ME 481/581
Chapter 2 HW
January 27, 2012
Chapter 2 HW Solution
Problem 1. We are given the dierence equation yk = 0.5yk1 + 0.5yk2 + 0.25uk1 .
(a) The discrete transfer for this system may be found by Z -transforming the dierence equation:
Y (z ) = 0.5z 1
ME 481/581
Chapter 7 HW 3 Solution
April 27, 2012
Chapter 7 HW 3 Solution
Problem 1. (a) Here we want to nd the controlled system equations in terms of state vector
x
x
(1)
First consider the state and output equations for the SISO plant:
x(k + 1) = x(k )
ME 481/581
Chapter 7 HW 2 Solution
April 23, 2012
Chapter 7 HW 2 Solution
Problem 1. (a) To nd the combined state equation for the plant+estimator+control law, the necessary equations
are:
Plant state equation: x(k + 1) = x(k ) + u(k )
Plant measurement e
ME 481/581
Chapter 7 HW 2 Hints
April 20, 2012
Chapter 7 HW 2 Hints
Problem 1. In this problem you should (a) nd the system equations like (7.45), but also (b) nd the state-space
(i.e. state and output) equations for the controller. Assume that matrix C p
ME 481/581
Chapter 7 HW 1 Solution
April 16, 2012
Chapter 7 HW 1 Solution
Problem 1. First compute the matrix, which is given by series expansion
=I+
A2 T 2
AT
+
+ ,
2!
3!
(1)
and when A and B and T are substituted we obtain
=
1
0
0
0
+
1
0
0.05
0
+
0
0
0
ME 481/581
Chapter 7 HW 1 Hints
April 11, 2012
Chapter 7 HW 1 Hints and Answers
Problem 1. This should be a matter of entering matrices A, B, and sample time T to MATLAB and computing the
series. The resulting and should agree with that from MATLAB c2d. T
ME 481/581
Chapter 6 HW Solution
April 6, 2012
Chapter 6 HW Solution
Problem 1. We have an armature voltage-controlled DC motor driving a load inertia via a gear train. All necessary
numerical parameters are given.
T
= x1 x2 x3
(a) The state vector is x =
ME 481/581
Chapter 5 HW 2 Hints
March 26, 2012
Chapter 5 HW 2 Hints
Problem 1. This is an unstable plant whose linear transfer results from the linearization of the inverse-square
magnetic law.
(a) Be careful when you factor the denominator of the transfe
ME 481/581
Chapter 5 HW I Solution
March 9, 2012
Chapter 5 HW I Solution
Problem 1. These three characteristic equations were already in root-locus form. They can easily be restored to
polynomial form, e.g.
1+K
s+1
=0
s2 (s + 9)
s2 (s + 9) + K (s + 1) = 0
ME 481/581
Chapter 5 HW Hints
February 29, 2012
Chapter 5 HW Hints
Problem 1. These should be fairly straightforward using the MATLAB rlocus function. All three are already
expressed in root locus form. Note that you should be able to convert from this fo
ME 481/581
Chapter 4 HW Solution
February 20, 2012
Chapter 4 HW Solution
Problem 1. Here we want to verify the Fourier series representing the impulse train:
(t kT ) =
k=
1
T
ejns t
(1)
n=
I wrote a MATLAB function called train.m (after all, were trying
ME 481/581
Chapter 3 HW
February 6, 2012
Chapter 3 HW Solution
Problem 1. Here youre given a lead network often used in control systems to improve the transient responsewhich
adds around 60 of phase angle at about 1 = 3 rad/s. The lead network transfer fu
ME 481/581
Chapter 8
February 27, 2012
Chapter 8 HW Solution
Problem 1. In this problem you are doing separate ts of x vs time and y vs time. Ill outline the procedure for x(t)
in what follows.
A mass moving without an applied force will have constant vel