system dynamic and control

MECH 4438 Dynamics and Control Quiz 2 (Take Home)

Due Feb. 23, 2016

1. (50 points).

The pair of roots of a second order system is given in the

figure.

You are required to write a MATLAB program to

1. plot the response of the system subject to unit step input 2. calculate the time response characteristics of the system 3. move the poles around (in 3 directions, meaning fixing

d , changing dj ; fixing dj , changing d ; fixing ,

changing both d and dj ), observe the changes in time

responses

4. plot the time responses for the four cases (original + 3 relocations) on one graph

5. prepare a one-page report, discussing how the relocation of the poles affects the system response (in terms of time

response characteristics, i.e., Tp, Ts, Tr, Os).

Attach your program code in the report.

2. (10 points) Find the output response c(t) for the following system. Also find its time constant, rise time and settling time.

3. (20 points) The transfer function of a second order system is given below:

8

8

s

04.02.

04. )(

2 

 ss

sG

a). Find the locations of the poles and zeros of the system, plot them on the s-plane.

b). Write an expression for the general form of the sept response without solving for the

inverse Laplace transform.

c). Find n, , Ts, Tp, and %OS.

d). What is the nature of this system’s response (over damped, underdamped, critically

damped?)

Why?

Sketch the response below.

4. (20 points) Unit responses for 2 nd

order systems are shown below.

a). If system 1 is a critically damped response, what is its damping ratio?

What is the nature of response of system 2?

What is the possible range of damping ratio of system 2?

b). Find the transfer function for the following system.

Time in seconds

1 2