# Ball and beam transfer function pdf

Therefore, we will require some method of controlling the ball. In the next few sections, the timebased motion equations are developed. Motion equations for the ball and beam and the ball and arc. The transfer function for the ball and beam module with all. The ball and beam dynamics are nonlinear in nature, however, using a. So the transfer function becomes as shown in equation 1. Recall from reference 7, that the srv02 voltagetoload angle transfer function is pss k. Among the interesting challenges of such a system is the indirect control of the ball using the angles of the plate. Experimental control design for ball and beam system published on jul 17, 20 the aim of the project is to control the position of the ball placed on a beam tilting on both sides using control. May 27, 2016 here considering the beam angle of servo motor and designing controllers to control the ball position. Ball and beam plant can be used for a wide range of control system design implementations from basic linear controllers to advance nonlinear methods. Srv02 ball and beam control laboratory student manual.

The 1dbb transfer function describes the displacement of the ball with respect to the load angle of the servo. Modelling and control of ball and beam system using pid. The ball and beam system can usually be found in most university control labs since it is relatively. Consider the free body diagram of the ball and beam system shown in figure 4. Ball and beam control system simulation with simulink ball and beam control system simulation with.

A free body diagram of the physical ball and beam system. The ball and beam module consists of a steel rod in parallel with a nickelchromium, wirewound resistor forming the track on which the metal ball is free to roll. The bb01 transfer function describes the displacement of the ball with respect to the load angle of. Assume the ball is light with massm much smaller than the mass m of the beam, the beam will stay close to level when in operation, the rotational effects of the ball are negligible, and the friction of. This project aims to balance the ball on the plate at the centre or predefined coordinate by. Ball and beam control system simulation with simulink 3d. The ball plate system is an unstable openloop and nonlinear system having 2 degrees of freedom dof. The ball and beam system is laboratory equipment with high nonlinearity in its dynamics. The main ideas of the paper are to model the ball and beam system considering nonlinear factors and coupling effect and to design proportional integral derivative pid controller to control the ball position. Model of the ball position with respect to the beam angle hxs the total transfer function from the input voltage to the voltage that indicates the ball position is then. Third international conference on advances in control and optimization of dynamical systems march 15, 2014.

Ball on plate balancing system progress report for ecse4962. In order to design a controller for the ball and beam system, a transfer function for the system was derived. Design and implementation of ball and beam system using pid. Control of a ball and beam system mechanical engineering. The objective of ball balancing on a beam is to use an actuator to command a tilt angle on the beam and balance the ball, which rolls in one dimension along the beam, at different reference locations, as prescribed the user. It consists of rigid beam which is free to rotate in the vertical plane at the pivot, with a solid ball.

Modeling and control of ball and beam system using model based and nonmodel based control approaches article pdf available in international journal on smart sensing and intelligent systems 51. Presently, most derivations of the equations of motion for the ball and beam and ball and arc systems model the ball as a point mass. If you refer to any of the pid control problem for continuous systems, the pid transfer function was expressed as 2 as you noticed the above transfer function was written in terms of. The purpose of this project was to control ball position on a beam by varying the angle of a servo gear connected to the beam through a lever arm. The transfer function for the ball and beam module with all the model from ee 3530 at louisiana state university. The quanser ball and beam module consists of a track on which the metal ball is free to roll. Ball and beam workbook university of central florida. The ball and beam lagrange function have the equation of transfer function. First, a transfer function for the ball and beam was derived relating an input of theta to a ball position x. Modelling and control of ball and beam system using coefficient. One side of the beam is attached to a lever arm that can be coupled to the load.

For the ball and beam system shown determine the transfer function relationship xsqs between ball position xt and motor positionqt. Experimental control design for ball and beam system issuu. Digital pid controller discrete transfer function openloop response proportional control proportionalderivative control. Pdf the ball and beam system is laboratory equipment with high nonlinearity in. Modeling and control of ball and beam system using model based and nonmodel based control approaches article pdf available in international journal. The relationship between the input voltage and the angle of the beam is defined by the dc motor transfer. The track is effectively a potentiometer, outputting a voltage thats proportional to the position of the ball.

Ball and beam system dynamics definitions prior to commencing with the derivation of the dynamics we will make a few definitions. Ball and beam position control using quarc student manual. For the love of physics walter lewin may 16, 2011 duration. Lagrange approach is used to find the ball position of the system. Kanpur, india modelling and control of ball and beam system using coefficient diagram method cdm based pid controller b. Ball and beam balance final report tom trapp and wil selby department of mechanical engineering. A linear differential equation describing the dynamic of the ball and beam to model transfer function. The track is fitted with a linear transducer to measure the position of the ball, i. File name description 09 ball and beam user manual. Modelling the ballandbeam system from newtonian mechanics. Modelling and control of ball and beam system using. The ball and beam system can usually be found in most university control labs since it is relatively easy to build, model and control theoretically. Insert a transfer function block from the linear block library to the left of the ball and beam block, and connect its output to the input of the ball and beam block.

Ball and beam system dynamics mechanical engineering. Engineering 58control theory and design final projectball. On rearranging, the transfer function of the ball positionrs. In this paper, a complete physical system and controller design is. In the next few sections, the timebased motion equations are developed and, from these equations of motion, its transfer function is obtained. Introduction system modeling is an extremely important part of the control system design process. Jul 02, 2014 balancing of a ball on beam using arduino as a pid controller. The ball position is unstable in open loop, and so a feedback loop is usually. Control of a ball and beam system university of adelaide. Mathematical modeling, simulation and control of ball and. Bb01 control ball and beam position control using quarc student. Pdf modelling and control of ball and beam system using pid.

Ball and beam realize control theory with acrome ball and beam. System analysis system model the transfer function from the gear angle. Implementation of a pid controller for a ball and beam system, running in matlab. Table 1 below lists and describes the various files supplied with the srv02 ball and beam position control laboratory. The bb01 transfer function describes the displacement of the ball with respect to the load angle of the servo. Taking the laplace transform of the equation above, the following equation is found. Bring up your openloop ball and beam model window or download ours here delete the line which connects the step block to the ball and beam model block. Ball and beam srv02 pv vi v to degrees ets e mm 0p 3. The system includes a ball, a beam, a motor and several sensors. The transfer function for the ball and beam module with. We created three different pd controllers, one was underdamped, one was optimally damped 7, and one was overdamped. Pdf modeling and control of ball and beam system using. Rosales submitted to the department of mechanical engineering on may 7, 2004 in partial fulfillment of the requirements for the degree of bachelor of science in mechanical engineering abstract an apparatus of the classical ball on beam problem was designed and constructed to be.

Introduction the ball and beam system is a simple mechanical system which usually difficult to control. Pdf design and implementation of ball and beam system using. The ball and beam balance problem is a classic open loop unstable system. For low frequencies, the transfer functions are therefore approximately given by. The nxp development platform lcp1768 works as an acquisition and a signal c.

The complete derivation can be seen in appendix 1 and the final transfer function is shown in equation 1 below. Fixed parameters lm is the length of the beam, d m is the distance from the pivot to the plane of ball contact on the beam, dm is the distance from the pivot to the centre of mass of the beam. In addition to the plate system, a model for the ball dynamics must be developed as well. In this digital control version of the ball and beam experiment, we are going to use the pid control method to design the digital controller. Balancing of a ball on beam using arduino as a pid controller. The first part with the feedback loop is representative of the dc motor dynamics and the next block corresponds to the ball on beam balancer transfer function.

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