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Unformatted text preview: SRV02Series Rotary Experiment # 3 Ball & Beam LSU, EE3530, Fall 2008 Student Handout SRV02Series Rotary Experiment # 3 Ball & Beam Student Handout 1. Objectives The objective in this experiment is to design a controller for the ball and beam module such that the position of the ball accurately tracks a defined path. Upon completion of the exercise, you should have have experience in the following: • How to mathematically model the Ball & Beam system. • To linearize the model about an operating point. • To control the position of the ball on the track by manipulating the servo angle. • To design and simulate a controller for the system. 2. System Requirements To complete this Lab, the following hardware is required: [1] Quanser UPM 2405/1503 Power Module or equivalent. [1] Quanser MultiQ PCI / MQ3 or equivalent. [1] Quanser SRV02E(T) servo plant. [1] Quanser BB01 – Ball & Beam Module. [1] Quanser SS01 – Remote Sensor ( Optional). [1] PC equipped with the required software. • The required configuration of this experiment is the SRV02E(T) in the HighGear configuration with a UPM 2405/1503 power module and a suggested gain cable of 1 . • • It is also assumed that all the sensors and actuators are connected as per dictated in the Experiment #0 as well as the SRV02 User Manual and the Ball & Beam User Manual. Page # 2 Revision: 01 3. Mathematical Model Figure 1 below depicts the Ball and Beam module coupled to the SRV02 plant in the correct configuration. The beam 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 position of the ball is obtained by measuring the voltage at the steel rod. When the ball rolls along the track, it acts as a wiper similar to a potentiometer resulting in the position of the ball. The following table is a list of the nomenclature used is the following illustration and derivations. Symbol Description Symbol Description L Beam Length (L = 16.75 in) r Lever arm offset (r = 1 in) x Ball Position m Mass of the ball α Beam pitch (radians) R Radius of the ball θ Servo load gear angle (radians) J Ball's moment of inertia F tx Translational force on the Ball F rx Rotational force on the ball g Earth's gravitational constant Page # 3 Revision: 01 Figure 1 Ball & Beam Module Let us begin by examining the forces acting on the ball. We have the translational force due to gravity, and we have a rotational force due to the torque produced by the rotational acceleration of the ball. The 2 forces are: Gravitational force in the xdirection: F tx = m g sin [3.1] The torque produced by the ball's rotational motion is equal to the radius of the ball multiplied by the rotational force (opposing the direction of travel). Using Newton's 2 nd equation of motion, we also know that the torque is equal to the ball's moment of inertia multiplied by its angular acceleration, which then can be written as its moment of inertia multiplied by the doublederivative of its translational motion (...
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This note was uploaded on 02/06/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.
 Fall '07
 Chen

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