This document describes the design of a full-state feedback controller with an integral controller for a DC motor system to control angular position. It first presents the mathematical model and parameters of the DC motor. It then shows the open-loop response has infinite rise time. A full-state feedback controller is designed to meet criteria of settling time < 2s, overshoot < 5%, and steady-state error < 1%. Pole locations are varied to analyze responses. Finally, the model is modified to simulate a disturbance response by adding a load torque term.
This document proposes a mechanical system to automatically retract a motorcycle's side stand when the vehicle starts moving. The system uses a small sprocket connected to the bike's drive chain to power a lever that lifts the side stand. It is a simple, low-cost design that does not require external power or electronics. The proposed side stand retrieval system could improve safety by preventing accidents caused when riders forget to raise the side stand before driving.
This document compares kinematic and dynamic models for robotics. The kinematic model studies robot motion without considering forces/torques, and can be used to determine end effector position from joint positions. The dynamic model relates joint torques to motion, and is important for analyzing a robot's dynamic behavior. Key differences include the kinematic model using Denavit-Hartenberg notation while dynamic models employ Lagrange-Euler and Newton-Euler formulations. Both models are essential for robot control and simulation.
This document discusses vehicle handling and summarizes key concepts related to steady state and transient handling behavior. It covers topics such as Ackerman steering geometry, low and high speed cornering, tire cornering stiffness, understeer and oversteer characteristics, and factors that influence steady state response including weight distribution and tire properties. Metrics for evaluating vehicle response like understeer gradient, characteristic speed, and static margin are also introduced.
This document discusses balancing rotating masses on a shaft. It provides examples of balancing a single mass, balancing multiple masses in the same plane, and balancing masses in different planes. It then gives two example problems:
1) A shaft carries four masses rotating at different radii and angles, and asks to find the balancing mass and its position if placed at a given radius.
2) A shaft carries four masses at different radii and angles across three planes, and asks to find the magnitudes and positions of balancing masses placed at a given radius in two other planes.
This document contains a presentation by Prof. Mukesh N. Tekwani on various topics related to gravitation and orbital mechanics. It includes definitions and explanations of Newton's laws of gravitation and motion, Kepler's laws, gravitational constant, acceleration due to gravity, critical velocity and orbital velocity of satellites, time period of satellites, binding energy, escape velocity, weightlessness, and variation of gravitational acceleration with altitude, depth, and latitude. Equations are derived for many of these topics. Examples and assignments involving calculations are also provided. The document serves to instruct students on fundamental concepts in gravitation, orbital mechanics, and related physics.
This upload is actually experimental, so sorry for the lost animations. This is my first post on SlideShare. Future presentations will take into account the loss of animation.
Also, I saw that the titles of all my slides got covered by something, so I'll never use this theme again. The titles of the slides are:
Slide 1: Vectors and Scalars
Slide 2: In this lecture, you will learn
Slide 3: What are vectors?
Slide 4: What are scalars?
Slide 5: A joke
Slide 6: A joke
Slide 7: What was that for?
Slide 8: What was that for?
Slide 9: Vectors
Slide 10: Geometric Representation
Slide 11: Vector Addition
Slide 12: Scalar Multiplication
Slide 13: The Zero Vector
Slide 14: The Negative of a Vector
Slide 15: Vector Subtraction
Slide 16: More Properties of Vector Algebra
Slide 17: Magnitude of a Vector
Slide 18: Vectors in a Coordinate System
Slide 19: Unit Vectors
Slide 20: Algebraic Representation of Vectors
Slide 21: Algebraic Addition of Vectors
Slide 22: Algebraic Multiplication of a Vector by a Scalar
Slide 23: Example 1
Slide 24: Example 2
Slide 25: A few words of caution
Slide 26: Problems
BSC_Computer Science_Discrete Mathematics_Unit-IRai University
This document discusses successive differentiation and provides examples of finding the nth derivative of common functions such as polynomials, exponentials, logarithms, trigonometric functions, and rational functions. Some key points covered include:
- The nth derivative of a function y with respect to x is denoted as d^n y/dx^n.
- Standard formulas are given for finding the nth derivative of functions such as x^m, e^ax, a^x, 1/(ax+b), (ax+b)^m, log(ax+b), sin(ax+b), and cos(ax+b).
- Examples demonstrate calculating specific high-order derivatives such as the 10th derivative of x
This document discusses the rocker-bogie suspension system used on past and present Mars rovers. It provides background on NASA's Mars Exploration Rovers (MER) Spirit and Opportunity from 2004, which used a rocker-bogie system to allow the rovers to traverse rough terrain. More recently, NASA's Curiosity rover from 2011 also employed a rocker-bogie suspension to enable it to climb over obstacles larger than its wheels while on Mars. The document reviews key features of rover mobility systems, such as autonomous navigation and specialized wheel designs, that have enabled success in prior Mars missions.
This document proposes a mechanical system to automatically retract a motorcycle's side stand when the vehicle starts moving. The system uses a small sprocket connected to the bike's drive chain to power a lever that lifts the side stand. It is a simple, low-cost design that does not require external power or electronics. The proposed side stand retrieval system could improve safety by preventing accidents caused when riders forget to raise the side stand before driving.
This document compares kinematic and dynamic models for robotics. The kinematic model studies robot motion without considering forces/torques, and can be used to determine end effector position from joint positions. The dynamic model relates joint torques to motion, and is important for analyzing a robot's dynamic behavior. Key differences include the kinematic model using Denavit-Hartenberg notation while dynamic models employ Lagrange-Euler and Newton-Euler formulations. Both models are essential for robot control and simulation.
This document discusses vehicle handling and summarizes key concepts related to steady state and transient handling behavior. It covers topics such as Ackerman steering geometry, low and high speed cornering, tire cornering stiffness, understeer and oversteer characteristics, and factors that influence steady state response including weight distribution and tire properties. Metrics for evaluating vehicle response like understeer gradient, characteristic speed, and static margin are also introduced.
This document discusses balancing rotating masses on a shaft. It provides examples of balancing a single mass, balancing multiple masses in the same plane, and balancing masses in different planes. It then gives two example problems:
1) A shaft carries four masses rotating at different radii and angles, and asks to find the balancing mass and its position if placed at a given radius.
2) A shaft carries four masses at different radii and angles across three planes, and asks to find the magnitudes and positions of balancing masses placed at a given radius in two other planes.
