Sheet 1 Control

King Khalid University Faculty of Engineering Electrical department

Automatic Control Sheet (1)

1- Find the Laplace transform for the following functions: a- f(t) = u(t) b- f(t) = (t) c- f(t) = t3 f- f(t) = e-atcost

e- f(t) = sint

d- f(t) = e-at

g- f(t) = tsint i-f(t) = u(t-2)

2- Find the inverse Laplace transform for the following functions: a-

( )

b-

( )

c-

( )

d-

( )

e-

( )

(

)

(

)

(

) (

(

)( ) (

)(

)

)

3- Find the solution of the following differential equations using Laplace transform: ( ) a( ) ( ) ( ) 0 b( ) ( ) c4- Find Vo(s)/Vin(s) for the circuits shown in Fig. 1

Figure 1

5- Find (s)/Vf(s) for the system shown in Fig. 2



Figure 2 6- For electromechanical systems that require large power amplification, rotary amplifiers are often used. An amplidyne is a power amplifying rotary amplifier. An amplidyne and a servomotor are shown in Fig. 2. Obtain the transfer function (s)/Vc(s), and draw the block diagram of the system. Assume vd = k2iq and vq = kxic. 1

Figure 3 7- Simplify the block diagram shown in Fig. 4 and obtain the closed loop transfer function C(s)/R(s).

(4) ‫شكل‬

2

8- Draw the signal flow graph for the control systems shown in Fig. 5 and obtain the closed loop transfer function using Mason's formula.

Figure 5

9- Use Mason's formula to obtain the closed loop transfer function of the system described by the signal flow graph shown in Fig. 6.

Figure 6

3