Modern Control System Theory and Design, 2nd Edition

6.18.  DIGITAL COMPUTER PROGRAM FOR OBTAINING THE ROOT LOCUS

For those who do not have access to MATLAB, which has now become an industry standard (more or less), this book also provides another digital computer program for obtaining the root locus. This approach for providing both MATLAB and other digital computer programs which are not dependent on COTS (commercial-off-the-shelf software) is used throughout this book.

The root locus can be plotted automatically using a variety of methods, including utilizing a digital computer [29–31]. This section presents a working digital computer program for obtaining the root locus. In our discussions, we will only consider the case of negative feedback. The program can be modified with a few simple changes for positive feedback.

The digital computer is a very versatile and flexible tool that is easily adaptable for automatically determining the roots in the complex plane. The method preseted, based on the material of References [29–31], starts at the poles of the control system and searches for the overall root locus in a segmented manner.

Reference [29] discusses this conceptual algorithm for obtaining the root locus using a digital computer. It presents the logic that can be used to code a digital computer in order to determine the locus of points which satisfy Eqs. (6.132), (6.133), (6.151). The program presented in this section is written in Fortran IV.

The computer logic flow diagrams of the technique are illustrated in Figures 6.70 ...