This document contains a presentation by Prof. Mukesh N. Tekwani on various topics related to gravitation and orbital mechanics. It includes definitions and explanations of Newton's laws of gravitation and motion, Kepler's laws, gravitational constant, acceleration due to gravity, critical velocity and orbital velocity of satellites, time period of satellites, binding energy, escape velocity, weightlessness, and variation of gravitational acceleration with altitude, depth, and latitude. Equations are derived for many of these topics. Examples and assignments involving calculations are also provided. The document serves to instruct students on fundamental concepts in gravitation, orbital mechanics, and related physics.
This upload is actually experimental, so sorry for the lost animations. This is my first post on SlideShare. Future presentations will take into account the loss of animation.
Also, I saw that the titles of all my slides got covered by something, so I'll never use this theme again. The titles of the slides are:
Slide 1: Vectors and Scalars
Slide 2: In this lecture, you will learn
Slide 3: What are vectors?
Slide 4: What are scalars?
Slide 5: A joke
Slide 6: A joke
Slide 7: What was that for?
Slide 8: What was that for?
Slide 9: Vectors
Slide 10: Geometric Representation
Slide 11: Vector Addition
Slide 12: Scalar Multiplication
Slide 13: The Zero Vector
Slide 14: The Negative of a Vector
Slide 15: Vector Subtraction
Slide 16: More Properties of Vector Algebra
Slide 17: Magnitude of a Vector
Slide 18: Vectors in a Coordinate System
Slide 19: Unit Vectors
Slide 20: Algebraic Representation of Vectors
Slide 21: Algebraic Addition of Vectors
Slide 22: Algebraic Multiplication of a Vector by a Scalar
Slide 23: Example 1
Slide 24: Example 2
Slide 25: A few words of caution
Slide 26: Problems
BSC_Computer Science_Discrete Mathematics_Unit-IRai University
This document discusses successive differentiation and provides examples of finding the nth derivative of common functions such as polynomials, exponentials, logarithms, trigonometric functions, and rational functions. Some key points covered include:
- The nth derivative of a function y with respect to x is denoted as d^n y/dx^n.
- Standard formulas are given for finding the nth derivative of functions such as x^m, e^ax, a^x, 1/(ax+b), (ax+b)^m, log(ax+b), sin(ax+b), and cos(ax+b).
- Examples demonstrate calculating specific high-order derivatives such as the 10th derivative of x
This document discusses the rocker-bogie suspension system used on past and present Mars rovers. It provides background on NASA's Mars Exploration Rovers (MER) Spirit and Opportunity from 2004, which used a rocker-bogie system to allow the rovers to traverse rough terrain. More recently, NASA's Curiosity rover from 2011 also employed a rocker-bogie suspension to enable it to climb over obstacles larger than its wheels while on Mars. The document reviews key features of rover mobility systems, such as autonomous navigation and specialized wheel designs, that have enabled success in prior Mars missions.
THIS DOCUMENT MAINLY CONTAINS THE HOW TO MODLE DC SERVO MOTOR BY USING THE MATLAB SIMULINK AND HOW IT WILL BEHAVE IS SHOWN IN THE MATHEMATICAL EQUATIONS AND THE PLOTTINGS ARE ALSO KEPT IN THIS DOCUMENT SO BY THIS IT IS USEFUL TO STUDY THE CHARACTRISTICS OF A DC SERVO MOTOR
The document discusses different types of gears including spur, helical, bevel, and worm gears. It explains gear terminology like pitch circle, diametral pitch, and pressure angle. Factors that influence gear design strength like dynamic loads, load distribution, reliability, and geometry are covered. The AGMA (American Gear Manufacturers Association) standard method for calculating gear bending strength is presented along with examples. Design of gear boxes including configuration, materials selection, and lubrication are also addressed.
Lagrangian mechanics is a reformulation of classical mechanics introduced by Joseph-Louis Lagrange in 1788. The Lagrangian is a function of generalized coordinates (parameters that define a system's configuration), their time derivatives, and time. It contains information about a system's dynamics. Systems are described by their degrees of freedom, which is the number of independent parameters needed to specify the configuration. Lagrangian mechanics provides a standard form of equations of motion using the Lagrangian L, which is the kinetic energy T minus the potential energy V. Several examples are given to illustrate Lagrangian mechanics, including mass-spring systems, simple pendulums, Atwood machines, and double pendulums.
Magnetic Levitation Train by Shaheen Galgali_seminar report finalshaheen galgali
Magnetic levitation is a highly advanced technology which uses the principle of Electromagnetic suspension & Electrodynamics suspension technology. It has various uses, The common point in all applications is the lack of contact and no friction. This increases efficiency, reduces maintenance costs, and increases the useful life of the system. Magnetic levitation is a technique to suspend an object without any support other than that of a magnetic field. There are already many countries that are attracted to maglev system. Many system have been proposed in different parts of the worlds. Maglev can be conveniently considered as a solution for the future needs of the world. This contribution deals with magnetic levitation. An overview of types, principles and working of magnetic levitation is given with the example by train are presented.
The document discusses the design and fabrication of an automobile gearbox. It outlines the objectives to design a helical gearbox and study gear manufacturing processes. It then discusses various aspects of gearbox design like gear ratios, materials selection, automatic vs manual transmissions, and presents some results like pitch line velocities. Market research was also conducted to determine costs. The conclusion states that gear and shaft design is complete and fabrication will begin soon.
The four-bar linkage is the simplest and most common type of linkage, consisting of four links connected by four pin joints. It has one degree of freedom and requires one driver to operate fully. The document discusses different configurations of four-bar linkages like the parallel-crank, nonparallel equal-crank, crank and rocker, and slider-crank mechanisms. Quick return mechanisms are also described which give a tool a slow cutting stroke and fast return stroke.
This document proposes and describes the design of an automatic side stand for motorcycles. It begins by noting that 36% of motorcycle accidents are caused by riders forgetting to retract the side stand when starting. The proposed system will automatically retract the side stand when the rider engages the gear. It then details the problem definition, proposed innovation, literature review on existing solutions, methodology, working mechanism including use of a motor, gearbox and switches, components and specifications, and progress of the project. The goal is to finish construction by October 21st to prevent accidents caused by forgetting to retract the side stand.
This document defines scalar and vector quantities in physics. Scalars have only magnitude, while vectors have both magnitude and direction. Examples of scalars include time, mass, and temperature, while vectors include displacement, velocity, and force. Vectors are represented by arrows. Scalar quantities can be simply added or subtracted, while adding vectors requires considering both magnitude and direction, such as combining velocities in the same or opposite directions.
