Linear Time-invariant Control Systems Research Articles

CAutoCSD-evolutionary search and optimisation enabled computer automated control system design

This paper attempts to set a unified scene for various linear time-invariant (LTI) control system design schemes, by transforming the existing concept of “computer-aided control system design” (CACSD) to novel “computer-automated control system design” (CAutoCSD). The first step towards this goal is to accommodate, under practical constraints, various design objectives that are desirable in both time and frequency domains. Such performance-prioritised unification is aimed at relieving practising engineers from having to select a particular control scheme and from sacrificing certain performance goals resulting from pre-commitment to such schemes. With recent progress in evolutionary computing based extra-numeric, multi-criterion search and optimisation techniques, such unification of LTI control schemes becomes feasible, analytical and practical, and the resultant designs can be creative. The techniques developed are applied to, and illustrated by, three design problems. The unified approach automatically provides an integrator for zero-steady state error in velocity control of a DC motor, and meets multiple objectives in the design of an LTI controller for a non-minimum phase plant and offers a high-performance LTI controller network for a non-linear chemical process.

Eigenstructure Assignment by State-derivative and Partial Output-derivative Feedback for Linear Time-invariant Control Systems

This paper introduces a parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear control time-invariant systems. This problem is always solvable for any controllable systems if the open-loop system matrix is nonsingular. In this work, the parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve the robustness of the closed-loop system. Finally, the eigenstructure assignment problem via partial output-derivative feedback is introduced. Numerical examples are included to show the effectiveness of the proposed approach.

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

Model Following Adaptive Control of Multirate Sampling Systems

This paper deals with model following adaptive control of linear time-invariant systems with two sampling rates : a slower one for the output and a faster one for the input. It is known that intersample ripples often arise in the outputs of the closed-loop multirate sampling systems although multirate control has interesting advantages. In this paper, a ripple-suppressed multirate model following control scheme is presented. A state observer is designed at the output sampling instants and a filter is constructed at the input sampling instants in order to estimate the output at the intersample instants of the outputs. Next, an adaptive version of the algorithm for systems with unknown parameters is shown. Experimental results applied to a position servo system with a supersonic sensor are given to indicate the effectiveness.

Transient response control via characteristic ratio assignment

This note develops an approach to directly control the transient response of linear time-invariant control systems. We begin by considering all-pole transfer functions of order n for which we introduce a set of parameters /spl alpha//sub i/, i=1,...n called the characteristic ratios. We also introduce a generalized time constant /spl tau/. We prove that /spl alpha//sub 1/ and /spl tau/ can be used to characterize the system overshoot to a step input and the speed of response, respectively. By independently adjusting /spl alpha//sub 1/ and /spl tau/ in all-pole systems, arbitrarily small or no overshoot as well as arbitrarily fast speed of response can be achieved. These formulas are used to develop a procedure to design feedback controllers with feedforward or two parameter output feedback type for achieving time response specifications. For a minimum phase plant we show that arbitrary transient response specifications, namely one with independently specified overshoot and specified rise time or speed of response can be exactly attained.

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.

Behavior analysis for approaching the desired trajectory in every trial of learning control

AbstractMuch research has been carried out on learning control in which the desired trajectory is completed during repetition of the same operation. Many application classes from linear systems to certain classes of nonlinear systems have been investigated, along with the conditions of their learning stability. However, there seems to be no discussion of the manner of approach of the real trajectory to the desired trajectory in each trial. The reason for investigating this behavior in each trial is that the approach to the desired trajectory may be limited to certain directions, depending on the procedure to which the learning control is applied. In general, as a first step to considering the problem of learning control of the approach of a system with multiple degrees of freedom from a restricted region to the desired target in each trial, a linear time‐invariant learning control system with one input and one output is characterized. In this system, the real trajectory approaches the desired trajectory, given as a function of time, from one of the regions sandwiching the desired target. The obtained results are confirmed by simulation. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 61–71, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10021

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.

Pole placement preconditioning

The partial pole placement problem has received considerable attention in Control Theory, where it is applied to stabilize time-invariant linear control systems. This paper discusses application of the partial pole placement problem to the construction of preconditioners for linear systems of equations. Numerical examples show that these preconditioners can improve the rate of convergence of the restarted GMRES methods significantly.

330 初期状態の不確かさを考慮した H_∞DIA 制御の磁気軸受への応用

This paper deals with an application of H_∝DIA control attenuating initial-state uncertainties to the Magnetic Bearing. An H_∝ control problem, which treats a mixed Disturbance and an Initial-state uncertainty Attenuation (DIA) control for linear time-invariant systems in the infinite-horizon case, is examined. The mixed DIA problem supplies H_∝ controls with good transients and assures H_∝ controls of robustness against initial-state uncertainty. We derive a mathematical model of the magnetic bearing which has complicated rotor dynamics and nonlinear magnetic property. Then we apply this proposed H_∝DIA control for the magnetic bearing, and evaluate its property with the H_∝DIA control for MIMO systems via simulations.

