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Unformatted text preview: CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 101 D. G. MacMynowski Fall 2009 Problem Set #7 Issued: 16 Nov 09 Due: 23 Nov 09 Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading). 1. Consider the system in Example 11.1. Choose the parameters a =- 1 and compute the time and frequency responses for all the transfer functions in the Gang of Four for controllers with k = 0 . 2 and k = 5. (“Time response” refers to the step response of the system.) 2. The figure below shows a simple mechanism for positioning a disk drive read head and the associated equations of motion: Disk Motor τ θ J ¨ θ =- b ˙ θ- kr sin θ + τ m ˙ τ m =- a ( τ m- u ) The system consists of a spring-loaded arm that is driven by a small motor. The motor applies a force against the spring and pulls the head across the platter. The input to the system is the desired motor torque, u . In the diagram above, the force exerted by the spring is a nonlinear function of the head position due to the way it is attached. All constants are positive. We wish to design a controller that holds the drive head at a given location θ d . (a) Show that the transfer function of the process can be written as P ( s ) = a a + s · k s 2 + 2 ζω n s + ω 2 n ....
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- Fall '09
- Nyquist plot, loop transfer function, TECHNOLOGY Control and Dynamical Systems