This document provides an overview and table of contents for a textbook on control systems by Dr. N.C. Jagan. The textbook covers various topics related to modeling, analysis, and design of control systems, including mathematical modeling of physical systems, time response analysis, stability analysis using Routh-Hurwitz and root locus methods, frequency response analysis using Bode and Nyquist plots, and closed loop control design. It contains 7 chapters and provides problems at the end of each chapter. The textbook is copyrighted and published by BSP BS Publications in Hyderabad, India.
NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)Niraj Solanki
This document discusses nonlinear control systems using phase plane and phase trajectory methods. It defines nonlinear systems and common physical nonlinearities like saturation, dead zone, relay, and backlash. Phase plane analysis is introduced as a graphical method to study nonlinear systems using a plane with state variables x and dx/dt. Key concepts are defined like phase plane, phase trajectory, and phase portrait. Methods for sketching phase trajectories include analytical solutions and graphical methods using isoclines. Examples are given to illustrate phase portraits for different linear systems.
Introduction
The accidents from a vehicle can be done by two reasons mainly. First is due to others fault and second is our neglectancy. One of the most seen condition is to forget removing side stand. So in our project we are trying to give a mechanical arrangement which can remove the side stand at the start motion of the vehicle. It si desired to avoid the automatic arrangement because these systems have many king of disadvantages and dependencies. So the removal system will be a mechanical arrangement which will be simple in mechanism and would not interfere with ride and comfort. In all over world everywhere motorcycle are used. The side stand plays major roll while the vehicle is in rest position. But it has some disadvantages takes place as while the driver starting the motorcycle, there may be possibility of forget to release the side stand this will caused to unwanted troubles.
• Vishal Srivastava, Tejasvi Gupta, Sourabh Kumar, Vinay Kumar, Javed Rafiq, Satish Kumar in his paper Automatic Side stand gives the anatomy of side stand that is a Side stand is a device on a bicycle or motorcycle that allows the bike to be kept upright without leaning against another object or the aid of a person. A "smaller, more convenient" kickstand was developed by Joseph Paul Treen, the father of former Louisiana Governor, Dave Treen. A kickstand is usually a piece of metal that flips down from the frame and makes contact with the ground. It is generally located in the middle of the bike or towards the rear. Some touring bikes have two: one at the rear, and a second in the front. A side stand style kickstand is a single leg that simply flips out to one side, usually the non-drive side, and the bike then leans against it. Side stands can be mounted to the chain stays right behind the bottom bracket or to a chain and seat stay near the rear hub. Side stands mounted right behind the bottom bracket can be bolted on, either clamping the chain stays or to the bracket between them, or welded into place as an integral part of the frame.
Simple side stand
Fig:-1.1 Simple side stand
• Our aim of prevent the two wheeler accident in our project.
• Now a day people transport one place to another place using mostly two wheeler vehicle.
• Same time late of accident in rods in human careless of side stand un hold
• For self transmission system it is sufficient to rotate at 1500 rpm.
• So that high torque is required to start the self transmission system then lift the side stand.
• We requirement this problem so solve in this our project.
Three Axis Pneumatic Modern Trailer By Using Single Cylinderpaperpublications3
Abstract: This project work titled “THREE AXIS PNEUMATIC MODERN TRAILER” has been conceived having studied the difficulty in unloading the materials. Our survey in the regard in several automobile garages, revealed the facts that mostly some difficult methods were adopted in unloading the materials from the trailer. The trailer will unload the material in only one single direction. It is difficult to unload the materials in small compact streets and small roads. In our project these are rectified to unload the trailer in all three sides very easily. Now the project has mainly concentrated on this difficulty, and hence a suitable arrangement has been designed. Such that the vehicles can be unloaded from the trailer in three axes without application of any impact force. By pressing the Direction control valve activated. The compressed air is goes to the pneumatic cylinder through valve. The ram of the pneumatic cylinder acts as a lifting the trailer cabin. The automobile engine drive is coupled to the compressor engine, so that it stores the compressed air when the vehicle running. This compressed air is used to activate the pneumatic cylinder, when the valve is activated.
This document provides an introduction to kinematics of machines. It defines kinematics as dealing with the geometric aspects of motion without consideration of forces. It also defines and classifies different types of kinematic pairs and mechanisms. The key points covered are:
1) Kinematics analyzes the relative motions between parts of a machine without regard to forces or power requirements.
2) Kinematic pairs can be classified based on the type of contact (lower vs higher pairs) and geometry (closed, forced closed, etc).
3) Mechanisms are analyzed to determine degrees of freedom and relative motions between links using methods like Kutzbach criterion and Grubler's criterion for plane mechanisms.
4) Kinematic
1) A mechanism is an assembly of rigid bodies connected by joints that allow constrained motion. A machine is a mechanism that transmits and modifies energy to perform useful work.
2) The document discusses the slider crank mechanism as an example and provides diagrams to illustrate it.
3) It defines the terms rigid body, resistant body, link, and the different types of links based on the number of joints connecting them.
This document discusses the components and operation of automatic transmissions. It describes that automatic transmissions contain a torque converter, planetary gear set, and hydraulic control unit instead of a clutch. The torque converter uses transmission fluid to transfer power from the engine to the transmission without direct mechanical contact. Planetary gears enable different speed ratios by holding different elements stationary. The hydraulic control unit uses pressurized fluid to operate clutches and bands to switch between gears. Automatic transmissions provide conveniences over manual transmissions but can be less fuel efficient.
Porter Governor is a modification of Watt Governor with central load attached to the sleeve. This load moves up and down the central spindle. The additional force increases the speed of revolution required to enable the balls to rise to any predetermined level.
The document discusses different types of steering systems used in automobiles. It describes rack and pinion, recirculating ball, worm and roller, and cam and lever steering systems. It then discusses power steering systems, including hydraulic, electric, and electric hydraulic systems. Electric power steering uses an electric motor to assist steering and can be customized to provide varying levels of assistance depending on driving conditions. While hydraulic systems were traditionally used, electric power steering has benefits like eliminating fluid leakage and being more energy efficient.
This document describes the design and fabrication of a rocker bogie mechanism. The rocker bogie system is a suspension used on Mars rovers to allow independent wheel movement over obstacles. The design includes two rocker arms that allow the left and right wheels to climb obstacles individually. Calculations are shown for tilt angle, wheel base, link lengths, and motor specifications. Components include shafts, links, wheels, bearings, and motors. The advantages of the rocker bogie system include its ability to climb obstacles twice the wheel diameter and distribute load evenly across independently moving wheels.
