Control Exercise Unit 2

FEEDBACK CONTROL SYSTEM UNIT 2

a. Give the definition of a transfer function and briefly discuss the importance of modeling in control systems.

b. Find the transfer function, .

i.

ii.

iii.

iv.

c. For the following differential equation:

Write the corresponding transfer function, .d. For the following transfer functions:

Write the corresponding differential equation.

e. Find the transfer function, .i.

ii.

f.

g.

h.

i.

j.

k.

l.

m. (a) For the electrical system shown in Figure 2.18, by assuming zero initial condition (no stored energy for t < 0), find the transfer function,.

Figure 2.18

(b)If the inductor is replaced by a short circuit, find the new transfer function.

n. Find the transfer function, , for electrical system shown in Figure 5.1.

Figure 5.1: Electrical System

o. Refer to Figure 2 and by Kirchhoffs voltage law,

Figure 2

i. determine the equation at Loop 1 and Loop 2. ii. calculate the transfer function p. Find the transfer function for the translational mechanical system shown in Figure 2.24.

Figure 2.24

q.

r.

s. The pulley shown in Figure 2.19 is ideal (it has no mass and no friction). There is no slippage between the cable and the surface of the cylinder, thus both masses move with the same velocity. The cable is always in tension, but not stretched. K1, K2 and K3 are the spring constants, fv is the coefficient of viscous friction and, M1 and M2 are the masses. Force, f(t), is applied on M1 as shown in the figure.

Figure 2.19(a)Obtain the free-body diagrams of the system by excluding the gravitational force.(b)Write-down the equations of motion.

(c)Find the transfer function

t. Find the transfer function,, for the translational mechanical network shown in Figure 1.2.

Figure 1.2 u. Find the transfer function, for the translational mechanical system shown in Figure 6.1

Figure 6.1

v.

w. For the rotational mechanical systems shown in Figure 3.1, find the transfer function, .

Figure 3.1

x.

y.

z. Given the motor, load and torque-speed curve shown in Figure 2.21. The transfer function of system is:

Using the transfer function given above, find the transfer function,.

Figure 2.21