Bsb Assessment 2

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Ian R. Manchester April, 2012 AMME3500: Systems Dynamics & Control Assignment 2 Note: This assignment contributes 10% towards your final mark. This assignment is due at 5pm on Tuesday, April 24th during Week 7. Submit your report to the assignment box on the 3rd floor outside of the drawing office in the Mechanical Engineering Building or via email by that time (i.manchester@acfr.usyd.edu.au). Late assignments will not be marked unless a doctor’s certificate or equivalent is provided. Plagiarism will be dealt with in accordance with the University of Sydney plagiarism policy. You must complete and submit the compliance statement available online. Mathematical derivations are expected to be done by hand except where the use of Matlab…show more content…
Sketch the location of the poles and zeros for the systems and use Matlab to generate the step response. Are the step responses consistent with the second order assumptions? Why or why not?[15 marks] 30 10 a. T(s) = 2 b. T(s) = 2 s + 4s +10 ( s + 3)(s + 4s +10) 100 4 ( s + 2) c. T(s) = d. T(s) = 2 2 ( s +10)(s + 4s +10) s + 4s +10 € € 4. You will now analyse a control system for a single link of a robot arm. To begin with, assume that the robot arm is completely rigid and has a moment of € € inertial of J=2kgm2. The motor, gearing, and joint mechanism has friction, which has been measured as c=0.25 Nms. Assume there is no gravity acting on the arm (e.g. the robot arm is in space, or operating horizontally). The ˙˙ ˙ equations of motion are: Jθ + cθ = T , where T is the total torque applied to the arm. Based on these system characteristics, answer the following [40 marks] a. Find the transfer function between the applied torque T and the € indicator angle θ. € b. Suppose the torque is computed so that θ tracks a reference command θr according to the proportional feedback law u = K (θ r − θ ) where K is the feedback gain. In interacting with the environment (picking up or pushing objects, etc) there is a reaction torque on the arm which we model as a disturbance torque w. Draw a block diagram of the resulting€ feedback system showing θ, the reference position θr as well as the disturbance torque w. So the total torque is T=u+w. Find the