Tutorial no. 5

1. Draw the root locus of 2

( 2)( )

2 3

K sG s

s s

, ( ) 1H s for 0K . Also find the value of K

for which 0.7

2. Sketch the root locus for given characteristic equation 2 ( 3)( 5) ( 1) 0s s s K s .

Find the value of K for which the system becomes marginally stable.

3. Sketch the root locus of the loop transfer function

2 2

( 40)( )

( 20)( 60 100 )

K sG s

s s s s

4. Consider the given characteristic polynomial 2( 2)( 2 5)s s s s K . For 0K

sketch the root locus.

5. Consider the system shown:

Sketch the root locus with respect to positive values of c.

6. The system shown in figure employs derivative of feedback in addition to unity

feedback.

a. Find the value of the constant K so that the damping ratio of the system is 0.7.

With this calculated value of K and unit ramp input, find the value of steady state

error. (A=10)

b. If K = 0, calculate the value of damping ratio and undamped frequency of

oscillations. What will be the steady state error resulting from unit ramp input.

(A=10)

c. The value of steady state error is required to be 0.2 radians with derivative

feedback and the damping ratio maintained at 0.7. How can this be achieved?

7. A unity feedback system has the following forward transfer function:

Find the steady state error for the following inputs

a) b) c)

8. A unity feedback system has the following forward transfer function:

Find the value of so that there is error in the steady state.

9. Consider a unity feedback control system with the closed loop transfer function

Find out the steady-state error for unit-ramp input.

10. Design the values of and for the system given below to meet the following

specifications

a) Steady state error due to unit step disturbance is -0.000012.

b) Steady state error due to unit ramp input is 0.003.

11. Find the steady-state error due to a unit step input and a unit step disturbance for the

following system

+

-

+ +

+

-

+ +