Unit iii---root locus concept
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The root locus technique is a graphical method used in control systems to adjust the locations of closed loop poles by varying system parameters to achieve desired performance. The root locus represents the possible locations of closed loop poles for different values of a parameter in the s-domain, forming a symmetrical plot about the real axis. It has advantages over other methods by being easy to implement and allowing prediction of system performance by indicating important parameters. Construction of the root locus involves 7 steps including finding pole and zero locations, the real axis path, asymptotes, and breakpoints.
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Analysis and Design of Control System using Root Locus
Root locus analysis is a powerful tool in control systems engineering used to analyze the behavior of a system's closed-loop poles as a function of a parameter, typically a controller gain. It provides engineers with valuable insights into how changing system parameters affect stability and performance, helping them design robust and stable control systems. Let's explore the key concepts, techniques, and practical implications of root locus analysis. At its core, root locus analysis focuses on the movement of the closed-loop poles in the complex plane as a control parameter varies. These poles represent the characteristic equation's roots, which determine the system's stability and transient response. By examining the pole locations as the parameter changes, engineers can gain a deeper understanding of the system's behavior and make informed design decisions.
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This document outlines the steps and procedure for performing a root locus analysis. It begins with an introduction to root locus analysis and its use in determining the stability of a closed-loop system. It then lists the general 8 steps for drawing a root locus as a parameter is varied. An example problem is worked through, showing the determination of poles, zeros, asymptotes, breakaway points, and drawing the overall root locus sketch. The document concludes with a brief MATLAB program for generating a root locus plot.
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This document discusses root locus analysis, which graphically shows how the closed-loop poles of a system change with a parameter. It outlines the general steps for drawing a root locus, which include determining open-loop poles and zeros, drawing the pole-zero plot, calculating asymptotes and breakaway points, and sketching the overall root locus. The document also briefly mentions that root locus analysis can provide insights into a system's stability and performance and be used to aid control system design.
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Servo-Motor Response and Mode Transition
1.0 Project Objective:
The objective of this project is to familiarize the students with the use and limitations of
models in understanding the response of a practical servo-system and evaluating its
usefulness. It introduces system modes as a tool of evaluating the quality of a system’s
output. It also explores the ability of a controller’s tuning parameters to affect the
system’s behavior and cause it to shift from one mode to another.
2.0 Equipment: Matlab, Simulink and the EE380 textbook.
3.0 Background:
This section provides a brief background about the tools and concepts needed to
understand the role of mathematical constructs in modeling, predicting and tuning the
behavior of a system.
3.1: System Modes and the Quality of its Response
Control systems are enablers whose objective is to make a servo-process (SP) yield to
the commands of an operator and provide him with useful work. When the operator
issues a command, the SP can only respond by being in one of the following modes:
o If the SP complies with the command of the operator it is in a stable mode
o If it does not comply with the command, the mode is called unstable
Figure-1: Stability does not imply useful outcome from the servo-process
Obviously, the minimum expectation of the operator from the servo-process is to be in a
stable mode. However, the system being in a stable mode need not necessarily mean
that it is providing the operator with useful work. The quality of the system response could
be too poor and practically useless. Take for example a car as a servo-process (figure-1).
If the car fails to reach the destination, one may call the process unstable. However, if the
process is stable and the car is able to reach the destination but the path it took is too
long, rough, consumes too much fuel and contains many detours, the effort derived from
the car cannot be called useful.
Measuring the usefulness of the outcome from a servo-process is important since a
response that is not useful defeats the purpose of control. One way to assess the quality
of a system’s response is though the use of performance measures such as overshoot,
settling time, rise time and steady state error. A more general way of describing the
quality of system behavior is through using system modes. System modes may be used
to qualitatively describe the whole state of the response not particular aspects of it, as in
performance measures. In industrial applications, six system modes are used to
describe the response of a practical servo-process. They are unstable, over-damped,
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This document outlines the steps and procedure for performing a root locus analysis. It begins with an introduction to root locus analysis and its use in determining the stability of a closed-loop system. It then lists the general 8 steps for drawing a root locus as a parameter is varied. An example problem is worked through, showing the determination of poles, zeros, asymptotes, breakaway points, and drawing the overall root locus sketch. The document concludes with a brief MATLAB program for generating a root locus plot.
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The document describes a new metric for classifying autoregressive (AR) models and linear dynamic systems based on their pole representations. It discusses existing pole-based distance measures like OSPA and MAX-OSPA distance, which find the optimal assignment of poles to minimize summed or maximum distances. The document also describes the ARMA metric, which is based on cepstrum domain processing. It proposes a novel metric in this work that defines the "distance" between systems or models as the sum and differences of the magnitude and angles of their poles in pole-space.
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This document discusses root locus analysis, which graphically shows how the closed-loop poles of a system change with a parameter. It outlines the general steps for drawing a root locus, which include determining open-loop poles and zeros, drawing the pole-zero plot, calculating asymptotes and breakaway points, and sketching the overall root locus. The document also briefly mentions that root locus analysis can provide insights into a system's stability and performance and be used to aid control system design.
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models in understanding the response of a practical servo-system and evaluating its
usefulness. It introduces system modes as a tool of evaluating the quality of a system’s
output. It also explores the ability of a controller’s tuning parameters to affect the
system’s behavior and cause it to shift from one mode to another.
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This section provides a brief background about the tools and concepts needed to
understand the role of mathematical constructs in modeling, predicting and tuning the
behavior of a system.