Discrete Sliding‐Mode Control of Mimo Linear Systems

ABSTRACTThis paper introduces a discrete sliding‐mode control for linear time‐invariant systems in the presence of matched uncertainties. The switching surface is constructed by applying the pole‐assignment method applying to the overall system, not the system in the sliding mode. Importantly, the control algorithm is derived to handle the rate of convergence to the sliding mode and to prevent the control law from encountering any unreasonably large variations. As for the system stability, it can be found that the system is stabilized and finally restricted to a known region. A numerical example is also included to demonstrate all the features of the developed discrete sliding‐mode control.

RIPPLE-SUPPRESSED MULTIRATE ADAPTIVE CONTROL

This paper deals with adaptive control of linear time-invariant systems with unknown parameters and with two sampling rates: a slower one for the output and a faster one for the input. It is known that intersample ripples often arise in the outputs of the closed-loop multirate systems although multirate control has interesting advantages. In this paper, a ripple-suppressed multirate adaptive control scheme is proposed. A simulation example is given to show the effectiveness of the presented algorithm.

Stable controller synthesis for linear time-invariant systems

This paper is concerned with the problem of suboptimal stable mixed H 2 / H X control for linear time-invariant systems. The designed controller with the same order as that of the considered system is required to satisfy a prescribed H X performance bound or a prescribed degree of stability. By reducing the stable controller synthesis problem to a multiobjective state feedback control problem for two different state models, sufficient conditions for the solvability of the considered problem are given in terms of solutions to algebraic Riccati equations and matrix inequalities. An LMI-based iterative algorithm is developed to solve the stable controller synthesis problem. The proposed algorithm is shown to be convergent. Examples are given to illustrate the proposed methods.

On the finite Fourier transforms of functions with infinite discontinuities

The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time‐invariant singular control systems, based on the causal relationship between Jordan′s theorem from the theory of Fourier series and Laurent′s theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

POLYNOMIAL CONTROLLABILITY IN LINEAR TIME-INVARIANT SYSTEMS: SOME FURTHER RESULTS AND APPLICATIONS TO OPTIMAL CONTROL

Previous studies have shown that a controllable linear system can be driven from a given initial condition to a desired target by means of a polynomial input function whose coefficients are obtained simply by solving a set of linear algebraic equations. This paper shows how the application of the concept of polynomial controllability is useful for solving a suboptimal control problem. In particular we present a simple procedure for searching for a control function that minimizes a quadratic performance measure while the system is transferring between specified end-points. The approach is implemented for both state-space and singular linear time-invariant controllable systems.

Designing Automatic Control Systems with Desired Parametric Reliability

The central topic of this paper is the parametric reliability of time invariant linear control systems. First we define a mathematical model for a system from point of view of parametric reliability. Further the parametric reliability is defined and evaluated with thepurpose to use it in the improving the design of the systems. Finally an example of calculation of parametric reliability of a second order system is presented.

Analysis of stability robustness for linear time invariant singular control systems

Singular systems are those the dynamics of which is governed by a mixture Of algebraic and differential equations. In that sense the algebraic equations represent the constraints to the solution of the differential part. These systems are also known as descriptor, semi-state and generalized systems. They appear as a linear approximation of systems models, or linear system models in many applications such as electrical networks, aircraft dynamics, neutral delay systems, large-scale systems, interconnected systems economics, optimization problems, feedback systems, robotics, etc. The basic dynamic analysis in time domain is devoted to the question of stability in the sense of Lyapunov as well as in the sense of finite time stability. Besides that, it is of particular interest to maintain the systems characteristics under the action of undesirable perturbations. This question is in the connection with the problems treated well by the modern concept of stability robustness within the area of control engineering.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H

An LMI-Based Algorithm for Designing Suboptimal Static $\cal H_2/\cal H_\infty$ Output Feedback Controllers

We consider the problem of designing a suboptimal ${\cal H}_2/{\cal H}_{\infty}$ feedback control law for a linear time-invariant control system when a complete set of state variables is not available. This problem can be necessarily restated as a nonconvex optimization problem with a bilinear, multiobjective functional under suitably chosen linear matrix inequality (LMI) constraints. To solve such a problem, we propose an LMI-based procedure which is a sequential linearization programming approach. The properties and the convergence of the algorithm are discussed in detail. Finally, several numerical examples for static ${\cal H}_2/{\cal H}_{\infty}$ output feedback problems demonstrate the applicability of the considered algorithm and also verify the theoretical results numerically.

Quantized feedback stabilization of linear systems

This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear time-invariant feedback, this approach yields global asymptotic stability.