certificates of strong stability can be obtained at a reasonable computational cost for state dimension and number of delays not exceeding 4 or 5

Positive trigonometric polynomials for strong stability of difference equations

Egalement paru dans: Automatica, Vol 48, n°9, pp. 2207-2212, Sept 2012.International audienceWe follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial, assessing strong stability amounts to deciding positive definiteness of a multivariate trigonometric polynomial matrix. This latter problem is addressed with a converging hierarchy of linear matrix inequalities (LMIs). Numerical experiments indicate that certificates of strong stability can be obtained at a reasonable computational cost for state dimension and number of delays not exceeding 4 or 5

Spectral design of output feedback controllers for systems pre-compensated by input shapers

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The primary objective is to investigate the applicability of spectral methods for designing feedback controllers for a closed loop system with an input shaper with time delays. The shaper is included in the feedback loop in order to pre-compensate low-damped oscillatory modes of a flexible subsystem. However, after inserting a shaper into the feedback loop, the closed loop dynamics becomes infinite dimensional. A robust controller design then requires guaranteeing that all the infinitely many poles of the closed loop system will safely be located in the left half of the complex plane. Besides, the closed loop dynamics need to be sufficiently fast in order to take over and keep filtering properties of the input shaper. For the spectral design of the controller, the recently developed spectral abscissa minimization approach for interconnected time delay systems is applied. The presented methods are tested on a case study simulation example, which is a multi-degree of freedom mechanical system.status: publishe

A comparison of shaper-based and shaper-free architectures for feedforward compensation of flexible modes

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A method to determine heating power and heat up time for intermittent heating of churches

Intermittent heating, common in churches, requires higher heating power than steady state heating. With respect to energy use and preservation aspects, the heat up time should be short. Systems for intermittent heating are often designed using rule of thumb estimates or inadequate steady state calculations. This paper presents a method to relate heating power and heat up time for a specific building where thermal characteristics of a building are determined using a step response test

Distributed delay input shaper design by optimizing smooth kernel functions

© 2017 The Franklin Institute The aim of this paper is the development of a general class of input shapers with distributed time delay which leads to retarded spectral properties. The design of the shaper is formulated as a multi-objective optimization problem, where response time and robustness, expressed in terms of residual vibrations, are the main objectives. As a part of the optimization formulation, common requirements for input shapers such as non-decreasing step response and unity steady state gain are considered in the design. Moreover, additional optional requirements, such as smoothness of a step response, jerk and even jounce limits can be added to optimization procedure. The resulting problem can be solved using convex optimization techniques. Several illustrative examples are presented in comparison with classical input shaping techniques. Finally, implementation aspects are discussed. The paper is accompanied by an implementation in MATLAB, including a user-friendly interface for the interactive shaper design.status: publishe

A comparison of shaper-based and shaper-free architectures for feedforward compensation of flexible modes

status: publishe

Humidity change rate control in intermittently heated historic buildings

Many massive historic buildings such as stone churches are intermittently heated. The predominant heating strategy is to heat the building with as high heating power as possible to achieve a fast and energy efficient heat-up process. However, the fast change rate of temperature induces a high change rate of relative humidity, which can be dangerous for interiors and objects in churches. It has been suggested that the change rate of relative humidity should be limited with respect to conservation. Desorption from the walls has a significant effect on the change rate of relative humidity. Typically, the absolute humidity can increase by 50% when the church is heated. Based on a hygrothermal model that allows for a prediction of both temperature and absolute humidity as function of time, this paper presents a model-based feed-forward control algorithm that calculates the maximum hourly heating power increase allowed for limit the change rate in relative humidity to a pre-defined value. The control algorithm is validated using simulations