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Control systems are enablers whose objective is to make a servo-process (SP) yield to
the commands of an operator and provide him with useful work. When the operator
issues a command, the SP can only respond by being in one of the following modes:
o If the SP complies with the command of the operator it is in a stable mode
o If it does not comply with the command, the mode is called unstable
Figure-1: Stability does not imply useful outcome from the servo-process
Obviously, the minimum expectation of the operator from the servo-process is to be in a
stable mode. However, the system being in a stable mode need not necessarily mean
that it is providing the operator with useful work. The quality of the system response could
be too poor and practically useless. Take for example a car as a servo-process (figure-1).
If the car fails to reach the destination, one may call the process unstable. However, if the
process is stable and the car is able to reach the destination but the path it took is too
long, rough, consumes too much fuel and contains many detours, the effort derived from
the car cannot be called useful.
Measuring the usefulness of the outcome from a servo-process is important since a
response that is not useful defeats the purpose of control. One way to assess the quality
of a system’s response is though the use of performance measures such as overshoot,
settling time, rise time and steady state error. A more general way of describing the
quality of system behavior is through using system modes. System modes may be used
to qualitatively describe the whole state of the response not particular aspects of it, as in
performance measures. In industrial applications, six system modes are used to
describe the response of a practical servo-process. They are unstable, over-damped,
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This document discusses using fuzzy logic control for voltage stability in a power system. It proposes calculating a fuzzy-based voltage stability index at each step of load flow simulation to identify critical buses. The method is tested on the 18-bus IEEE test system under different disturbances and load models. A fuzzy controller with 7 predicates is applied to maintain voltage stability. Simulation results show the terminal voltage response at bus 7 for a short circuit at bus 12 lasting 300ms under different load models.
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This document discusses several applications of fuzzy logic in electrical systems, including induction motor control, switched reluctance motor control, excitation control in automatic voltage regulators, and fuzzy logic control in an 18 bus power system. It focuses on using fuzzy logic for automatic voltage regulation, describing the typical components of a power system, challenges with conventional controllers, and presenting simulation results that demonstrate how a fuzzy logic controller can effectively regulate the voltage of a synchronous generator.
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This document provides an overview of artificial neural networks. It defines ANNs as highly interconnected networks of neurons inspired by the human brain. The document then discusses key aspects of ANNs like biological neurons, network architecture, learning rules, activation functions, and specific ANN models including perceptrons, backpropagation networks, associative memories, and Hopfield networks. It provides details on the basic building blocks and functioning of various ANN concepts.
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Artificial intelligence techniques like artificial neural networks, fuzzy logic, and expert systems can help address complex problems in power systems that were previously difficult to solve. They have applications in areas like economic load dispatch, load forecasting, transmission capacity and optimal power flow, generator limits, and system protections. By using environmental sensors and AI techniques together, the performance of transmission lines can be improved by changing line parameters based on conditions and diagnosing and addressing any faults. AI provides benefits like increased reliability, efficiency, and cost savings within power systems.
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Iv unit-fuzzification and de-fuzzification
Fuzzification transforms crisp quantities into fuzzy quantities by identifying deterministic values as uncertain and represented by membership functions, such as describing a temperature of 45°C as "favorable", "hot", or "cold". Defuzzification is the inverse process, converting fuzzy results back into crisp results by mapping a possibility distribution of an inferred fuzzy control action into a nonfuzzy control action.
Iv defuzzification methods
This document discusses various methods for defuzzification, which is the process of converting a fuzzy quantity into a crisp quantity. It describes seven common defuzzification methods: 1) max membership principle, 2) centroid method, 3) weighted average method, 4) mean max membership, 5) center of sums, 6) centre of largest area, and 7) first of maxima, last of maxima. For each method, it provides details on the calculation approach and formulas used to determine the defuzzified crisp value. The centroid method is noted as the most commonly used defuzzification technique.
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This document discusses energy efficient motors and power factor improvement. It provides details on the construction, operation, and benefits of energy efficient motors. Key points include:
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2. The higher upfront cost of efficient motors is often paid back quickly through energy savings. Life cycle cost is lower despite the higher initial price.
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1) The document discusses DC and AC circuits, defining key concepts like voltage, current, resistance, inductance, and capacitance.
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Unit iii---root locus concept
- 1. ROOT LOCUS TECHNIQUE IN CONTROL SYSTEM
- 2. Definitions: It is a graphical method for adjusting the locations of closed loop poles to achieve the desired system performance by varying one (or) more system parameters. The root locus of a feedback system is the graphical representation in the complex s-plane of the possible locations of its closed loop poles for varying values of a certain system parameter. The root locus is a graphical representation in s-domain and it is symmetrical about the real axis. Because the open loop poles and zeros exist in the s-domain having the values either as real or as complex conjugate pairs.
- 3. Advantages of Root Locus Technique: Root locus technique in control system is easy to implement as compared to other methods. With the help of root locus we can easily predict the performance of the whole system. Root locus provides the better way to indicate the parameters.
- 4. PROCEDURE FOR CONSTRUCTING ROOT LOCUS (OR) PLOT THE ROOT LOCUS Step-1:- location of poles and zeros Step-2:- determine the root locus on real axis Step-3:- find angles of asymptotes and centroid Step-4:- find the breakaway and breakin points Step-5:- find angle of departure and angle of arrival Step-6:- find point of intersection of root locus with imaginary axis Step-7:- find the value of gain k.