Design Of Linear Control Systems Research Articles

H∞-control problem for linear systems with multiple time-delays via dynamic output feedback

This paper focuses on the problem of H ∞-control design for linear systems with multiple time-delays, in which the controlled output contains delayed states and disturbance input. The proposed H ∞-control problem for a class of linear systems with time-delays is realized as an H ∞-control problem for an auxiliary linear system free of time-delay. A new explicit design for dynamic output feedback H ∞ controllers is obtained. In addition, a numerical example is presented to illustrate the effectiveness of the proposed approach.

PERTURBATION ANALYSIS OF 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. Equations of this type arise in the robust analysis and design of linear control systems.

Reliable H∞ controller design for linear systems

Reliable H∞ controller design for linear systems

Reliable H∞ controller design for linear systems

This paper is concerned with the reliable design problem for linear systems. A more practical model of sensor and actuator failures than outage is considered. Procedures for designing reliable controllers are presented for the case of sensor failures and actuator failures that can be modeled by a scaling factor and a disturbance. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and H ∞ performance when all control components (sensors and actuators) are operational as well as when some control components experience failures. A numerical example is also given to illustrate the design procedures and their effectiveness.

Reliable LQG control with sensor failures

The paper deals with reliable LQG controller design for linear systems with sensor failures. A model of sensor failures more practical than outage is adopted. Two procedures of designing reliable LQG controllers are presented: stabilising solutions of three coupled Riccati equations; and solutions to one Riccati equation and two linear matrix inequalities. The resulting control systems are guaranteed to be robustly stable and with a known cost bound on the LQG cost against sensor failures. Algorithms are developed to obtain a solution and illustrated via numerical examples.

Proper solutions of polynomial equations

Abstract The linear equation AX + BY = C is studied, where A, B, and C are given polynomial matrices such that A−1 B is a strictly proper rational matrix. All polynomial matrix solution pairs X, Y such that YX−1 is a proper rational matrix are parametrized. The study is motivated by the polo placement techniques in the design of linear control systems.

Sliding mode controller design for linear systems with mismatched uncertainty

Abstract The present paper deals with sliding mode controller design problem. The linear systems with mismatched uncertainties are considered. A sliding mode controller with guaranteed cost typed sliding surfaces is proposed, such that the sliding motion is stable and a guaranteed cost bound is provided. Both the sliding motion and the reaching motion are robust against the mismatched uncertainties.

User friendly CACSD for complex industrial processes

In this paper the concept of an industrial CACSD (computer aided control system design) system is outlined which is geared at making available efficient theoretical control system design methods to the process industry. After discussion of general requirements the focus is set on the ICAC (Industrial Computer Aided Control) toolbox developed for MATLAB/SIMULINK™. This toolbox is aimed at industrial users like process engineers or commissioners who are not necessarily specialists in control system design. The ICAC toolbox provides specific methods for the design of linear and nonlinear single and multivariate control systems composed of industrially available function blocks such as PID controllers and typical nonlinear characteristics. Furthermore it allows simplified optimisation of arbitrary industrial control schemes. The ICAC user interface supports 3 user levels with different degrees of functionality adapted to the user's knowledge.

A bridge between state-space and transfer-function methods

A synthesis of the two major approaches to linear control system design, namely the state-space and the transfer-function ones, can be achieved by use of dynamics assignment, a convenient reference design problem. Students, teachers, and researchers can all benefit from a deeper understanding of the relationships between these two approaches.

H∞-output feedback controller design for linear systems with time-varying delayed state

This paper considers the H/spl infin/-controller design problem for linear systems with time-varying delays in states. The authors obtain sufficient conditions for the existence of H/spl infin/ controllers in terms of three linear matrix inequalities (LMIs). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, they briefly explain how to construct such controllers from the positive-definite solutions of their LMIs and give an example.

Nonlinear Controller Design for Linear Systems via the Parametrization of Nonlinear Stabilizing Controllers

This paper concerns a nonlinear controller design for linear systems. We give a concrete method to design a nonlinear controller which smoothly switches linear compensators depending on the state of the plant. Then we apply the method to a plant with an input saturation and evaluate its effectiveness by simulations.

