哈工大惯性技术(导航原理)大作业.doc

Assignment of Inertial Technology 《惯性技术》作业 My Chinese Name My Student ID 15S004001 Autumn 2015 Assignment 1: 2-DOF response simulation A 2-DOF gyro is subjected to a sinusoidal torque with amplitude of 4 g.cm and frequency of 10 Hz along its outer ring axis. The angular moment of its rotor is 10000 g.cm/s, and the angular inertias in its equatorial plane are both 4 g.cm/s2. Please simulate the response of the gyro within 1 second, and present whatever you can discover or confirm from the result. In this simulation, we are going to discuss the response of a 2-DOF gyro to sinusoidal torque input. According to the transfer function of the 2-DOF gyro, the outputs can be expressed as: The original system transfer function is a 2-input, 2-output coupling system. But the given input only exists one input, we can treat the system as 2 separate FIFO system As a consequence, we can establish the block diagram of the system in simulink in Fig 1.1. Substitute the parameters into the system and input, then we have the input signals as follow: Then the inverse Laplace transform of the output equals the response of the gyro in time domain as follows: Fig 1.1 The block diagram of the system in simulink And the simulation results in time domain within 1 second are shown in the follwing pictures. Fig1.2 is the the output of outer ring . Fig1.3 is the output of inner ring . Fig1.4 is the trajectory of 2-DOF gyro’s response to sinusoidal input. As we can see from the Fig1.3,there are obvious sawtooth wave in the output of the inner ring. It’s a unexpected phenomenon in my original theoretical analysis. Fig1.2 The output of inner ring Fig 1.3 The output of outer ring I believe the sawtooth wave is caused by the nutation. For the frequency of the nutation is obtained as , which is far higher than the frequency of the applied