Linear Control Hard-Disk Read/Write Controller AssignmentIsham Rashik
Classic Hard-Disk Read/Write Head Controller Assignment completed using MATLAB and SIMULINK. To see the diagrams in detail, please download first and zoom it.
Modeling, simulation and control of a robotic armcesarportilla8
This document presents the modeling, simulation, and control of a robotic arm system using a DC motor. It describes the mathematical modeling of the DC motor and robotic arm dynamics. An open-loop simulation is performed to analyze stability and response. A closed-loop system is then designed using a PID controller. Different controller parameters are tested to meet design specifications of less than 5% overshoot, settling time less than 2 seconds, and zero steady-state error. Both P and PID controllers are able to achieve the specifications, with the PID controller providing faster response.
THIS DOCUMENT MAINLY CONTAINS THE HOW TO MODLE DC SERVO MOTOR BY USING THE MATLAB SIMULINK AND HOW IT WILL BEHAVE IS SHOWN IN THE MATHEMATICAL EQUATIONS AND THE PLOTTINGS ARE ALSO KEPT IN THIS DOCUMENT SO BY THIS IT IS USEFUL TO STUDY THE CHARACTRISTICS OF A DC SERVO MOTOR
The document discusses different types of gears including spur, helical, bevel, and worm gears. It explains gear terminology like pitch circle, diametral pitch, and pressure angle. Factors that influence gear design strength like dynamic loads, load distribution, reliability, and geometry are covered. The AGMA (American Gear Manufacturers Association) standard method for calculating gear bending strength is presented along with examples. Design of gear boxes including configuration, materials selection, and lubrication are also addressed.
Lagrangian mechanics is a reformulation of classical mechanics introduced by Joseph-Louis Lagrange in 1788. The Lagrangian is a function of generalized coordinates (parameters that define a system's configuration), their time derivatives, and time. It contains information about a system's dynamics. Systems are described by their degrees of freedom, which is the number of independent parameters needed to specify the configuration. Lagrangian mechanics provides a standard form of equations of motion using the Lagrangian L, which is the kinetic energy T minus the potential energy V. Several examples are given to illustrate Lagrangian mechanics, including mass-spring systems, simple pendulums, Atwood machines, and double pendulums.
Magnetic Levitation Train by Shaheen Galgali_seminar report finalshaheen galgali
Magnetic levitation is a highly advanced technology which uses the principle of Electromagnetic suspension & Electrodynamics suspension technology. It has various uses, The common point in all applications is the lack of contact and no friction. This increases efficiency, reduces maintenance costs, and increases the useful life of the system. Magnetic levitation is a technique to suspend an object without any support other than that of a magnetic field. There are already many countries that are attracted to maglev system. Many system have been proposed in different parts of the worlds. Maglev can be conveniently considered as a solution for the future needs of the world. This contribution deals with magnetic levitation. An overview of types, principles and working of magnetic levitation is given with the example by train are presented.
The document discusses the design and fabrication of an automobile gearbox. It outlines the objectives to design a helical gearbox and study gear manufacturing processes. It then discusses various aspects of gearbox design like gear ratios, materials selection, automatic vs manual transmissions, and presents some results like pitch line velocities. Market research was also conducted to determine costs. The conclusion states that gear and shaft design is complete and fabrication will begin soon.
The four-bar linkage is the simplest and most common type of linkage, consisting of four links connected by four pin joints. It has one degree of freedom and requires one driver to operate fully. The document discusses different configurations of four-bar linkages like the parallel-crank, nonparallel equal-crank, crank and rocker, and slider-crank mechanisms. Quick return mechanisms are also described which give a tool a slow cutting stroke and fast return stroke.
This document proposes and describes the design of an automatic side stand for motorcycles. It begins by noting that 36% of motorcycle accidents are caused by riders forgetting to retract the side stand when starting. The proposed system will automatically retract the side stand when the rider engages the gear. It then details the problem definition, proposed innovation, literature review on existing solutions, methodology, working mechanism including use of a motor, gearbox and switches, components and specifications, and progress of the project. The goal is to finish construction by October 21st to prevent accidents caused by forgetting to retract the side stand.
This document defines scalar and vector quantities in physics. Scalars have only magnitude, while vectors have both magnitude and direction. Examples of scalars include time, mass, and temperature, while vectors include displacement, velocity, and force. Vectors are represented by arrows. Scalar quantities can be simply added or subtracted, while adding vectors requires considering both magnitude and direction, such as combining velocities in the same or opposite directions.
This document provides an overview and table of contents for a textbook on control systems by Dr. N.C. Jagan. The textbook covers various topics related to modeling, analysis, and design of control systems, including mathematical modeling of physical systems, time response analysis, stability analysis using Routh-Hurwitz and root locus methods, frequency response analysis using Bode and Nyquist plots, and closed loop control design. It contains 7 chapters and provides problems at the end of each chapter. The textbook is copyrighted and published by BSP BS Publications in Hyderabad, India.
NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)Niraj Solanki
This document discusses nonlinear control systems using phase plane and phase trajectory methods. It defines nonlinear systems and common physical nonlinearities like saturation, dead zone, relay, and backlash. Phase plane analysis is introduced as a graphical method to study nonlinear systems using a plane with state variables x and dx/dt. Key concepts are defined like phase plane, phase trajectory, and phase portrait. Methods for sketching phase trajectories include analytical solutions and graphical methods using isoclines. Examples are given to illustrate phase portraits for different linear systems.
Introduction
The accidents from a vehicle can be done by two reasons mainly. First is due to others fault and second is our neglectancy. One of the most seen condition is to forget removing side stand. So in our project we are trying to give a mechanical arrangement which can remove the side stand at the start motion of the vehicle. It si desired to avoid the automatic arrangement because these systems have many king of disadvantages and dependencies. So the removal system will be a mechanical arrangement which will be simple in mechanism and would not interfere with ride and comfort. In all over world everywhere motorcycle are used. The side stand plays major roll while the vehicle is in rest position. But it has some disadvantages takes place as while the driver starting the motorcycle, there may be possibility of forget to release the side stand this will caused to unwanted troubles.
