Motion Of Train Control System
Syed Zulfiqar Haider Bukhari(11TC51)1,Syed Noor-ul-Hassan Bukhari(11TC63)2
Department of Telecommunication Engineering, University College of Engineering & Technology, The Islamia University of Bahawalpur, Pakistan. engr.szhb@gmail.com1, syednoorulhassanbukhari@gmail.com2

Abstract— This project Automatic Street Light Control System aims at designing and executing the advanced development in embedded systems for energy saving of street lights by using light dependent resistor (LDR). Nowadays, human has become too busy and he is unable to find time even to switch the lights on or off. This can be seen more effectively in the case of street lights. The present system is like, the street lights will be switched on in the evening before the sun sets and they are switched off the next day morning after there is sufficient light on the roads. But the actual timing for these street lights to be switched on are when there is absolute darkness on the roads. This project gives the best solution for electrical power Keywords—: Small Toy train system (STTS), Small Toy Train System-Railway Track(STTS-RT)

I. INTRODUCTION rain system has become very popular means for transportation of passengers and exchanging goods from one place to another in this modern era. Every developing country use the train system for these purposes. Thousands of people travel by the train system hundreds of miles far from one destination to another destination in a day. Even that the train system is also used for the purposes of import and export e.g. Oil and LPG gas cylinders and many other goods are imported and exported among the international levels. Train system can travel on specific railway track path which are linked with every cities, districts, provinces or countries called Railway station or Railway junction. The train consist of engine, number of coaches, rolling wheels which travel on the railway track and lot of other machinery. Research indicate the motion of the train system. First we will examine the output velocity of the train system by the simulation and will also see the output velocity of the same system by the PID controller and we will compare the response. Here we discuss the small such as a toy train system. This system consist of an engine, one coach and rolling wheel on the track. We consider that the train is travelling in one particular direction as shown in figure 1.

II. SYSTEM DESIGN We should control the train motion so that it run smoothly with constant speed and stop carefully. Let’s suppose that there are two masses Me and Mc. Me is mass of engine in kilograms and Mc is the mass of coach in kilograms of the STTS. These two masses Me & Mc are bounded together with help of spring having the coefficient of the stiffness ‘K’. Mass Mc is held behind the Me as shown in figure 2. There is rolling friction between the rolling wheels of two masses of the STTS and STTS-RT which is represented by Greek letter mu (µ). The rolling Wheels of the STTS run on the STTS-RT with some gravitational acceleration g which is equal to the constant value (g=9.8 m/sec).Therefor the total damping effect between STTS and STTS-RT is equal to µMngs. Where Mn will be equal to Me (mass of engine) or Mc(mass of coach) as shown in figure 2.

Figure: 2. Systemic Diagram

(a) DIFFERENTIAL EQUATIONS APPROCH To get the right approach of differential equation of STTS, we can use the free body diagram which help us to make the transfer function. The free body diagrams are given in Figure 3(a) & (b).

Figure:3 Free Body Diagram

As we know that the product of mass times its acceleration is equal to sum of applied forces acting on that mass (Newton’s Law of Motion). The following forces are acted on mass Me

all parameters which are used above. The parameters values are given in the following table.1. Table:1

 The force of inertia  friction between the running wheel and the STTS-RT.  spring between the mass Me and Mc  The applied force by the engine. as shown in figure 3(a). 04 K 5N/m The following forces are acted on mass Mc..  The force of inertia.  Friction between the running wheel and the STTS05 g 9.8ms-2 RT.  Spring between the mass Me and Mc. 06 F 5N as shown in figure 3(b) Further that gravitational acceleration g is cancelled Now by using these values the transfer function by by the normal applied force by earth ground. So that the effect of vertical acceleration will be nothing. In other words none of using MATLAB is given below. 2.5 s^2 + 0.245 s + 5 the acceleration in vertical direction. The train will move in ---------------------------------------------the horizontal direction. Thus the equation of motion will 12.5 s^3 + 2.45 s^2 + 37.62 s + 3.675 become following. (b) STATE SPACE REPRESENTATION “State space representation is a mathematical model of the physical system as the set of input and state variables related by first order differential equation.” After obtaining the transfer function we will focus the state space representation of the equation of motion.

Sr# 01 02 03

Parameters Mass of Engine Mass of Coach Coefficient of Rolling Friction Coefficient of Stiffness Gravitational Acceleration Applied force By the Engine

Symbol Me Mc µ

Value 5kg 2.5kg 0.01sec/m

To obtain the transfer function, first of all Laplace transformation of above differential equation of the motion required. Which is given bellow.

Consider that train is moving in horizontal direction when the applied force of the engine F(s) act upon it. The output Y(s) is the velocity of the engine Ve(s) which will be equal to sX1(s).

As we know that the transfer function is the relation between the output & the input. Thus by considering the initial condition must zero, the transfer function of the STTS will be equal to There is an important step to represent the state space in MATLAB. As we know that MATLAB cannot manipulate the symbolic variable. Therefore we assume the numerical values of all parameters which are given in table 1. Now by using these values for these parameters in MATLAB the state space is given below.

a=
Figure: 4 Transfer function To ensure the MATLAB representation. MATLAB cannot manipulate the symbolic variables. Therefor we have to assume the numerical values to the symbolic variables for

x1 x2 x3 x4 b=

x1 x2 0 1 -1 -0.098 0 0 2 0

x3 x4 0 0 1 0 0 1 -2 -0.098

x1 x2 x3 x4 c= y1 d= y1

u1 0 0.2 0 0 x1 x2 x3 x4 0 1 0 0 u1 0

By the state space result we
II. SIMULATION IN MATLAB

III. PID CONTROLAR

IV. COMPRESSION

V. CONCLUSION

ACKNOWLEDGMENT We wish to thank all our respected teachers and friends for their excellent contribution and support for the completion of this project. Specially we are very much thankful to Dr. Mohammad Mukhtar the Vice Chancellor of the university, and Professor Jan Mohammad Keerio the Principal of UCET, for their efforts to facilitate and provide us most suitable environment for research and development.

REFERENCES
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