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ME 155B - HW Assignments and Solutions
HW #1
Due Tuesday 10/7
Problems 2.2, 2.3 (assume for simplicity that the “D” matrices of all systems are zero)
Problem 2.5 (For the simulation in part (c), use you can use SIMULINK or some other
linear system response simulator in MATLAB such as “lsim” or “ltiview”)
Problem 2.19 (additional part: (c) Write the linearized equation (around the upright position for both arms) in state space form)
HW #2
Due Tuesday 10/14
Go through the help section in MATLAB for the “Control Systems Toolbox”, in particular, the sections on building system models and simulations of linear models.
Study Example 2.2 in Belanger and do the following problem outlined in this
PDF file.
Problems 3.1, 3.2 in Belanger
HW #3
Due Wednesday 10/22
HW #4
Due Wednesday 10/29
Problem 3.36 (do part (a) numerically as follows: plot the minimum singular value of the controllability
matrix for a fixed value of l1 and as l2 rangers near l1, e.g. l1-0.1 <= l2 <= l1+0.1)
Problem 3.43 (find the state transformation that converts this realization into diagonal form, do not do
the canonical decomposition part).
HW #5
Due Wednesday 11/5
Problem 3.28, 3.29 (Note: 3.28 should be done analytically, and 3.29 in MATLAB)
Problem 3.55 (for part (b), you can use results from HW 1)
Problem 3.59
Problem 7.10
HW #6
Due Tuesday 11/11
Midterm Solutions PDF file
HW #7
Due Tuesday 12/9
(NOTE: This HW set must be turned in and
can not be dropped from the calculation of HW average)
Problem 7.37 (use MATLAB for this problem)
Problem 7.27 (Note: Parts (a-c) represent an LQR problem with Q=0.
The lqr routine in matlab may
choke on this. Instead, use Q = epsilon I. Chose epsilon small,
like 10e-3 or 10e-4.
In fact, make epsilon progressively smaller and observe that there’s
a well defined limit of gains K as epsilon goes to zero)
Problem 7.46
7.48, 7.68
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