• Vishal Srivastava, Tejasvi Gupta, Sourabh Kumar, Vinay Kumar, Javed Rafiq, Satish Kumar in his paper Automatic Side stand gives the anatomy of side stand that is a Side stand is a device on a bicycle or motorcycle that allows the bike to be kept upright without leaning against another object or the aid of a person. A "smaller, more convenient" kickstand was developed by Joseph Paul Treen, the father of former Louisiana Governor, Dave Treen. A kickstand is usually a piece of metal that flips down from the frame and makes contact with the ground. It is generally located in the middle of the bike or towards the rear. Some touring bikes have two: one at the rear, and a second in the front. A side stand style kickstand is a single leg that simply flips out to one side, usually the non-drive side, and the bike then leans against it. Side stands can be mounted to the chain stays right behind the bottom bracket or to a chain and seat stay near the rear hub. Side stands mounted right behind the bottom bracket can be bolted on, either clamping the chain stays or to the bracket between them, or welded into place as an integral part of the frame.
Simple side stand
Fig:-1.1 Simple side stand
• Our aim of prevent the two wheeler accident in our project.
• Now a day people transport one place to another place using mostly two wheeler vehicle.
• Same time late of accident in rods in human careless of side stand un hold
• For self transmission system it is sufficient to rotate at 1500 rpm.
• So that high torque is required to start the self transmission system then lift the side stand.
• We requirement this problem so solve in this our project.
Three Axis Pneumatic Modern Trailer By Using Single Cylinderpaperpublications3
Abstract: This project work titled “THREE AXIS PNEUMATIC MODERN TRAILER” has been conceived having studied the difficulty in unloading the materials. Our survey in the regard in several automobile garages, revealed the facts that mostly some difficult methods were adopted in unloading the materials from the trailer. The trailer will unload the material in only one single direction. It is difficult to unload the materials in small compact streets and small roads. In our project these are rectified to unload the trailer in all three sides very easily. Now the project has mainly concentrated on this difficulty, and hence a suitable arrangement has been designed. Such that the vehicles can be unloaded from the trailer in three axes without application of any impact force. By pressing the Direction control valve activated. The compressed air is goes to the pneumatic cylinder through valve. The ram of the pneumatic cylinder acts as a lifting the trailer cabin. The automobile engine drive is coupled to the compressor engine, so that it stores the compressed air when the vehicle running. This compressed air is used to activate the pneumatic cylinder, when the valve is activated.
This document provides an introduction to kinematics of machines. It defines kinematics as dealing with the geometric aspects of motion without consideration of forces. It also defines and classifies different types of kinematic pairs and mechanisms. The key points covered are:
1) Kinematics analyzes the relative motions between parts of a machine without regard to forces or power requirements.
2) Kinematic pairs can be classified based on the type of contact (lower vs higher pairs) and geometry (closed, forced closed, etc).
3) Mechanisms are analyzed to determine degrees of freedom and relative motions between links using methods like Kutzbach criterion and Grubler's criterion for plane mechanisms.
4) Kinematic
1) A mechanism is an assembly of rigid bodies connected by joints that allow constrained motion. A machine is a mechanism that transmits and modifies energy to perform useful work.
2) The document discusses the slider crank mechanism as an example and provides diagrams to illustrate it.
3) It defines the terms rigid body, resistant body, link, and the different types of links based on the number of joints connecting them.
This document discusses the components and operation of automatic transmissions. It describes that automatic transmissions contain a torque converter, planetary gear set, and hydraulic control unit instead of a clutch. The torque converter uses transmission fluid to transfer power from the engine to the transmission without direct mechanical contact. Planetary gears enable different speed ratios by holding different elements stationary. The hydraulic control unit uses pressurized fluid to operate clutches and bands to switch between gears. Automatic transmissions provide conveniences over manual transmissions but can be less fuel efficient.
Porter Governor is a modification of Watt Governor with central load attached to the sleeve. This load moves up and down the central spindle. The additional force increases the speed of revolution required to enable the balls to rise to any predetermined level.
The document discusses different types of steering systems used in automobiles. It describes rack and pinion, recirculating ball, worm and roller, and cam and lever steering systems. It then discusses power steering systems, including hydraulic, electric, and electric hydraulic systems. Electric power steering uses an electric motor to assist steering and can be customized to provide varying levels of assistance depending on driving conditions. While hydraulic systems were traditionally used, electric power steering has benefits like eliminating fluid leakage and being more energy efficient.
This document describes the design and fabrication of a rocker bogie mechanism. The rocker bogie system is a suspension used on Mars rovers to allow independent wheel movement over obstacles. The design includes two rocker arms that allow the left and right wheels to climb obstacles individually. Calculations are shown for tilt angle, wheel base, link lengths, and motor specifications. Components include shafts, links, wheels, bearings, and motors. The advantages of the rocker bogie system include its ability to climb obstacles twice the wheel diameter and distribute load evenly across independently moving wheels.
Linear Control Hard-Disk Read/Write Controller AssignmentIsham Rashik
Classic Hard-Disk Read/Write Head Controller Assignment completed using MATLAB and SIMULINK. To see the diagrams in detail, please download first and zoom it.
Modeling, simulation and control of a robotic armcesarportilla8
This document presents the modeling, simulation, and control of a robotic arm system using a DC motor. It describes the mathematical modeling of the DC motor and robotic arm dynamics. An open-loop simulation is performed to analyze stability and response. A closed-loop system is then designed using a PID controller. Different controller parameters are tested to meet design specifications of less than 5% overshoot, settling time less than 2 seconds, and zero steady-state error. Both P and PID controllers are able to achieve the specifications, with the PID controller providing faster response.
The document describes modeling and simulating DC-DC power converters using MATLAB/Simulink. It presents:
1) Models for basic DC-DC converters like buck, boost, buck-boost and Cuk using state-space equations implemented in Simulink blocks.
2) A procedure for obtaining system models including determining state variables and semiconductor states.
3) Open-loop simulations of the converter models showing inductor current and capacitor voltage responses.
4) A closed-loop simulation of a boost converter using cascaded control with stable output despite line and load variations.
The document summarizes a project to design a controller for a radar antenna. It describes analyzing the plant system, deriving transfer functions, and designing a lead compensator controller. Simulation results in Simulink verified that the designed controller met all specifications, with overshoot of 17% and settling time within 3 seconds. Key steps included: 1) Analyzing the electrical circuit and antenna armature to derive plant transfer functions; 2) Designing a lead compensator controller using typical steps; 3) Building a Simulink model to test the controller design meets specifications for tracking aircraft with minimal error.
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2. DC MOTOR STATESPACE CONTROL
1. Full-state Feedback Controller DC motor Speed.
A. Mathematical Model of DC motor
A common actuator in control systems is the DC motor. It directly provides
rotary motion and, coupled with wheels or drums and cables, can provide
translational motion. The electric circuit of the armature and the free-body
diagram of the rotor are shown in the following figure 1.1:
Figure 1.1 Mathematical Model Dc motor.
