Automatic Generation of Root Locus Plots for Linear Time Invariant Systems (original) (raw)
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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.
A Method for Plotting the Complementary Root Locus Using the Root-Locus (Positive Gain) Rules
IEEE Transactions on Education, 2004
The root-locus method is a well-known and commonly used tool in control system analysis and design. It is an important topic in introductory undergraduate engineering control disciplines. Although complementary root locus (plant with negative gain) is not as common as root locus (plant with positive gain) and in many introductory textbooks for control systems is not presented, it has been shown a valuable tool in control system design. This paper shows that complementary root locus can be plotted using only the well-known construction rules to plot root locus. It can offer for the students a better comprehension on this subject. These results present a procedure to avoid problems that appear in root-locus plots for plants with the same number of poles and 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.
The Application of the Root Locus Method for the Design of Pitch Controller of an F-104A Aircraft
2009
This paper presents an application of the root locus technique for the design of a feedback control system of an F-104A aircraft. The analysis of the longitudinal aircraft stability was performed for the Single Input Single Output (SISO) open-loop system, using linearised equations of aircraft motion and aerodynamic derivatives of an F-104A aircraft taken from the NASA report . The dynamical behavior of the open-loop system was unsatisfactory and led to the introduction of the feedback control system. The closed-loop system was designed using the root locus technique, developed by Evans in 1948. The transfer function parameters of each element of the feedback control system are determined according to previously set design requirements. Although, the analysis of the closed-loop step response showed that all of the design requirements were realised, the controller designed within the proposed control system structure is not the only one, and there are different controller designs that lead to a satisfactory solution.
Design of controllers for electrical power systems using a complex root locus method
IEEE Transactions on Industrial Electronics, 2016
A large class of three-phase electrical power systems possess symmetry conditions that make it possible to describe their behavior using single-input single-output transfer functions with complex coefficients. In such cases, an extended root locus method can be used to design control laws, even though the actual systems are multi-input multi-output. In this paper, the symmetric conditions for a large class of power systems are analyzed. Then, the root locus method is revisited for systems with complex coeffcients and used for the analysis and control design of power systems. To demonstrate the benefits of the approach, the paper includes two examples: a doubly-fed induction machine and a three-phase LCL inverter.
Advances in systems science and applications, 2021
Break points, break-away and break-in points, are an essential part in root locus technique for single input single output linear invariant control systems. The importance of Break points comes from the fact that at the Break points at least two roots of the characteristic equation of the closed loop control system change their type from real to a complex at the break away point, and from complex to real at break-in point. This change affects the response of the system which can be crucial for some of systems’ applications. The conditions for being a Break point are analysed and a new formulated systematic method for finding the Break points and their corresponding gains is presented. An efficient algorithm was developed and can be solved analytically. There is no mathematical differentiation during calculation, and the algorithm can be programmed easily. The developed algorithm is applicable for any order of transfer function of a linear invariant control system. This method is com...
Array Technique to Calculate the Breakpoints on Root Locus Graph and Related Gains
International Journal of Engineering Science and Application, 2020
The root locus technique is a powerful and efficient mean to examine stability, and to analyze single input single output linear time invariant system. In addition, the gain range for any response type of the control system be determined. Some of the important points on a root locus graph of control system are the Breakaway, and Break-in points. In this article those points are called Break points, and the polynomial that some of its roots are Break points, is called Break polynomial. After leaving a Break point on root locus graph, the type of some roots of the system characteristic equation changes. The change is from real to a complex at Breakaway point, and from complex to real at break-in point. The type change of roots causes a type change of the system response. The response type of a system is a crucial matter for industrial machines applications. The development of a new method called the Array method is presented. The Array method is a technique to obtain the Break polynomial where several of its roots are the Break points. This technique is based on constructing an array. Then the array is filled by the polynomials' coefficients of the open loop transfer function's denominator and numerator. The mathematical proof of the method bases, and correctness is presented. It shows that the obtained Break polynomial by the proposed method is the same derived polynomial by the most used methods. The proposed method is compared with other methods in solution of examples of control systems to demonstrate its simplicity for the user and its correctness for any order of a single input single output linear invariant control system. .
Computer Aided Design of Lead compensator using Root Locus Method
This paper introduce the Lead,lag,lag-Lead compensator design of root locus using single composite Matlab programme.A number of Matlab function are developed for the compensator design method. With this computer aided design, compensator can be obtained of any control system to meet the desired response specification.