A Behavioral Approach By Using Pencil Based System Models

Abstract In this article we consider the problem of analysis and design of linear time-invariant control systems by using the system models which are based on matrix pencils. Behaviors, poles, zeros, stability, controllability, observability, transfer function, and other traditional concepts are discussed mainly besed on the Willems’ behavioral approach. Moreover the extensions to LQ optimal control problem and computation of H norm are investigated.

Kalibond - a Tool for Teaching Bond Graph Modeling

The presented software tool KaliBond makes bond graph modeling possible within MATLAB®. It allows the menu driven drawing of bond graphs, the automatic causality assignment and the computation of the system state space representation in MATLAB format. Since it is the intended purpose of KaliBond to provide a system model for linear control system analysis and design, its functionality is limited to linear system models.

A Bridge between State-Space and Transfer-Function Method

Abstract A synthesis of the two major approaches to linear control system design, namely the state-space and die transfer-function ones, can be achieved by use of dynamics assignment, a convenient reference design problem. Students, teachers, and researchers can all benefit from a deeper understanding of die relationships between these two approaches.

Periodic Lyapunov equations: Some applications and new algorithms

The discrete-time periodic Lyapunov equation has several important applications in the analysis and design of linear periodic control systems. Specific applications considered are the solution of state- and output-feedback optimal periodic control problems, the stabilization by periodic state feedback and the square-root balancing of discrete-time periodic systems. Efficient and numerically reliable algorithms based on the periodic Schur decomposition are proposed for the solution of periodic Lyapunov equations. The proposed algorithms are extensions of the direct solution methods for standard discrete-time Lyapunov equations for the case of indefinite as well as non-negative definite solution.

Robust H∞ state feedback control for linear systems with state delay and parameter uncertainty

This paper addresses the problem of robust H ∞ state feedback control design for linear systems with state delay and parameter uncertainty. Based on a positive-definite solution of a modified algebraic Riccati equation, the proposed robust H ∞ static state feedback controller stabilizes uncertain time-delay systems independently of delays, and guarantees an H ∞ norm bound constraint on disturbance attenuation for all admissible uncertainties. Furthermore, it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback. Illustrative examples are given to demonstrate the applicability of the proposed approach.

S-54-2 - The integration of intrinsic properties and synaptic inputs in locus coeruleus

In this paper, a package of programs for the computer aided design of discrete multivariable linear control systems is shown. It is based on frequency-domain techniques. Also, a new stability design method for multivariable systems is described. The package performs the following tasks: calculation of the equivalent z-transfer function of a continuous system, stability design; interaction improvement; operations with transfer functions matrices and simulation of closed loop discrete multivariable systems. The solution of these tasks leads to the manipulation of transfer functions matrices. It is carried out with the aid of the Graph Theory. A design example is included to illustrate the use of the stability design method and the efectiveness of the package.

An Optimal Design of Constrained Linear Control Systems Using the Set of Admissible Gains

In the design problem of linear control systems with input and state constraints, a feedback gain is admissible if all the constraints are satisfied. This paper presents a new design method for obtaining a suboptimal linear admissible control law using a criterion for admissible gain when the set of initial states is given by a convex polyhedron. A function of gain on the constrained conditions, α(f), is defined so that a. stable gain f is admissible α(f)≤1. An effective method for computing α(f) by means of an LP algorithm is proposed, which is based on the method of constructing the maximal set of admissihle initial states in the dual space.

Co-states for sliding mode design in linear systems

A control design for linear systems with uncertainties is presented where a particular time-varying sliding mode manifold is specified utilizing co-states of the plant. We introduce design methods for both continuous time and sampled data systems. It is shown that robustness of the closed-loop systems with continuous time control degrades when an equivalent sampled data control is used.

An algorithm for inverting rational matrices

We propose an algorithm for computing the inverses of rational matrices and in particular the inverses of polynomial matrices. The algorithm is based on minimal state space realizations of proper rational matrices and the matrix inverse lemma and is implemented as a MATLAB 1 function. Experiments show that the algorithm gives accurate results for typical rational matrices that arise in analysis and design of linear multivariable control systems. Illustrative examples are given.