Root locus for time-delay systems
M. Kahánek, M. Hromčík
Czech Technical University in Prague
Abstract
This work focuses on the development of an accurate and efficient root locus algorithm for time-delayed systems and its implementation as a graphical user interface in the MATLAB environment. The root locus algorithm builds on QPmR algorithm (Vyhlídal, T. – Zítek, P.: QPmR v.2 – Quasipolynomial rootfinder, algorithm and examples, Advances in Delays and Dynamics, 2013) with utilization of the properties of the root locus and quasipolynomial functions to efficiently plot the branches of the root locus. Poles of the system can be firstly calculated by the QPmR algorithm as roots of quasipolynomial in denominator of the system’s transfer function. By utilizing quasipolynomial holomorphic properties, the sensitivity of pole position change depending on changed proportional value of regulator can be estimated by modification of the first order Taylor series and refined using numerical methods such as Newton’s method, greatly improving computation time. The whole algorithm is then implemented inside custom MATLAB GUI, callable as a function. This interface provides many functions such as interactive pole position change depending on regulator gain value, adding poles/zeros by clicking on complex plane, exporting designes system to the matlab workspace, analysing Bode characteristics and step responses inside the tool and much more. First free to use version of the tool is available in GitHub repository (https://github.com/kahanmic/Time-delay-root-locus).
Session
Linear and Nonlinear Control (Poster)