NAMIBIA UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF MECHANICAL AND MARINE ENGINEERING
BACHELOR OF ENGINEERING
ELECTRICAL POWER AND MECHANICAL ENGINEERING
SYSTEMS MODELLING 315 (SYM710S)
DETAILED WORKSHEET OF SEMESTER PROJECT
PENDULUM ON A CART
Date of Submission: 26/03/2018
Name: Namwandi Julius S.H215087313
Van Kent Ieuan213104938
Mr. T. Kaputu
Table of Contents
TOC o “1-3” h z u Introduction PAGEREF _Toc511650106 h 1Literature Review PAGEREF _Toc511650107 h 2Objectives PAGEREF _Toc511650108 h 2Motivation PAGEREF _Toc511650109 h 3Work plan PAGEREF _Toc511650110 h 3List of components PAGEREF _Toc511650111 h 4Budget PAGEREF _Toc511650112 h 4Conclusion PAGEREF _Toc511650113 h 5Bibliography PAGEREF _Toc511650114 h 5References PAGEREF _Toc511650115 h 5Appendix PAGEREF _Toc511650116 h 5Appendix A: worksheet PAGEREF _Toc511650117 h 5
IntroductionAlmost everyone has once tried to balance broom stick on their finger or palm of their hand. The balancing was made easier by moving your hand up, down, left to right. Our project can to relate the same principals involved. As the cart will act as your hand and the inverted pendulum as the broom stick. An inverted pendulum is a pendulum that has its centre of mass above its pivot point. A simple diagram is shown below in figure 1. For this project purpose, an inverted pendulum is mounted on a cart acted upon by an applied force. The purpose for this project was to set up the modelling and designs of the control and mechanical systems.
This project report will have a full in-depth of all the and all the expected results about the control of the inverted pendulum on a cart. This inverted pendulum on a cart system has been proposed as a suitable State space demonstration and experimentation device that is solvable using engineering tools such as MATLAB to give an aid in the process of modeling and analyzing data. An inverted pendulum is one in which the center of mass is above the axis of rotation or pivot point. It is major application is in dynamics and control system, and it is widely used in testing control algorithms (PID). It is a very common control theory problem. This project will consist of three main section namely, the controller, feedback network and the mechanical system. The inverted pendulum has characteristics of being unstable, thus needs balance for it to remain stable. This is achieved by making use of feedback network. To achieve the balancing concept, a proportional integral derivative (PID) controller is used as the closed loop feedback for the system. The most important scenario is when a pendulum is placed on a cart which can move left and right in a linear direction. The pendulum is then maintained balanced in an upright position by moving the cart in the linear direction. In this proposal, the modeling and obtaining of physical materials will be discussed. The main focus is to build a low cost but yet easy to design inverted pendulum that can be easily adopted by other students to enhance their design and control theory practices.
Figure SEQ Figure * ARABIC 1
Literature ReviewThis project due to its modularity can be broken down into multiple sub-systems as in figure. However, it is important the way these various sub systems interact with each other should be kept in mind, this is because each module can be solved on its own but will influence the other modules in the system. As a result, this can lead to undesirable outputs and failure of intended tasks. We have classified our project into four different sub-systems namely, PC for user interface, controller system, mechanical system and the feedback network. PC user interface will be made user friendly so that operation of project can be simple. The controller system will contain a microprocessor(Arduino) this will be the main part of the control system. Arduino UNO is commonly used type of micro controller (also called Atmega328). It contains 14 digital input/output pins and 6 analog pins. Other features include a 14MHz ceramic resonator, a USB connector, power jack and a reset button. The Arduino operates at a voltage of 5V. The mechanical system will contain most of the components. This is where the cart, pendulum and motors will be placed.
2667001394460Figure 2Figure 2286542156512500366212763151700431482542291035718754133852266950403860113347539433523717251061085Feedback network
4591050241935Pendulum and cart
0Pendulum and cart
3038475137160Motor controlcircuit00Motor controlcircuit1581150260985Controller
ObjectivesThe main purpose of this project is to analyses the working of a product or mechanical body known as a Pendulum which is mounted on a cart, in addition to that the other main objective is to design a pendulum on a cart control system and in the process, use the tools and methods needed to achieve the required designed control system. The tools mention earlier is to learn how to use Mathematica to run systems analysis. The second method is to understand and verify the concept of stability and its properties in a dynamic system.
Firstly, the Mathematical approach being used to run system analysis makes use of differential equations being solved using a method or a tool known as the Laplace transform to transform equations in the t domain to those in the s domain. This is necessary because it appears in the description of linear time invariant systems, where it changes convolution operators into multiplication operators and allows defining the transfer function of a system.
