Past_Controls_Project

Past_Controls_Project - EE 3530 Ball & Beam...

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Unformatted text preview: EE 3530 Ball & Beam Project Table of Contents Page 1. Introduction...3 2. Model Specifications......4 3. Inner Loop Analysis.......4 4. Outer Loop Analysis...7 5. First Simulation..9 6. Second Simulation..11 7. Ideal case Simulation.13 8. Actual Controller Implementation.15 9. Post Lab Questions.18 I.Introduction The ball and beam system is one of the most enduringly popular and important laboratory models for teaching control systems engineering. The ball and beam system consists of a long beam which can be tilted by a servo or electric motor together with a ball rolling back and forth on top of the beam. The significance of the ball and beam system is that it is a simple system which is open-loop unstable. Even if the beam is restricted to be very nearly horizontal, without active feedback, it will swing to one side or the other, and the ball will roll off the end of the beam. To stabilize the ball, a control system which measures the position of the ball and adjusts the beam accordingly must be used. In two dimensions, the ball and beam system becomes the ball and plate system, where a ball rolls on top of a plate whose inclination can be adjusted by tilting it frontwards, backwards, leftwards, or rightwards. The objective of this experiment was to design the controller for the ball and beam module such that the position of the ball accurately tracks a defined path. This project will also help the student to understand how to mathematically model a ball and beam system, how to linearize the model about an operating point and ultimately how to design and simulate a controller for the system. Figure1. Ball & Beam Module II. Model Specifications The controller to be was designed by implementing two independent control loops. The Inner loop and the Outer loop. The function of the inner loop was to control the position of the servo gear to a commanded angle while the purpose of the outer loop was to control the position of the ball on the beam by manipulating the servo angle. The design of the controller needs the inner loop to be a lot faster than the outer loop to make sure there was no interference with the ball controller dynamics by the servo plant dynamics. The time specifications for the loops in the model are shown in the table below: Time to peak (Tp) Damping Ratio () Natural Frequency (Wn) Percent Overshoot (%OS) Inner Loop 0.200 s 0.707 22.2 rd/s 4.6% Outer Loop 1.5 s 0.707 2.96 rd/s 4.6% Outer Loop 1S 0.6 3.92 rd/s 10% Table 1: Controller time Specifications III. Inner Loop Analysis Fig 2: Inner Loop Controller Schematic The transfer function for the ball and beam module with all the model parameters entered is...
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Past_Controls_Project - EE 3530 Ball & Beam...

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