(http://ctms.engin.umich.edu)
For this project the following values for the physical parameters already
knowns and listed in tabel 1.1.
Tabel 1.1 Physical Dc motor parameters.
No Parameters Unit
1 Moment of Inertia of the rotor (J) 0.01 kg.m2
2 Motor viscous fricttion constant (b) 0.1 N.m.s
3 Electromotive force constant (Ke) 0.01 V/rad/sec
4 Motor torque constant (Kt) 0.01 N.m/Amp
5 Electrical resistance (R) 1 Ohm
6 Electircal Inductance (L) 0.5 H
3. B. Drive The Equation motion of the system.
B.1 FBD Electrical System.
Figure 1.2 FBD Electrical System
𝑇𝑒 = 𝐾∅𝑖 = 𝐾𝑡 𝑖 Electromagnectic Torque
𝑒 = 𝐾∅𝜔 = 𝐾𝑒 𝜃̇ Armature back e.m.f
𝐿 𝑎
𝑑𝑖
𝑑𝑡
= −𝑅𝑖 + 𝑉 − 𝑒
B.2 FBD Mechanical System
∑ 𝑀 = 0
𝐽
𝑑2
𝜃
𝑑𝑡2
= 𝑇𝑒 − 𝑏
𝑑𝜃
𝑑𝑡
4. C. Drive State-space model of the system
Total Equation Motion of the system :
𝑑2
𝜃
𝑑𝑡2
=
1
𝐽
(𝐾𝑡 𝑖 − 𝑏
𝑑𝜃
𝑑𝑡
)
𝑑𝑖
𝑑𝑡
=
1
𝐿
(−𝑅𝑖 + 𝑉 − 𝐾𝑒
𝑑𝜃
𝑑𝑡
)
The state-space model have the standard form shown below where the
state vector x = 𝜃𝑖̇ and the input for the system is u = V, and the output velocity
which is thetha_dot will be my output desire.
𝑥 = 𝐴𝑥 + 𝐵𝑢
𝑦 = 𝐶𝑥 + 𝑑𝑢
̇
𝑥 =
𝑑
𝑑𝑡
[ 𝜃̇
𝑖
] =
[
−
𝑏
𝐽
𝐾
𝐽
−
𝐾
𝐿
−
𝑅
𝐿]
[ 𝜃̇
𝑖
] + [
0
1
𝐿
] 𝑉
𝑦 = [1 0] [ 𝜃̇
𝑖
]
D. Simulink Model without control
Figure 1.3 Open Loop system Simulink diagram block
5. E. Matlab Commands.
% Define motor Parameters
J = 0.01; % Moment Inertia of the rotor
b = 0.1; % Motor viscous friction constant
K = 0.01; % Electromotive force constant,motor torque
constant
R = 1; % Electrical Resistance
L = 0.5; % Electrical Inductance
% Define motor state variable model
A = [-b/J K/J;-K/L -R/L];
B = [ 0;1/L ];
C = [ 1 0 ];
D = 0;
plot(t,y,'g','linewidth',2);
xlabel('time in second');
ylabel('Angular Velocity (rad/s)');
title('Step respon for Open Loop System');
grid on
F. Plotted result of open loop system
Figure 1.4 Step respon plot for Open loop system
6. By using stepinfo command below, we obtain the performances of the openloop
system.
%Obtain Open-loop Performance
S = stepinfo(sys)
And the result are:
S =
RiseTime: 1.1351
SettlingTime: 2.0652
SettlingMin: 0.0899
SettlingMax: 0.0998
Overshoot: 0
Undershoot: 0
Peak: 0.0998
PeakTime: 3.6758
As you can see , when the system was given an input voltage about 1 Volt, the
motor can only achieved the maximums angular speed about 0.1 rad/sec and
become stable at 3 second, the system has a large steady state error when the final
value of the step input reference was given by default 1 rad/s.
G. Designing the full-stateback controller
Full state feedback (FSF), or pole placement, is a method employed in feedback
control system theory to place the closed-loop poles of a plant in pre-determined
locations in the s-plane. Placing poles is desirable because the location of the poles
corresponds directly to the eigenvalues of the system, which control the
characteristics of the response of the system.
Figure 1.5 Closed Loop Full state feedback controller in state-space model
7. G.1 Design Criteria
For a 1-rad/sec step reference, the design criteria are shown in table 1.2
Table.1.2 Design criteria
G.2 Simulink Block Diagram
The Simulink block diagram are used to get the model and design the pole
placement controller with goal to achieved the design criteria.
Figure 1.6 Simulink Block Diagram State-feedback Controller DC motor.
First Statespace block contains the initial state and output matrix of Dc motor and
the second statespace block contains the estimator matrix where the feedback
matrix came in the form look like this sI - (A - B*Kc) here s is the Laplace variable.
Since the matrices A and B*Kc are both 2x2 matrices, there should be 2 poles for
the system. To eliminate the steady state error we need to adding precompensator
. It could be done by simply using rscale function in matlab command, but in this
project we’ve using gain by the value of ten, so that the output in turn is scaled to
the desired level.
Settling time < 2 second
Overshoot < 5%
Steady-state error < 1%
8. G.3 Matlab Source-Code
Before running the simulink file, the matlab command to define all the parameters
must be done.
% Define motor Parameters
J = 0.01; % Moment Inertia of the rotor
b = 0.1; % Motor viscous friction contant
K = 0.01; % Electromotive force constant, motor torque constant
R = 1; % Electrical Resistance
L = 0.5; % Electrical Inductance
% Define motor state variable model
A = [-b/J K/J;-K/L -R/L]
B = [ 0;1/L ]
C = [ 1 0 ]
D = [ 0]
% check observability
O = obsv(A,C)
rank(O)
% Obtain feedback gain by placing 2 poles with vary value
p1 = -7; % Change based on table 1.3
p2 = -7; % Change based on table 1.3
K = acker(A,B,[p1 p2])
% Define the Estimator statespace
Aes= A-B*K % Change matrix A , the rest still same
sys=ss(Aes,B,C,D);
% plot the root locus
subplot(2,1,1);
pzmap(sys)
% Plotting State Respon with State-Feedback controller
Uncontrolled_system = un;
With_state_feedback = con;
subplot(2,1,2);
plot
(t,Uncontrolled_system,'r',t,With_state_feedback,'b','linewidth',2
);
xlabel('Time in second');
ylabel('Amplitude (rad/s)');
title ('State Respon Uncontrolled VS State-feedback controller')
legend ('Uncontrolled system','With state feedback');
grid on
hold off
% Obtain the system performances
S= stepinfo(con,t)
9. G.4 Vary pole location
To know how the system behave cause of changing of the poles value, we need to
try several poles value. Table 1.3 shown vary poles location.
