Dynamic Systems with Three Variable Parameters (original) (raw)

Automatic Generation of Root Locus Plots for Linear Time Invariant Systems

Nigerian Journal of Technology, 2016

Design and analysis of control systems often become difficult due to the complexity of the system model and the design techniques involved. This paper presents the development of a Tools Box in Microsoft Excel for control engineer that uses root locus as a time domain technique for system design and analysis. The Tool Box can also serve as a computer-aided graphical analytical tool for trainers. The work was done in two phases: the first phase is the development of a programmable algorithms for root locus using the angle condition and bisection method while the second phase is the implementation of the developed algorithms. The implementation was done using Microsoft Excel (R) Visual Basic Application (VBA). Results of simulations for different systems show the potential of the Tool Box as an alternative for other software package and the ease of using it on the readily available Microsoft Excel environment.

Root-Locus Analysis of Delayed First and Second Order Systems

2018

For finite dimensional linear system the root-locus method is well established however for the case of delayed systems the method has some problems due to the transcendental term involved. This work intends to illustrate the problems that arises when a root-locus diagram is performed as well as to develop a Matlab function that provides the root-locus diagram for delayed low order systems. In this way, some comments about the problems that should be tackled to obtain a generalization of the computational method for delayed systems with real m poles and n zeros

NEW SIMPLE ALGEBRAIC ROOT LOCUS METHOD FOR DESIGN OF FEEDBACK CONTROL SYSTEMS

consists of two decompositions. The first one, decomposition of the characteristic equation into two lower order equations, was performed in order to simplify the analysis and design of closed loop systems. The second is the decomposition of Laplace variable, s, into two variables, damping coefficient, ζ, and natural frequency,ω n . Those two decompositions reduce the design of any order feedback systems to setting of two complex dominant poles in the desired position. In the paper, we derived explicit equations for six cases: first, second and third order system with P and PI. We got the analytical solutions for the case of fourth and fifth order characteristic equations with the P and PI controller; one may obtain a complete analytical solution of controller gain as a function of the desired damping coefficient. The complete derivation is given for the third order equation with P and PI controller. We can extend the number of specified poles to the highest order of the characteristic equation working in a similar way, so we can specify the position of each pole. The concept is similar to the root locus but root locus is implicit, which makes it more complicated and this is simpler explicit root locus. Standard procedures, root locus and Bode diagrams or Nichol Charts, are neither algebraic nor explicit. We basically change controller parameters and observe the change of some function until we get the desired specifications. The derived method has three important advantage over the standard procedures. It is general, algebraic and explicit. Those are the best poles design results possible; it is not possible to get better controller design results.

2-PARAMETER Root-Loci Concepts and Some Applications

International Journal of Circuit Theory and Applications, 1977

Root-locus concepts are expanded to treat characteristic expressions of systems and circuits with two parameters which vary along straight lines through the origin of the complex plane. Theorems are stated and proved by which the problem of finding the boundary of root regions of such expressions is reduced to the problem of plotting 1-parameter root loci. The concepts of 2-parameter root loci are then used to investigate the absolute stability of arbitrarily passively

Dynamic Analysis of a Three-dimensional Non-linear Continuous System

Pure and Applied Mathematics Journal

Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.

Generalized root locus assignment of all the poles of a multivariable system by output feedback

International Journal of Control, 1976

A new approach to the problem of assigning all the poles of a multivariable system by output feedback is presented. The problem associated with the allowable a-plane regions for the closed-loop system poles under constant output feedback is investigated. It is shown that under certain conditions, results which can be Been as a natural extension of the classical root-locus ideas can be obtained. 2. The necessary and sufficient condition Consider a linear, time-invariant, completely controllable and observable dynamical system described by the state equations x=Ax+Bu; y=Ox

Stability of some driving systems analyzed by means of roots geometric locus

2008

This paper analyzes the stability of the driving systems fitted out with asynchronous motors. In order to do this the used equations systems (written in the two axes theory) and the principle of the study method are presented. A Matlab program has been conceived with their help; this program has allowed to obtain some significant results and conclusions regarding the influences of the system parameters on stability.

Design and Analysis of a Control System Using Root Locus and Frequency Response Methods

Control systems play a very important role in the domain of Electrical Engineering. Without them, it is impossible to comprehensively analyze and design electrical systems. This paper successfully attempts to model a practical real control system using root locus (time domain) and frequency response (Bode Plots) techniques. A brief review of root locus and Bode plots is given. Major focus has been placed on controller design and how the required goal criteria can be achieved. MATLAB has been used exclusively for simulation and design purpose.

Geometric Methods in Study of the Stability of Some Dynamical Systems

2009

In this paper we aim to analyse the stability of two dynamical sys- tems given by differential equations or by systems of differential equa- tions. The first model is a mechanical system which is described by a system of differential equations of the first degree. We study the sta- bility of this system using the method of the Lyapunov function. The second studied model is the model of a vibrant tool machine described by a differential equation of second degree with two delay arguments. For the study of the stability of these models, we use the stage analysis of the differential equations systems with delayed arguments.

Analysis of Correction in Automatic Control Systems with Root Locus

Deleted Journal, 2018

The article addresses the major challenges of automated control systems and solutions. One way is to choose the appropriate correction for the system and analyze parameters. For the synthesis of corrective device parameters, the article uses the root locus method.Root locus can be constructed by changing one or more parameter, which allows a thorough analysis of the stability of the system.In article one of the types the integrating corrective scheme with r, L, C source of an input signal is considered. The problem of synthesis of parameters of an integrated corrective scheme with root locus is is solved; The root locus is constructed, and with their help, the possibility of the approach of roots of the characteristic equation, to roots of the ideal transfer function is considered.