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## Short Assignment Requirements

For the prelab part, please try to make the hand write clean. The detail requirement of the file is described in the blue box.

## Assignment Description

Cyber Exploration Laboratory

### Experiment 4.1

Objective To evaluate the effect of pole and zero location upon the time response of first- and second-order systems.

Minimum Required Software Packages MATLAB, Simulink, and the Control System Toolbox

### Prelab

a

1.      Given the transfer function Gs , evaluate settling time and rise time for the

sa

following values of a: 1, 2, 3, 4. Also, plot the poles. b

2.      Given the transfer function Gs :

s2  asb

a.    Evaluate percent overshoot, settling time, peak time, and rise time for the following values: a  4; b  25. Also, plot the poles.

b.   Calculate the values of a and b so that the imaginary part of the poles remains the same but the real part is increased two times over that of Prelab 2a, and repeat Prelab 2a.

c.    Calculate the values of a and b so that the imaginary part of the poles remains the same but the real part is decreased by one half over that of Prelab 2a, and repeat Prelab 2a.

3.      a. For the system of Prelab 2a, calculate the values of a and b so that the real part of the poles remains the same but the imaginary part is increased two times over that of Prelab 2a, and repeat Prelab 2a.

b.   For the system of Prelab 2a, calculate the values of a and b so that the real part of the poles remains the same but the imaginary part is increased four times over that of Prelab 2a, and repeat Prelab 2a.

4.      a. For the system of Prelab 2a, calculate the values of a and b so that the damping ratio remains the same but the natural frequency is increased two times over that of Prelab 2a, and repeat Prelab 2a.

b.   For the system of Prelab 2a, calculate the values of a and b so that the damping ratio remains the same but the natural frequency is increased four times over that of Prelab 2a, and repeat Prelab 2a.

5.      Briefly describe the effects on the time response as the poles are changed in each of Prelabs 2, 3, and 4.

### Lab

1.    Using Simulink, set up the systems of Prelab 1 and plot the step response of each of the four transfer functions on a single graph by using the Simulink LTI Viewer (See Appendix E.6 online for tutorial). Also, record the values of settling time and rise time for each step response.

2.    Using Simulink, set up the systems of Prelab 2. Using the Simulink LTI Viewer, plot the step response of each of the three transfer functions on a single graph. Also, record the values of percent overshoot, settling time, peak time, and rise time for each step response.

3.    Using Simulink, set up the systems of Prelab 2a and Prelab 3. Using the Simulink LTI Viewer, plot the step response of each of the three transfer functions on a single graph. Also, record the values of percent overshoot, settling time, peak time, and rise time for each step response.

4.    Using Simulink, set up the systems of Prelab 2a and Prelab 4. Using the Simulink LTI Viewer, plot the step response of each of the three transfer functions on a single graph. Also, record the values of percent overshoot, settling time, peak time, and rise time for each step response.

### Postlab

1.    For the first-order systems, make a table of calculated and experimental values of settling time, rise time, and pole location.

2.    For the second-order systems of Prelab 2, make a table of calculated and experimental values of percent overshoot, settling time, peak time, rise time, and pole location.

3.    For the second-order systems of Prelab 2a and Prelab 3, make a table of calculated and experimental values of percent overshoot, settling time, peak time, rise time, and pole location.

4.    For the second-order systems of Prelab 2a and Prelab 4, make a table of calculated and experimental values of percent overshoot, settling time, peak time, rise time, and pole location.

5.    Discuss the effects of pole location upon the time response for both first- and secondorder systems. Discuss any discrepancies between your calculated and experimental values.

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