RATRIX : A RATional matRIX calculator for computer aided analysis and synthesis of linear multivariable control systems P. Tzekis, N.P. Karampetakis and A.I. Vardulakis Department of Mathematics Aristotle University of Thessaloniki Thessaloniki 54006, Greece

Why we develop this program ? Program description. Examples of use. Overview

Symbolic computation programs Why we develop this program ? Programs that handle both numbers and symbols such as Mathematica, Maple, Matlab, MACSYMA, Reduce,..

Advantages of symbolic computation programs Symbolic storage. (Variables can be stored in exact form I.e. 1/3 instead of 0.333) Inbuilt procedures (Existing procedures for special areas of mathematics) Programming Language (High Level programming languages allowing procedures to be written) Why we develop this program ?

Disadvantages of symbolic computation programs Large size of memory they use. Slow speed they have. No existing procedures for the study of rational matrices and its applications in analysis and design of control systems. (Except the polynomial toolbox of Matlab, created by PolyX) Require knowledge of the procedures from the user. Why we develop this program ?

How to overcome these disadvantages ? Why we develop this program ? User friendly environment Procedures for rational matrices and control RATRIX

Description of the main window ? Program Description Shortcut icons Menu Matrices Procedures Maple environment Results

Program Description Description of the main procedures

Program Description Description of the main procedures

Program Description You can save your session !

Program Description You can use the kernel of Maple !

Program Description Benefits of RATRIX The user friendly Windows based interface. Internal use of the powerful kernel of Maple. Is working over the four well known rings. (polynomials, proper rational functions, proper and Shur stable rational functions and proper and Hurwitz stable rational functions) The user can work both on the windows application environment (beginner) and the standard Maple environment (advanced).

Creation of a matrix EXAMPLES Create a matrix

Complete the entries of the matrix Use the icons

Find the Smith McMillan form in Ω S Smith McMillan Form

The Smith Form The name of the procedure

The left transforming matrix U(s) is proper and Hurwitz Stable

We can check that the condition T=USV is satisfied

A right MFD of T(s) in Ω S MFD

The McMillan Degree of T(s) McMillan Degree

Find a polynomial matrix solution of D1*X+N1*Y=T Dioph. Equ.

Define the matrices A,B,C

Find the polynomial solution of A*X+B*Y=C

Check if the solutions X,Y satisfy the condition A*X+B*Y=C

Find a Hurwitz stable stabilizing compensator R for the matrix A. Stabilizing Compensators

The compensator is too arbitrary.

We select specific values for the arbitrary parameters.

and the solution is ….

Find the finite decoupling zeros of the PMD defined by A,B,C. Decoupling Zeros

You can save your session.

with the extension.con

Conclusions The paper has presented a user-friendly Windows based application program for the manipulation of rational matrices and the solution of basic Analysis and Synthesis problem of linear systems. This program can be used for educational, research and industrial uses.