Secondly, the verification of the concepts of stability and its properties, this method uses the concept of center of mass, which means the pendulum has it center of mass above the pivot point and it will fall if there is no additional help to keep the pendulum stable and balanced. The angles of degree of freedom are to be taken into account. There are other methods as well of stabilization of a non-linear control system such as the Immersion and Invariance method (I&I) which looks at the notions of system immersion and manifold invariance and, in principle.
Since the Cart-Pendulum is a non- linear control system the control objective is to control the system such that when the cart reaches a desired position the inverted pendulum stabilizes in the upright position, by using specific controllers such as the PID, LQR and MPC for controlling the system. The final objective is to use the engineering software known as MATLAB & Simulink for the simulations of the control system as well as analyze its working and functions that are required for it to perform.
MotivationAs engineering students, we always felt the need to do more practical work to learn more about a specific field, to test our knowledge and to be exposed to what can be expected of us in a few years. We saw the inverted pendulum on a cart as a big opportunity to learn while we design and build an autonomous device, its autonomous operation requirements. This will help us get a broad knowledge on control design implementation, and this will allow us to easily incorporate the control design within the hardware and the software architecture. We the students went to do the research through reading of journals on the modeling, designing and controlling mechanism of an invented pendulum system and came up with a report. As third year engineering students we have already achieved broad background in many field in Electrical Engineering, Mechanical Engineering and computer engineering. This includes, but not limited, the micro controller design, Digital signal processing, control theory, project management and mechanical design. For the course SYM710S (Systems modeling), different techniques from various fields will be used to create the system.
Work planEvery project has time plan because we have been given a limited time frame to complete our project. The work schedule will help to as not to fall behind and prioritize our work. For bigger companies, a time plan will reduce idle time or ordering parts that will not be used at that time. A well-designed work plan also helps to keep the work team up-to-date and well organized. For this project, a time plan will mean was drawn up to ensure that the project is completed and delivered on time. It will also help us to keep up and manage the pressure that the project will generate.
List of components1x Micro-controller (Arduino)
2x DC motor
1x motor driver(L298N)
Wires and additional PCB board
2x power supply’s
BudgetComponent Estimated Cost
Micro-controller (arduino) Free
motor driver(L298N) N$ 60.00
DC motor Free
Running gear Free (recycled materials)
Wheels N$ 20.00
Chassis Price still to be determined
Wires and additional PCB board Free
Power supply Free
Steel Cable Free (recycled materials)
Total Still to be determined
One of the aims of this project is to use as much recycled materials and pre-existing source components as possible to keep our budget low.
From the journals we have gone through give a lot of insight to the project in fact there is a lot of information to base the design of the Pendulum on a cart. The goal of the project report is to lay down a frame work and be guideline for a system that is feasible in the real world and can be brought from the “drawing board” and be implemented in the real world. Often when designing there can be little insight to the deliverables of the project. This can be influenced by a large number of factors such as financial constraints and availability of components, just to name a couple. Ultimately this can lead to the failure project. This makes systems modeling such an important aspect of the design process, for the overall success of the project.
BibliographyReferencesElisa Sara Varghese, Anju K Vincent and V Bagyaveereswaran, Optimal control of inverted pendulum system using PID controller, LQR and MPC
Alessandro Astolfi, Senior Member, IEEE, and Romeo Ortega, Fellow, IEEE Immersion and Invariance: A New Toolfor Stabilization and Adaptive Control of Nonlinear Systems
Franklin; et al. (2005). Feedback control of dynamic systems, 5, Prentice Hall. ISBN 0-13-149930-0http://exploration.grc.nasa.gov/education/rocket/rktstab.html
AppendixAppendix A: worksheetWeek Date Task Deligated group member(s) Completed Sign-atureWEEK 1 26/03/18 Research (Journals ; Puplications)
Make WhatsApp group Albertina (executive summary)
Wilfred (literature review)
Hillary (design description)
Julius(WhatsApp group) 29/03/18 Meeting (To choose a preliminary model) All Group members 30/03/18 Mathematical modeling Albertina
Wilfred 31/03/18 01/04/18 Type progress report 1 Hillary
Julius WEEK 2 02/04/18 Resarch programs used for design
Materials (selection ; testing) Jose
Ieuan03/04/18 04/04/18 05/04/18 06/04/18 Research control ; feedback mechanism IeuanFestus 07/04/18 Start typing final Report Albertina
Hillary 08/04/18 Type progress report 2 Albertina
WEEK 3 09/04/18 MATLAB ; Simulink (simulations) Wilfred
Ieuan10/04/18 11/04/18 Meeting (Prepare for final presentation) All Group members 12/04/18 13/04/18 preparation of report All Group members 14/04/18 15/04/18 Final project proposal All Group members