Linear Multivariable Control Systems Research Articles

The deadbeat control of linear multivariable systems with inaccessible state

The problem of deadbeat controller design for a class of discrete-time linear multi-variable systems with inaccessible state is considered. A deadbeat controller, based upon a minimal-order observer, and specified by two gain matrices in compact form, is presented which can drive the system state from any arbitrary initial state to the origin in at most νc + ν0 — 1 steps where νc and ν0 respectively are the controllability and observability indices of the system. The simplicity and generality of the design is demonstrated by numerical example.

Mapping stability regions in planar slices

A method is developed for determining the stability region in the loop-gain space for a linear multivariable control system. Two new interpretations of the return difference determinant are employed, allowing the stability region boundaries to be determined accurately by means of an algorithm.

On the Design of PID Output Feedback Controllers for Linear Multivariable Systems

A time-domain technique is proposed for the design of proportional-plus-integral-plus-derivative (PID) output feedback controllers resulting in a closed-loop system having prespecified static accuracy, disturbance rejection, and transient response performance.

Minimal response time design for linear multivariable sampled-data control systems

The method of minimum, finite settling time design used for single-loop systems is extended to cover multivariable systems. Sensitivity analysis is applied and results of considerable generality are derived which indicate the effects of gain changes and pole or zero movement in the plant transfer functions. A design policy is developed which satisfies the need for low sensitivity in implementation. Further development evolves a design technique in which speed of response can be systematically traded for sensitivity. At the same time the technique satisfies the need to achieve a digital control algorithm of minimal complexity. The method of design has been shown to be particularly relevant to systems with lightly damped open-loop modes and an example of this type of system is analysed in detail.

On the Design of a Class of Non Linear Multivariable Control Systems

The design of a class of multivariable feedback system which is characterised by a set of coupled non linear elements of a general multivalued form is considered. Harmonic linearisation is first used to investigate limit cycling conditions in the autonomous system and to generate frequency domain arrays which indicate the structure of a suitable compensator to avoid critical regions In the freauency domain. A numerical procedure based on a method of inequalities is then employed to meet additional performance functionals in the time domain subject to specified system constraints.

Computer Aided Design Program for Linear Multivariable Control Systems

CAD program package named DPACS-F for a linear multivariable control system analysis and synthesis is presented. The systems to be treated in the CAD can be in the form of state space description, transfer function or input-output data, and algorithms based on both state space and frequency domain approaches are provided and anyone of them can be executed by the command line which is given by a simple rule. As an example of a control system designed by CAD, the control system for a position control of a double inverted pendulum on an inclined rail is presented.

Computer Aided Frequency Response Design with Given Poles

Many design problems in the field of linear multivariable control systems can be reduced to the following: Given a set of transfer functions whose numerator polynomial coefficients depend linearly on some parameters. Determine the parameters such that the transfer function frequency responses fit to desired frequency responses as good as possible. A simple and straightforward solution of this problem is given with provision to concentrate the fitting on the desired frequency ranges. Some applications are outlined such as reference variable feedforward to dynamic compensators, disturbance response design, model reduction and single-input pole assignment compensator design.

On the Application of Nonlinear Programming to the Solution of Optimal Output-constrained Regulator Problems

Optimization techniques based on nonlinear programming are used to compute the constant, optimal output feedback gains, for linear multivariable control systems. The computation of these feedback gains provides a useful design tool in the development of aircraft active control systems. Broyden-Fletcher-Goldfarb-Shanno (BFGS), Davidon-Fletcher-Powell (DFP), and Newton methods are used in conjunction with appropriate starting values to compute the optimal gains; and a comparison of the effectiveness of the techniques is given. Also a modification of the DFP Method in which an analytical approximation of the inverse Hessian is used as a priming value is developed and evaluated. An example problem, the optimal control of a flexible aircraft, is used to evaluate the techniques. Results indicate that the methods provide an efficient and cost effective solution of the optimal output feedback problem.

Programme Suite for CAD of Multivariable Control Systems by Poles Assignment Technique

A programe suite for Computer - Aided Design (CAD) of multivariable linear control systems by means of poles assignment technique is described. The suite provides two main parts analysis and syntesis. The part syntesis includes the majority of well known and novel computational procedures devoted to the mentioned problem. The control can be formed by unity or full rank feedback matrices. Special emphasis has been paid on the procedures for poles assignment and simultaneous satisfaction of additional design reguirements.

