Design Of Linear Control Systems Research Articles

Observer Based Controller Design for Linear Systems with Input Constraints

A systematic design method for observer based linear control of LTI systems with input constraints is introduced. The method allows to optimize the observer parameters with respect to the system's performance while at the same time the compliance with the constraints is guaranteed. To improve the results we further propose a method to design both the controller and the observer simultaneously. Since the presented methods are based on LMI techniques they are computationally very efficient. The proposed methods are demonstrated by means of an example.

L 2 -Gain based controller design for linear systems with distributed delays and rational delay kernels

We present a new controller synthesis algorithm for linear systems with distributed time-delays based on L2-gain optimization. The delay kernel is assumed to be rational, i.e., it can be written as a linear fractional representation. The algorithm expands a recently developed stability condition for this kind of delay systems. The applied Lyapunov-Krasovskii functionals result in a parametric matrix inequality. A solution for this inequality is proposed using the full-block Sprocedure and a convex hull relaxation. The synthesis algorithm uses explicitly the information about the rational delay kernel. At the same time, it is applicable to a large class of delay kernels. We test our design algorithm with a simple academic example and compare it to an analysis conditions from the literature.

Networked H∞ control of linear systems with state quantization

This paper addresses the problem of H ∞ controller design for linear systems over digital communication networks. A new model is proposed to describe both the network conditions and the state quantization of the networked control systems in a unified framework. From this model, a quantized state feedback strategy is developed for global and asymptotical stabilization of the networked control systems. The same H ∞ disturbance attenuation level as that in the case without quantization is achieved. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Feature - Multidimensional systems and signal processing: Good theory for good practice

The subject of multidimensional systems, as originally conceived, is concerned with a mathematical framework for tackling a broad range of paradigms whose analysis or synthesis require the use of functions and polynomials in either several complex or real variables. Its applications, which may range from the processing of spatial and temporal signals of diverse physical origin to the design of linear continuous-discrete multidimensional control systems, are already plentiful. This paper aims to promote interaction between a broad spectrum of scientists and engineers through clear exposition and interpretation of fundamentals, albeit a daunting task, so that complex theoretical results become useful to practitioners in distinct but related disciplines. The expanding arena of theory and applications of the original aims and scopes attest to the importance and vitality of the subject-matter.

Guaranteed cost control of linear systems over networks with state and input quantisations

The guaranteed cost control design for linear systems connected over a common digital communication network is addressed. A new model is proposed that takes into consideration the effect of both the quantisation levels and the network conditions. A control design criterion is derived on the basis of the Lyapunov functional method and the idea of the cone complementary linearisation algorithm. A numerical example is given to show the application of the method proposed.

HIFOO - A MATLAB PACKAGE FOR FIXED-ORDER CONTROLLER DESIGN AND H∞ OPTIMIZATION

H∞ controller design for linear systems is a difficult, nonconvex and typically nonsmooth (nondifferentiable) optimization problem when the order of the controller is fixed to be less than that of the open-loop plant, a typical requirement in e.g. embedded aerospace control systems. In this paper we describe a new MATLAB package called HIFOO, aimed at solving fixed-order stabilization and local optimization problems. It depends on a new hybrid algorithm for nonsmooth, nonconvex optimization based on several techniques, namely quasi-Newton updating, bundling and gradient sampling. The user may request HIFOO to optimize one of several objectives, including H∞ norm, which requires either the Control System Toolbox for MATLAB or, for much better performance, the linorm function in the SLICOT package. No other external package is required, but the quadratic programming code quadprog from either MOSEK or the Optimization Toolbox for MATLAB is recommended. Numerical experiments on benchmark problem instances from the COMPleib database indicate that HIFOO could be an efficient and reliable computer-aided control system design (CACSD) tool, with a potential for realistic industrial applications.

Robust Control Design for a Master-Slave Robotic System Considering Environmental Uncertainties and Communication Delay

In this paper, a linear robust control system design based on μ-synthesis is proposed for impedance shaped 2-DOF robot manipulators in bilateral master-slave robotic system with environmental uncertainties and communication delay. A general condition based on the structured singular value μ for robustness of a bilateral master-slave robotic system is derived. The proposed control methodology can guarantee the robust stability and the robust performance for environmental uncertainty, perturbation of operator dynamics, perturbation of master and slave robot manipulator dynamics and constant communication delay of the master-slave robotic system. Several experimental results show the effectiveness of our proposed approach for various environmental uncertainties and constant communication delay.

Analysis of linear systems in the presence of actuator saturation and -disturbances*1

This paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and L2-disturbances. A simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid. The stability and disturbance tolerance/rejection ability of the closed-loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them. Based on the above mentioned condition, the problem of estimating the largest inner ellipsoid and/or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem. All the constraints are shown to be equivalent to LMIs. In addition, disturbance rejection ability in terms of L2 gain is also determined by the solution of an LMI optimization problem. By viewing the feedback gain as an additional free parameter, the optimization problem can easily be adapted for controller design. Numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems.

Analysis of linear systems in the presence of actuator saturation and [formula omitted]-disturbances

This paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and L 2 -disturbances. A simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid. The stability and disturbance tolerance/rejection ability of the closed-loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them. Based on the above mentioned condition, the problem of estimating the largest inner ellipsoid and/or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem. All the constraints are shown to be equivalent to LMIs. In addition, disturbance rejection ability in terms of L 2 gain is also determined by the solution of an LMI optimization problem. By viewing the feedback gain as an additional free parameter, the optimization problem can easily be adapted for controller design. Numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems.