Table 1.3 Vary poles location
Type of poles Poles 1 Poles 2
Real number same
value
-7 -7
Real number different
value
-6.5 -4.35
Complex number -5+1.5i -5-1.5i
Complex number -3+3.5i -3-3.5i
G.4.1 System respon.
1. The root locus and respon for twin pole (±7) in the real part
Figure 1.7 Root locus and respon with poles place at (±7)
10. The system has performance shown below:
2. The root locus and respon of differents poles (-6.5 and -4.35) in the real part.
Figure 1.8 Root locus and respon with poles place at (-6.5 and -4.35)
The system has performance shown below:
Settling time 0.8359s
Overshoot 0
Steady-state error <1%
Rise time 0.4804
Peak time 3
Settling time 1.1417
Overshoot 0
Steady-state error <1%
Rise time 0.6523
Peak time 3
11. 3. The root locus and respon of complex poles (-5±1.5i)
Figure 1.9 Root locus and respon with poles place at (-5±1.5i)
The system has performance shown below:
Settling time 1.0270
Overshoot 0.0027
Steady-state error <1%
Rise time 0.6069
Peak Time 2.1252
12. The root locus and respon of complex poles (-3±3.5i)
Figure 1.9 Root locus and respon with poles place at (-3±3.5i)
The system has performance shown below:
Settling time 1.3029
Overshoot 6.711
Steady-state error <1%
Rise time 0.4347
Peak Time 0.9252
13. H. Analysis of poles location.
We’ve been simulate and plotted all the poles location in table 1.3 and the result
has shown above. The relationship between the pole location and the specification
of the system are demostrate by figure 1.20 below.
Figure 1.20 pole location in the s-plane
Since horizontal lines on the s-plane are lines of constant imaginary value, they’re
also lines of constant peak time, and the vertical lines on the s-plane are lines of
constant real value, they’re also the lines of constant settling time. As the poles
move in a horizontal direction either right or left, the real part has change and
keeping the imaginary part remain constant. This condition will change the setlling
time performance, as we can see from figure 1.7-1.9, we were changing the poles
location move to the right it caused the settling time performance increased. But at
figure 1.6-1.7 has the same peak time, it maked sense because the system weren’t
having any imajinary part, so the imajinary part remain the same.
Let us now figure out what happens at figure 1.8-19, obviously the system now has
imajinary part, since ζ =cosθ represent overshoot and as we move the poles in
vertical direction its increasing the overshoots because its change the radial position
of θ.
14. 2. Full-state Feedback+ Integrall Controller DC motor Angular Position.
We’ve been created speed controller for Dc motor where the output comes out
from the statespace matrix is velocity. Now we’ll considering controller for angular
position of the rotor. To do that, we take the same model as shown above but we
need some modification through the statespace matrix and the parameters listed in
table 1.4 below to get poper model.
Table 2.1 Phsiycal parameters for Dc motor
No Parameters Unit
1 Moment of Inertia of the rotor (J) 3.2284E-6 kg.m2
2 Motor viscous fricttion constant (b) 3.5077E-6 N.m.s
3 Electromotive force constant (Ke) 0.0274 V/rad/sec
4 Motor torque constant (Kt) 0.0274 N.m/Amp
5 Electrical resistance (R) 4 Ohm
6 Electircal Inductance (L) 2.75E-6 H
A. Drive the state space model for the system
From the main problem, the dynamic equations in state-space form are given below.
𝑑
𝑑𝑡
[
𝜃
𝜃̇
𝑖̇
] =
[
0 1 0
0 −
𝑏
𝐽
𝐾
𝐽
0 −
𝐾
𝐿
−
𝑅
𝐿]
[
𝜃
𝜃̇
𝑖̇
] + [
0
0
1
𝐿
] 𝑉
𝑦 = [1 0 0] [
𝜃
𝜃̇
𝑖̇
]
For the initial respon from the system is pretty close the same with Dc motor speed
shown in sub section D until F with all we need just change the matrices
composition into 3x3 matrices and we good to go. The respon of uncotrolled system
shown in figure 1.21 below :
15. Figure 2.1 Respon the angular position of rotor without controller
As we can see, its seem like the amplitude of the angular position goes to the infinity
. The system performance listed below :
S =
Rise time : 0.0344 Settling time: 0.0493
Overshoot : 0 Peak time : 0.05
B. Designing the full-stateback controller
The control law for a full-state feedback system has the form u =r –K*x , the
characteristic polynomial for this closed-loop system os the derminant of sI-(A-
B*K) where s is the laplace variable, the associated block diagram is given by
figure1.5. Since the matrices of A and B*K are both 3x3 matices, it should be 3
poles exist in the system. Before we create the controller we need to verify our
system is controllable or not, by checking through the system order and its
deteminant. For this case the design criteria and the vary poles location has given
by table 2.1. and table 2.2
Table 2.1 Given Design Criteria with a 1-radian step reference
Settling time < 2 second
Overshoot < 5%
Steady-state error < 1%
16. Table 2.2 Vary poles location
C. Disturbance Respon
In order to observe the system’s disturbance response, we must provide the proper
input to the system. In this case, a disturbance will fit as a physically a load torque
that acts on the inertia of the motor. This load torque acts as an additive term in the
second state equation. We can simulate this by modifying our close-loop input
matrix, to have a 1/J in the second row what will act like our current input is only
the disturbance. We can perform this by define the B matrices in matlab command
below, so it can be use to simulate the whole system through our simulink file.
C.1 Simulink block Diagram
Figure 2.2 Dc motor position block diagram with feedback and disturbance
C.2 Matlab Source-Code
% Define motor Parameters
J = 3.2284E-6; % Moment Inertia of the rotor
b = 3.5077E-6; % Motor viscous friction contant
K = 0.0274; % Electromotive force constant, motor torque
R = 4; % Electrical Resistance
L = 2.75E-6; % Electrical Inductance
Type of poles Poles 1 Poles 2 Pole 3
Real number same
value
-450 -450 -450
Real number different
value
-735 -567 -325
Complex number -255+50i -255-50i -100
Complex number -100+100i -100-100i -200
17. % Define motor state variable model
A = [0 1 0; 0 -b/J K/J; 0 -K/L -R/L]
B = [0 ; 0 ; 1/L]
C = [1 0 0]
D = [0]
% check observability and controllable
determinant = det(ctrb(A,B))
O = obsv(A,C);
rank(O)
% Obtain feedback gain by placing 3 poles with vary value
p1 = -450; % Change based on table 2.2
p2 = -450; % Change based on table 2.2
p3 = -450; % Change based on table 2.2
K = place(A,B,[p1, p2, p3])
% Modifying the close-loop input matrix B
F = A-B*K % state feed back A matrices
Bd = [0; 1/J ; 0] % Disturbance input matrices, the rest are still
same.
