hw3 - (http://ocw.mit.edu), Massachusetts Institute of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
16.31 Handout #3 Prof. J. P. How September 21, 2007 T.A. TBD Due: September 28, 2007 16.31 Homework Assignment #3 1. Given the plant G ( s ) = 1 /s 2 , design a lead compensator so that the dominant poles are located at 1 ± 1 j 2. Determine the required compensation for the system K G ( s ) = ( s + 8)( s + 14)( s + 20) to meet the following speciFcations: Overshoot 10% 10-90% rise time t r 100 msec Simulate the response of this closed-loop system to a step response. Comment on the steady-state error. You should Fnd that it is quite large. Determine what modiFcations you would need to make to this controller so that the system also has K p > 6 thereby reducing the steady state error. Simulate the response of this new closed-loop system and conFrm that all the speciFcations are met. 3. Develop a state space model for the transfer function (not in modal/diagonal form). Discuss what state vector you chose and why. ( s + 1)( s + 3) G 1 ( s ) = (1) ( s + 2)( s + 4) (a) Develop a “modal” state space model for this transfer function as well. (b) ConFrm that both models yield the same transfer function when you compute G ˆ ( s ) = C ( sI A ) 1 B + D 1 Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 4. A set of state-space equations is given by: x 1 = x 1 ( u x 2 ) x 2 = x 2 ( + x 1 ) where u is the input and and are positive constants. (a) Is this system linear or nonlinear, time-varying or time-invariant? (b) Determine the equilibrium points for this system (constant operating points), assuming a constant input u = 2. (c) Near the positive equilibrium point from (b), Fnd a linearized state-space model of the system. 2 Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]....
View Full Document

This note was uploaded on 11/07/2011 for the course AERO 16.31 taught by Professor Jonathanhow during the Fall '07 term at MIT.

Page1 / 2

hw3 - (http://ocw.mit.edu), Massachusetts Institute of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online