ME155A S ’21 Sample Coversheet of Midterm
Instructions:
1. This is a take home midterm.
2. This is an open book, open notes exam. You may use MATLAB as well on your computer,
but not the internet. This is not an open neighbor exam.
3. You may print out the midterm and scan or snapshot a handwritten solution or type up
solutions in LaTeX.
4. Write or type your name on this answer booklet.
5. Read each question carefully.
6. If you find that you are spending too much time on a problem, move on to the next and come
back to it later.
7. Please, please, please write legibly.
8. The total number of points on this test is 100; each problem is worth 25 points and contains
two subproblems, each worth 12.5 points.
9. Reasonable explanations may receive partial credit.
10. To receive full credit you must explain and justify your answers.
11. Good luck!
NAME:
1
Problem 1 (Transfer Functions & State-Space Models)
• You will need to know how to take a Laplace transform of a system with linear dynamics.
• You will need to know how to solve for the transfer function of a system between a given pair
of two signals S1(t) and S2(t).
• You will need to know how to write down the dynamics of a physical system, e.g. a motor, a
pendulum, a servo, a dashpot, a spring, a body of mass coupled to a spring or dashpot, etc.
to form a transfer function.
• You will need to know how to write down the dynamics of electrical circuits and their com-
ponents, e.g. resistor, capacitor, an inductor, an operational amplifier, and combinations of
those components to form a transfer function.
• You will need to be able to take the inverse Laplace transform of a transfer function to generate
a vectorized state-space model of a system.
2
Problem 2 (Block Diagram Algebra with Transfer Functions, Stability of Transfer Functions)
• You will need to know how to derive the sensitivity, complementary sensitivity, load distur-
bance sensitivity, and the noise sensitivity functions using block diagram algebra.
• You will need to be able to identify and write down the characteristic polynomial/equation
of a system.
• You will need to be able to apply the Routh-Hurwitz criterion to evaluate stability of a closed
loop system parametrically in terms of controller gain.
• You need to have a solid understanding of when to use the Routh-Hurwitz array and when to
avoid using it, due to violations of the premises of the criterion.
3
Problem 3 (Transient Response for First and Second Order Systems)
• You need to be able to compute expressions for the impulse response, step response, and ramp
response of a first order system.
• You need to be able to compute expressions to estimate settling time for a first order system.
• You need to understand the notion of a time-constant, a pole, a zero, etc. for a first-order
transfer function.
• You need to understand how to convert a second order transfer function into standard form,
to compute the damping ratio, the natural frequency, the attenuation, the damped frequency,
and all associated constants.
• You need to know how to be able to use MATLAB to generate responses to all the standard
test signals. Note that there is no ramp function in MATLAB (recall our comments in class
about how the ramp is the integral of the step response). You need to be able to generate these
simulated responses quickly in MATLAB (it shouldn’t take you more than 10-15 minutes).
4
Problem 4 (Root Locus Plots)
• You need to be able to plot a root locus plot (mostly) by hand, to justify all the steps, and
clearly show your thought process in generating a root locus plot.
5




























































学霸联盟