A program for the design of linear time invariant control systems: CDMCAD

AbstractCoefficient Diagram Method (CDM) is a new method proposed for the analysis and design of linear time‐invariant control systems. The control system design by this method results with satisfactory stability, time response and robustness properties compatible with, and in most cases better than, the ones obtained by the other present design methods. In this study, the design procedure described in the literature for CDM is improved so that a systematic and easy tool with understandable sufficient detail is presented. A visual toolbox, which can be used efficiently both for education and research, is obtained based on the procedure presented by using MATLAB. © 2004 Wiley Periodicals, Inc. Comput Appl Eng Educ 12: 165–174, 2004; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20011

Using Robust Stability Analysis Theorems for Robust Controller Design

We propose a technique that extends the uses of robust stability analysis (RSA) theorems in a particular class over robust controller design of linear systems subjected to various classes of nonlinear time-varying uncertainties. The technique is based on a new approach of forcing some surfaces in n-space to have a certain relative orientation. A numerical example is included to demonstrate its effectiveness.

An Object-Based Software Package for Interactive Control System Design and Analysis

Ch is an embeddable C/C++ interpreter. It was developed to allow software developers to use one language, anywhere and everywhere, for any programming task. Ch supports C99, a latest C standard ratified in 1999, and contains salient features for two and three dimensional plotting and numerical computing for applications in engineering and science. Developed in Ch, Ch Control System Toolkit provides a control class with member functions for object-based interactive modeling, analysis, and design of linear time-invariant control systems. The software package, available for downloading on the web, has been widely used in industry to solve practical engineering problems and in universities for instructional improvement. The design and implementation of Ch Control System Toolkit are described in this paper. Two application examples of control system design and analysis using Ch Control System Toolkit demonstrate its power and simplicity.

On the semi-discretization method for feedback control design of linear systems with time delay

On the semi-discretization method for feedback control design of linear systems with time delay

Quasi-polynomial based design of time delay control systems

The prime objective of the paper is to extend the conventional algebraic control system design from rational to the meromorphic functions. By adopting a Youla-like affine parameterization and by introducing the ring of retarded quasi-polynomial meromorphic functions the algebraic approach is opened to the design of linear time delay control systems. Particularly the issues of parameterized set of stabilizing controllers and their causality and disturbance rejection are the main points addressed in the paper.

Repetitive control design for linear systems with time-varying uncertainties

The design of a repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented. Using a Lyapunov functional for the time-delay systems, a sufficient condition is derived in terms of either an algebraic Ricatti inequality or a linear matrix inequality (LMI), which ensures robust stability of the repetitive control system. Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint of the free parameter.

Design and Implementation of Digital Linear Control Systems on Reconfigurable Hardware

The implementation of large linear control systems requires a high amount of digital signal processing. Here, we show that reconfigurable hardware allows the design of fast yet flexible control systems. After discussing the basic concepts for the design and implementation of digital controllers for mechatronic systems, a new general and automated design flow starting from a system of differential equations to application-specific hardware implementation is presented. The advances of reconfigurable hardware as a target technology for linear controllers is discussed. In a case study, we compare the new hardware approach for implementing linear controllers with a software implementation.

Networked control design for linear systems

In this paper we study a systematic networked control method designed specifically to handle the constraints of the networked realization of a linear time invariant control system. The general structure of the proposed controller requires switching between the open loop and closed loop subsystems of the controller which is dictated by the behaviour of the communication network.

Linear Time-Invariant Milling Models Applicable to Chatter Suppression System Design

Milling models, applicable to chatter suppression system design, are derived by transforming an established nonlinear milling model into linear constant coefficient discrete time models. The derivation initially utilizes either a modified Tustin or zero-order-hold approximation to create a discrete time approximation of the original model. The resulting periodically time varying system, which includes time delays, is then transformed into a system with constants coefficient and no time delays by adding delay states to the system and computing the system's monodromy matrix. The resulting linear models are then compared to the established nonlinear model. The linear models, while of high order, can be used directly to design chatter suppression systems with traditional linear control system design techniques. An example chatter control system is designed using an optimal regulator. The example controller reduces chatter in a milling system with a four tooth cutter in an up-milling configuration.

Perturbation bounds for coupled matrix Riccati equations

Local and non-local perturbation bounds for real continuous-time coupled algebraic matrix Riccati equations are derived using the technique of Lyapunov majorants and fixed point principles. Asymptotic expansions of non-linear non-local bounds are also presented. Equations of this type arise in the H2/H∞ analysis and design of linear control systems.

A pole placement controller for non-linear dynamic plants

In this study a control-oriented model is proposed to represent a wide range of non-linear discrete-time dynamic plants. As a testimony to the efficiency of the model structure for control system design, a pole placement controller is designed for non-linear discrete-time plants. Mathematically the solution of the controller output is converted into resolving a polynomial equation in the current control term u( t), which significantly reduces the difficulties encountered in non-linear control system synthesis and computational complexities. The integrated procedure provides a straightforward methodology to use in linear control system design techniques when designing non-linear control systems. For a demonstration of the effectiveness of the proposed methodology used to deal with practical problems, pole placement controllers are designed for three non-linear plants, including the Hammerstein model, a laboratory-scale liquid level system and a continuous stirred tank reactor. The simulation results are presented with graphical illustrations.