Due 4:00 p.m., Monday, 12/13/99.

__INTRODUCTION:__

The block diagram for this project is seen to
consist of the plant transfer function *G _{p}*(

The output of this block is the heading angle, psi, and the input to the block is the
actual rudder angle, delta_{r}. In the absence of a disturbance, the actual and
commanded rudder angles are equal.

__TASKS:__

- Design a compensator
*G*(_{c}*s*) such that the following specifications are all satisfied:- when the reference input signal is 0, and the disturbance signal is a step function, the steady-state value of the actual heading angle must be 0;
- when the reference input signal is a step function, and the disturbance signal is 0, the settling time of the actual heading angle must not exceed 250 seconds;
- when the reference input signal is a step function, and the disturbance signal is 0, the actual heading angle must not exceed the desired heading angle by more than 15%;
- when the reference input signal is a unit ramp function, and the disturbance signal is 0, the steady-state error must not exceed 3;
- when the reference input signal is a step function equal to 10 degrees, and the disturbance signal is 0, the commanded control signal must not exceed 35 degrees in absolute value.

- Perform simulations in MATLAB with your compensator design to verify that all the specifications have been satisfied. Plots should be made that indicate the responses of the various signals are satisfactory. It should be noted that there is not a settling time requirement for a step input at the disturbance signal, so that response might take much longer than the other responses. Ramp responses may be longer than step responses.
- This part of the project deals with the stability robustness of your design, that
is, how much change can there be in the plant and/or controller models without losing
closed-loop stability? My MATLAB function
*tsypkin.m*can be used for this. The zipped version of this file should be downloaded and unzipped. (If you have trouble downloading the file, email me, and I will email it back to you). For your purpose in this project, the syntax for using the function can be

rho = tsypkin(dcl, 0.1*dcl); where

*dcl*is the closed-loop characteristic polynomial of your final compensated system. The function will create a figure with 3 plots on it, and will return a 3-element vector*rho*. A sample plot is shown for illustration. The elements in the*rho*vector are the maximum allowed perturbations to the coefficients of the closed-loop characteristic equation in terms of the 1-norm, 2-norm, and infinity-norm, respectively. The larger the values in*rho*, the more robust your control system is to changes in these coefficients. Evaluate your design using this function. It is hoped that all the values in*rho*will be greater than 1.

__REPORT:__

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*Lastest revision on
Wednesday, June 7, 2006 9:15 PM
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