State Space and Modeling
onsider the following differential equation:
d 2 y + 3 dy + 2 y = u dt2 dt

Write the state equations for this system

Add a new state in which x&3 = y − yd where yd is the unit step and represents the desired output of the system. Write the new state equations treating yd as another input.

Now,pickavector k=[k1,k2,k3]suchthatifu=−kx,thenewstateswillhaverootsofthe
characteristic equation at ‐2, ‐3, and ‐4.

Simulate the system and observe the output y and compare the response for yd = step input
to the step response of the system without control.
Brown University
1271 Tutors
California Institute of Technology
2131 Tutors
Carnegie Mellon University
982 Tutors
Columbia University
1256 Tutors
Dartmouth University
2113 Tutors
Emory University
2279 Tutors
Harvard University
599 Tutors
Massachusetts Institute of Technology
2319 Tutors
New York University
1645 Tutors
Notre Dam University
1911 Tutors
Oklahoma University
2122 Tutors
Pennsylvania State University
932 Tutors
Princeton University
1211 Tutors
Stanford University
983 Tutors
University of California
1282 Tutors
Oxford University
123 Tutors
Yale University
2325 Tutors