# ROSE-HULMAN INSTITUTE OF TECHNOLOGY ME 506 Advanced Controls

```ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
ME 506
Homework 5, Due October 6
1. Multivariable Frequency Response
For the following system:
0
0
0
1
0
0
80.9074
0
433.22
0
= −433.22 −5.5089
+
0
0
0
1
0
0
287.338
0
−287.338 −3.9477
0
−89.0056
=
1
0
0 0
0 1
0
0
+
0
0
0
0
a) Find the MIMO transfer function matrix and plot the singular value plot in Matlab
b) For the input frequence ω = 5 Hz, find the singular value decomposition of the transfer
function matrix, and determine the input signals required to generate the maximum and
minimum output amplitudes. (Magnitudes and phases).
c) Build the system in Simulink, and demonstrate the MIMO frequency response using
your results from b). Show that your singular value plot accurately reflects the ratio
between maximum output amplitude and minimum output amplitude at ω = 5 Hz.
2. Observer design
The longitudinal dynamics of the S-61 helicopter built by Sikorsky Aircraft Company are
given below in state space form. Design a full order observer for this system, such that the
observer poles are at s = {-5, -7, -10}, the pitch attitude state is associated with s = -10, and is
decoupled from the other two states. Demonstrate the decoupling by simulations with
initial state estimation error set to each of the closed-loop eigenvectors.
u&amp;  − 0.02 − 0.098 0.014 u  0.098 0.01
δ 
 &amp; 
 
0
1  θ  +  0
0   B 
θ  =  0
δ
q&amp;   1
0
− 0.4  q   − 6.3 1.2   C 
  
u 
 y1  0 1 0  
 =
 θ 
 y 2  0 0 1   q 
 
Homework 5
Page 1 of 1
```