Nonlinear control of linear multivariable systems via state-dependent feedback gains

It is often desirable to have controllers which respond fast to large errors and which respond slowly to the small errors that are often due to sensor noise. Some nonlinear controllers having these properties are developed here by modifying optimal linear state feedback controllers so that they have state-dependent gains. A general approach is developed for the nonlinear control of multivariable systems such that the transient responses exhibit the desired properties, and the closed loop systems are asymptotically stable.

Sequential design of linear multivariable systems

The paper describes and critically assesses, in the light of recent advances, the sequential return difference method for the computer-aided design of linear multivariable control systems. In this method, a sequence of single-loop designs, using classical procedures, yields a multivariable design satisfying various criteria such as stability, disturbance attenuation, low interaction and integrity.

On Certain Aspects of Linear Retarded Multi-variable Feedback Control Systems

A simple analytical method for the stability analysis and design of a multiple-delay multivariable plant based on Dual-Locus technique has been presented. The dual-phase computation in the frequency domain ascertains the generalized phase-margin (PM) and gain-margin (GM) conditions for critical stability. Quite useful results in system design, generalization of stability and extension of stability limits are obtained. A number of stability curves are drawn for the ready reference of control engineers. Examples have been taken to elucidate the procedure. Close agreement exists between the available and predicted results.

Design of high-gain state-feedback controllers for linear multivariable systems

It is shown that recent results in the theory of entire eigen-structure assignment greatly facilitate the design of high-gain state-feedback controllers. The design of such controllers is reduced to the separate computation of well-defined subspaces associated with the `slow´ and `fast´ modes of closed-loop systems incorporating high-gain controllers.

Design of PID controllers for multivariable systems

The paper develops a simple method for the design of PID controllers for linear multivariable systems where the controllers use only the available system outputs. The resulting closed-loop system has a specified set of poles and in the steady state the outputs follow step commands and reject disturbances of any form with constant final values. For an m-input, l-output system of order n, the PID controller can place 3m poles of the (n + J)th-order closed-loop system at any desired locations. The controller matrices are assumed to have unity-rank and are obtained from linear equations. The method is illustrated by an example.

A design technique for linear multivariable feedback systems

A systematic approach is developed for the design of linear multivariable feedback control systems based on a manipulation of the set of frequency-conscious eigenvalues and eigenvectors of an open-loop transfer-function matrix. The key idea behind the approach used is that of an approximately-commutative controller. An algorithm for approximation of a frame of complex vectors by a frame of real vectors is developed and plays a basic role in the systematic design approach. An example, based on industrial plant data, is given showing how the design method is used.

Decentralized control of linear multivariable systems

Abstract This paper studies the effect of decentralized feedback on the closed-loop properties of jointly controllable, jointly observable k-channel linear systems. Channel interactions within such systems are described by means of suitably defined directed graphs. The concept of a complete system is introduced. Complete systems prove to be precisely those systems which can be made both controllable and observable through a single channel by applying nondynamic decentralized feedback to all channels. Explicit conditions are derived for determining when the closed-loop spectrum of a k-channel linear system can be freely assigned or stabilized with decentralized control.

A generalization of the output control of linear multivariable systems with unmeasurable arbitrary disturbances

The results of a previous paper [1] on the regulation and tracking of a servomechanism problem are extended to include control inputs on the outputs of the system and for the case that the state is not available for measurement.

Decentralized Control of Linear Multivariable Systems

This paper studies the effects of decentralized feedback on the closed-loop properties of jointly controllable, jointly observable k-channel linear systems. Channel interactions within such systems are described by means of suitably defined directed graphs. The concept of a complete system is introduced and completeness is shown to be a generic property of systems with strongly connected graphs. Complete systems prove to be precisely those systems which can be made both controllable and observable through a single channel by applying nondynamic decentralized feedback to all channels. Explicit conditions are derived for determining when the closed-loop spectrum of a k-channel linear system can be freely assigned or stabilized with decentralized control. These conditions are shown to hold generically for systems with strongly connected graphs.

Group decoupling theory for a generalized linear multivariable control system

The problem of decoupling groups of inputs and outputs is unified and solved for a generalized multivariable linear control system involving most classes of linear systems, namely, time-invariant, time-varying, time-delay systems with derivatives in the input variables, systems in non-Markovian form, etc.

Compensator design for linear multivariable systems

A configuration and an orderly procedure for the design of linear multivariable control systems are presented. This procedure employs transfer function matrices to specify the system response to set point changes and disturbances. Neither a state-variable formulation nor solution of the matrix Riccati equation are required. The design procedure is illustrated by a simple example involving an unstable system.