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Auto Control l – Lab Part A Report

Hongzhi Yu  a1657200

INTRODUCTION

Use Matlab and Simulink to study the modelling facilities; the poles and zeros of open loop transfer function; the time response of control systems.

RESULTS        

The open-loop transfer function is:

Gol= 62.36

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Continuous-time transfer function is:

S^3+11.75s^2+17.55s

The poles are: 0, -10.0000, and -1.7548.

There are no zeros.

The closed-loop transfer function is:

62.36

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Continuous-time transfer function is:

S^3+11.75s^2+17.55s+62.36

The poles are: -10.6573, -0.5488+2.3560i, and -0.5488-2.3560i

There are no zeros.

DISCUSSION

The follow steps shows the explanation of the task.

Step 1: Clear any existing variables in memory.

Step 2: Input all conditions and constants.

Step 3: Display the open-loop transfer function and the open-loop poles and zeros.

Step 4: Calculate the closed-loop transfer function with unity proportional gain and feedback.

Step 5: Show the values of open-loop poles and zero.

Step 6: The closed-loop poles and zeros figure-1.

[pic 1]

                                                              Fig.1

Step 7: The closed-loop step response figure-2.

[pic 2]

                                                             Fig.2

Step 8: Vary the proportional gain (K) from 0.1 to 1.0 in 0.1 increments (Table-1). Show in figure-3.

             Choose the value gain (K)= 0.2 because the rise time is short and the peak response is low which means the airplane can rise in short time and keep stable will flying.

[pic 3] 

                                                                   Table 1

[pic 4]

                                                                     Fig.3

Step 9: Build a Simulink model of the plane roll control system figure-4.

 [pic 5]

                                                                      Fig.4

Step 10: Run the Simulink model and compare the scope results figure-5.

[pic 6]

                                                              Fig.5

As show in Fig.5, the diagram of Y(s) is similar to the closed-loop diagram in Fig.3. Start from 0 and constant at 1. The different is the diagram between 0 second and 1 second.