# ECE 720 -- Design Project #1

## Remotely Piloted Vehicle -- Eigenvector Assignment

ECE 720,
Spring 1996, Assigned 2/24/96, Due 3/28/96

The remotely piloted vehicle (RPV) is described in the
Appendix at the end of the text. It is a 2-input, 2-output,
6-state system model given in terms of its continuous-time
state equations. The closed-loop system will be achieved
through full state feedback with the control law

u(t) = -Kc*x(t) + u_ref

u_ref = [0; 1] for all t

The required closed-loop eigenvalues are:
{-0.75, -0.90, -1.25, -3.75, -25, -35}.

**TASKS TO BE PERFORMED**

- Using the MATLAB "PLACE" command, compute the gain
matrix K_MATLAB which places the eigenvalues at the required
locations. Verify that the eigenvalues are placed correctly,
determine the eigenvectors, and investigate the orthogonality
of the eigenvectors. With zero initial conditions for the
state vector, simulate the closed-loop system to determine
the output responses to the given reference input. Compute
the closed-loop transmission zeros for the system.

- Using the output results in part 1 as a standard,
compute at least four additional gain matrices using the
eigenvector assignment method discussed in class. One of
these gain matrices should be chosen to give "bad" performance,
and you should attempt to find at least one gain matrix
which gives better performance than that obtained with the
"PLACE" command. You may choose your method of evaluating
the quality of the performance, as long as it is reasonable.
For each of your gain matrices, determine the closed-loop
zeros, investigate the orthogonality of the eigenvectors,
and simulate the closed-loop system with the reference input.

- Write a report which compares your various designs
with that obtained from MATLAB. Discuss the performance
obtained from the simulation results in terms of the orthogonality of
eigenvectors, the locations of the
closed-loop zeros, and the norms of the gain matrices.
Discuss why you chose the various eigenvector placements,
and justify your selection of the performance evaluation
criterion.

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*Latest revision was made on 05/09/01 04:43 PM
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