Modern University for Modern Sciences and Arts

Faculty of Engineering

Automatic Control System

ESE 346/ESE416

Sheet 2

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Problem 1:

Determine the unit step response for the system described by

(D+2) y(t) = x(t)

Problem 2:

Find the Laplace Transform for the following signals:

x(t) = (t)

x(t)= u(t)

x(t) = e-at u(t)

Problem 3:

Use the initial value theorem and the final value theorem

Find the initial value and the final value of the following signals:

y(t) = e-3t

Y(S) = 1/(S+3)

Y(S)= (5S-12)/(S2+4S+13)

Problem 4:

Consider the simple circuit shown and the input signal x(t) = u(t), Find the

Transfer Function and the output signal y(t)

Problem 5:

Derive the transfer function of the network, the input variable is Vi(S), the

output variable is Vo(S).

Problem 6:

Obtain the T.F. between the displacement and the force X(s)/F(s) for the

mechanical system shown.

f(t)

X1

X2

Problem 7:

Determine the damping ratio, the undamped natural frequency, the rise

time, the settling time, and the overshoot of the circuit shown.

M

K1

K2 B