% Plotting State Respon with State-Feedback controller
Disturbance = con;
plot (t,Disturbance,'linewidth',2 );
xlabel('Time in second');
ylabel('Amplitude (rad)');
title ('Disturbance respon of rotor angular position')
grid on
% Obtain the system performances
S= stepinfo(con,t)
18. D. Plotted result for disturbance respon and vary poles location
1. The Disturbance and feedback respon when same poles place
at (-450)
Figure 2.3 Disturbance respon of rotor angular position
at poles location (-450)
The system performance listed below :
S =
Rise time : 0.0092 Settling time: 0.0159
Overshoot : 0 Peak time : 0.05
19. 2. The Disturbance and feedback respon when differents poles place
at (-735 -567 -325).
Figure 2.3 Disturbance respon of rotor angular position
at poles location (-735 ,-567, -325).
The system performance listed below :
S =
Rise time : 0.0089 Settling time: 3.3984
Overshoot : 0 Peak time : 0.05
20. 3. The Disturbance and feedback respon when complex poles place
at (-255+50i, -255-50i, -100).
Figure 2.4 Disturbance respon of rotor angular position
at poles location (-255+50i, -255-50i, -100).
The system performance listed below :
S =
Rise time : 0.0248 Settling time: 0.0414
Overshoot : 0 Peak time : 0.05
21. 4. The Disturbance and feedback respon when complex poles place
at (-100+100i, -100-100i -200).
Figure 2.5 Disturbance respon of rotor angular position
at poles location (-100+100i, -100-100i, -200).
The system performance listed below :
S =
Rise time : 0.018 Settling time: 0.0382
Overshoot : 0 2.1132 Peak time : 0.00359
E. Adding integral action
Putting an extra integrator in series with the plant it can remove the steady-state
error due to a step reference. If the integrator comes before the injection of the
disturbance, it will also cancel a step disturbance input in steady state. the associated
block diagram is given by figure 2.4.
22. Figure 2.6 Associated block diagram for series adding integral with the plant
We can model the addition of this integrator by augmenting our state equations with
an extra state for the integral of the error which we will identify with the variable
w. This adds an extra state equation, where the derivative of this state is then just
the error, e = y - r where y = theta. This equation will be placed at the bottom of
our matrices. The reference r, therefore, now appears as an additional input to our
system. We’re gonna need to rebuilt the estimator block in figure 2.1 into
augmented block by implemented the new 4x4 matrices shown below.
The augmented additional integrator state are represent by matrices Aa, Ba, Ca and
Da. In order to find the closed-loop equations, all we need to do is to look at how
the step input, affects the plant. In this case, it affects the system in exactly the same
23. manner as in the unaugmented equations except now u = -Kc x - Ki w. We can also
rewrite this in terms of our augmented state as u = -Ka xa where Ka = [ Kc Ki ].
Substituting this u into the equations above provides the following closed-loop
equations.
𝑋̇ 𝑎 = (𝐴 𝑎 − 𝐵𝑎 𝐾𝑎)𝑥 𝑎 + 𝐵𝑟 𝑟
𝑦 = 𝐶 𝑎 𝑥 𝑎
As we can see the integral of the error will fed back again, then it would eliminate
the steady state error goes to zero. Since the augmented matrices has 4x4 form,it
should have 4 poles inside, moreover we need to adding fourth pole into the system
we will use -600.
E.2 Matlab Source-Code
We used the same simulink block in figure 2.2 then we change all the parameters
based on the matlab command below.
% Obtain augmented 4x4 state matrices Aa, Ba, Ca, Da
Aa = [0 1 0 0; 0 -b/J K/J 0 ; 0 -K/L -R/L 0; 1 0 0 0];
Ba = [0 ; 0 ; 1/L ; 0 ];
Br = [0 ; 0 ; 0; -1];
Ca = [1 0 0 0];
Da = [0];
% Obtain feedback gain by placing 4 poles and other poles same as
before
p1 = -100+100i;
p2 = -100-100i;
p3 = -200;
p4 = -600;
Ka = acker(Aa,Ba,[p1, p2, p3,p4])
% Define the augmanted statespace
G = Aa-Ba*Ka
H = Br
I = Ca
J = Da
% Plotting State Respon with State-Feedback controller
integral = con;
plot (t,integral,'','linewidth',2 );
xlabel('Time in second');
ylabel('Amplitude (rad)');
ylim([0 1.05]);
title ('Rotor respon with Adding integral action')
grid on
% Obtain the system performances
S= stepinfo(con,t)
24. F. Plotted result for adding integral action
Figure 2.6 Disturbance respon of rotor angular position
at poles location (-100+100i, -100-100i, -200, -600).
The system performance listed below :
S =
Rise time : 0.0196 Settling time: 0.0331
Overshoot : 1.0634 Peak time : 0.0413
G. Analysis of poles location.
The effect of varying poles location it seem pretty close the same with case of
created controller for Dc motor speed. When we gave the system with real poles
move further to the left it will change the setlling time of the system, since we only
had poles in real part, no matter how far we drag it to the left the peak time of the
system will be the same due to constant imajinary part of the system. The inversly
for peak time, peak time only change when we drag the poles vertically since now
the imajinary axis take a part. But when we move the poles diagonaly since the 𝜔𝑛
is fuction of radial distance from the origin, it will increase the system frequency
while the envelope of the system remains the same. The number of imajinary part
25. in poles also effect the overshoot of the system since the overshoot is a fuction of
zheta. Adding extra integral will remove the steady state error of the system,
obviously this could happens because when we add integral in series with the plant,
it change the whole system type. Since steady state-state error are depend upon the
number ontegration in the forward path. We already know, since we define the
system type to be the value of n in the denominator or eqivalently, the number of
pure integration in the forward path. Therefore,a system with n = 0 is a Type 0
system. If n = 1 or n = 2, the coressponding system is a type 1 or type 2 system.
Thats why when we adding integral the type of system change into type 1 or 2 when
we know the value of steady state error with step input u(t) would be zero.