Homework 1 - MAE143B Spring 2010: due Thursday April 8
[Hint: get moving on this homework early, so that you can take advantage of the office hours and class times. The problems are not difficult but
Midterm - MAE143B, Summer II 2008 SOLUTIONS
Prof. R.A. de Callafon
August 25, 2008 2:00pm-3:20pm, CENTER 115
open-book and open-notes midterm exam
use the available space to derive your results, attac
Note: matlab files for Question 1 at end.
Note: Matlab files for Question 2 at end.
a = [1,0,0;-1,1,1;-4,-4,-3]; J = [1,0,0;0,-1,1;0,0,-1]; v = [1,0,0;2,1,0;3,2,1]; syms s t disp('verify part i') v*a-
Homework 4 - MAE143B Spring 2010: due Thursday April 29 Question 1: Matrix exponential computations by hand
[Hint: Do your computations by hand and check them using matlab.] Consider the matrix 1 A =
Question 1
We are given the system x(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t). (1) (2)
To relate y(0) to the state x(0), substitute t = 0 into (2) (note that u(0) and all derivatives of u(t) evaluate
Homework 3 - MAE143B Spring 2010: due Thursday April 22 Question 1: Initial state calculation
Consider the state-variable realization of the system described by the nth -order ordinary differential eq
Question 1
The differential equation corresponding to the transfer function is . y (t) + 2.4(t) + 25.84y(t) + 50.08y(t) = 4u(t) + 4u(t). y Define a variable q(t) which satisfies . q (t) + 2.4(t) + 25.
Homework 2 - MAE143B Spring 2010: due Thursday April 15 Question 1 - State Variable Realization
Consider the system from input, u(t), to output, y(t), described by the transfer function s3 + 2.4s2 4s
Question 2
The proceeding simulations compares the effects of the proportional and integral gains on the closed-loop dynamic behavior of the car cruise control system.
20.3 kp = .5, kI = .1 kp = .8, k
Midterm - MAE143B, Summer II 2009
August 25, 2009 2:00pm-3:20pm, CSB 102
SOLUTIONS Prof. R.A. de Callafon
open-book and open-notes midterm exam use the available space to derive your results, attach e