Me 303 Term Project - ME303TermProject...

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ME 303 Term Project Control of a Spring Mass System Project Team Muhsincan Şeşen Cem Akkartal Mehmet Onur Korkut Can Palaz Irmak Kip Süleyman Çağrı Çağlar Introduction
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In this project, several control mechanisms for two masses and a  spring system will be designed. First mass will be connected to a motor  and its position will be directly controlled by input current. The second  mass will be connected to the first mass by a spring and its position will  be   the   output   of   the   system.     System   control   mechanisms   will   be  designed   using   both   the   transfer   function   and   the   state-space  representation   of   the   model.   Control   designs   in   frequency-response,  root-locus and state-space domains will be considered.  Physical Configuration of the System Physical configuration of the system include two masses, a spring,  a DC motor, DSpace Connecter Panel, motor driver card, power source,  two   rail   systems,   two   gears   connected   by   a   trigger   belt   and   a  potentiometer. DC motor is coupled with the first gear and the first gear  is connected to the second gear by the trigger belt. Thus rotational  motion is converted to linear motion along the trigger belt. Then the  trigger   belt   is   coupled   with   the   first   mass.   The   first   mass   is   then  connected to the second mass with a spring and position of the second  is mass is calculated through the potentiometer.  Mathematical Representation of the System To begin; rotational motion of the motor is converted to linear  motion through Where;
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   is the inertia of all the gears and motor as a whole.  is the damping of all the gears, belt and motor as a whole.  is the motor torque constant.    is the current input to the motor.  is the radius of the gear attached to the motor.  is the force created along the belt linearly. @ is the angular position of the motor. Then equations for masses are calculated; where;  is the mass of the first mass.  is the mass of the second mass.  is the spring constant.  is the position of the first mass. is the position of the second mass.  is the frictional force on the first mass.  is the frictional force on the second mass.
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values are obtained;     Inertias, damping coefficients and frictional forces are harder to  obtain so a perfect system is assumed. After calculations, the transfer  function is obtained as; Calculated variables for different compensators: Lead K=0.3 P=-10 Z=-2 Lag P=-0.01 Z=-0.03 K=1 PID Kp = 50,  Ki = 0.5,   Kd = 5.   State space design:
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This note was uploaded on 01/07/2010 for the course MECHATRONI 303 taught by Professor Kemalettinerbatur during the Spring '09 term at Sabancı University.

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Me 303 Term Project - ME303TermProject...

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