Design Of Multivariable Control Systems Research Articles

Design of optimal multivariable linear control systems

The paper presents a method of designing optimal linear multivariable control systems with quadratic performance indices. The procedure is based on Pontryagin's maximum principle, which is first used to give the costate and system equations in state-space form. Using the Laplace transform method, it is then shown that the optimum trajectory equation contains unstable terms which may be eliminated by a simple choice of the terminal values of the costate variables. With this choice of terminal values, the optimal control strategy is obtained, which ensures a stable system whilst minimising a quadratic measure of performance over the infinite interval. The design procedure is illustrated by example, and the optimum controller is compared with a finite-interval optimum controller. Thus, it is concluded that the optimum controllers produced by the present design procedure will give a good approximation to most finite-interval controllers.

Mappings of the state space into the complex plane and their use in multivariable systems analysis

A complex number is defined which characterizes the behaviour of the velocity vector in an n-dimensionnl state space. Methods are then developed for the mapping of state space velocity fields into the complex plane. These techniques should be useful in the design of multivariable feedback control systems, and a simple example of their application is given.

Design of discrete multivariable control systems having prespecified dynamics via optimal control theory

Design of discrete multivariable control systems having prespecified dynamics via optimal control theory

Decoupling in the design and synthesis of multivariable control systems

Necessary and sufficient conditions for the "decoupling" of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> -input, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> -output time-invariant linear system using state variable feedback are determined. Given a system which satisfies these conditions, i.e., which can be decoupled by state variable feedback, the class φ of all feedback matrices which decouple the system is characterized. The characterization of φ is used to determine the number of closed-loop poles which can be specified for the decoupled system and to develop a synthesis technique for the realization of desired closed-loop pole configurations. Transfer matrix consequences of decoupling are examined and practice implications discussed through numerical examples.

Multivariable control system synthesis utilizing the generalized inverse of a matrix

By utilizing the concept of the generalized inverse of a matrix, it is possible to obtain more complete multivariable control system design equations than have previously been published. Also, condition equations can define the limitations which must be imposed upon the desired system H' in order to realize a mathematical solution.

Design of Non-linear Multivariable Control Systems†

ABSTRACT Given a piece-wise single valued non-linear multivariable plant a design procedure is suggested to meet the desired specifications for step inputs. The system is first designed as a linear system satisfying the design specifications and its performance as a non-linear system is checked. The method may involve trial and error. An example is worked out Illustrating the procedure. Analogue computer results are also included.

Generalization of the parameter plane method

This paper presents a generalization of the parameter plane method in that it considers the case when the characteristic equation coefficients are nonlinear functions of the system adjustable parameters. The generalized method is then applied to the system analysis in which the coefficients are linear functions of two parameters and their product. As a simple and rapid procedure for factoring polynomials in the parameter plane, the method is used in the design of linear continuous multivariable control systems. A non-linear system with two nonlinearities is also considered whereby the stability and existence of limit cycles are investigated.

Use of matrix transformation and system eigenvalues in the design of linear multivariable control systems

A method of using matrix transformations to obtain a diagonal open-loop transfer matrix and its application to the design of linear multivariable control systems are presented. Numerous examples are used to illustrate the usefulness of the design procedure, and a justification for it is presented by a discussion of system eigenvalues.

Linear multivariable control system design with root loci

The design of multivariable control systems utilizing matrix formulation has been considered by many writers. Problems of ultimate physical realizability and the effects of interaction are not conveniently considered by most of these methods. This paper describes the application of the root locus method to the problem of designing realizable interacting linear control systems. The application is not practical to systems of unlimited complexity. However, where the design specifications control system transient interactions rather than require noninteraction, the loci method provides a systematic application of familiar techniques to the design procedure.