Assignment – III
Dated: 19/03/2025 Dead Line: 28/03/2025
1. Load ‘U1’ and ‘U2’ enter at two different points as shown below. Show that for the closed
loop the response frequency is same for both load changes, but the offset is different.
2. (i) Explain Routh stability method.
(ii) The set point of the control system shown below is given a step change of 0.1unit
Determine (1) The maximum value of ‘C’ and the time at which it occurs. (2) The offset
(3) The period of oscillation (4) Sketch C(t) as a function of time (5) whether the closed
loop system is oscillatory.
3. Apply Routh’s criterion to test the stability of the system described by the Following
characteristic equation;
s5 + 0.5 s4 + 3 s3 + 1.5 s2 + 0.5 s + 0.5 = 0
4. (i) Compare Pneumatic and Electronic controller.
(ii) For a unit step change in set point, find the response ‘ C’ for the system given
below and represent graphically
5. (i) Discuss Servo and Regulator problem.(May 2016)
(ii) For the control system shown below,
(1) Obtain the closed loop transfer function C/U
(2) Evaluate the proportional gain for which the closed loop damping coefficient is 2.
(3) Find the offset for a unit step change in ‘U’, if KC = 2
6. For the system shown below, check the value of KC for which the system is stable
7. A feedback control system has the following transfer functions; Process:
Gp(s) = 5/[(2s + 1) (s + 1)]
Measurement: H(s) = 1/(0.5s + 1)
Valve: GV(s) = 0.2/(0.1s + 1)
Controller: GC(s) = KC
Using Routh’s stability criteria, find out the value of KC for which the system is stable.
8. (i) Derive the transfer function for different types of controllers.
(ii) Discuss the effect of P-controller on a first order process for servo and
regulator problems.
9. A control system has a transfer function as 2/(s+1)(s+2) and the measuring device transfer
function transfer function as 3/(s+3).If the proportional controller is used, check out the
values of the controller gain for which the system will be stable.
10. For the control system shown below ,determine an expression for c(t) if a unit step
change occurs in R. Sketch the response c(t) and compute C(2)
11. For the control system shown in Figure
i) Obtain the closed loop transfer function C/U
ii) Evaluate the proportional gain for which closed loop damping coefficient is 2
iii) Find the offset for a unit step change in U in Kc = 2.
12. (i) Write the characteristics equation for the control system shown in figure.
(ii) Use the Routh test to determine if the system is stable for Kc=4 and Kc = 0.1
(iii) Determine the ultimate value of Kc above which the system is unstable.
13. Apply Routh’s criterion to test the stability of the system described by the following
characteristic equation; s5 + 0.5 s4 + 3 s3 + 1.5 s2 + 0.5 s + 0.5 = 0
14. Apply Routh criterion to test the stability of the system described by the following
characteristics equation s4+4s3+6s2+4s+(1+K)=0.
15. For the system shown in figure , check the value of KC for which the system is stable
16.
Using the Ziegler –Nichols rule determine Kc and τI for the control system shown in fig.
17. Sketch root locus for the open loop transfer function of unity feedback control system is
given by
𝑘
𝐺(𝑠 ) =
𝑠(𝑠2 + 4𝑠 + 13)
18. Draw the root locus diagram for the open loop transfer function.
19. A temperature control system inputs the controlled variables as a range from 0 to 4 V. The
output is a heater requiring 0 to 8 V. A PID is to be used with KP = 2.4 (% / %), KI = 9
(%/%- min), KD = 0.7 (%/%/min). The period of fastest expected change is estimated to be
8 seconds.
Develop the PID circuit.
20. A Proportional –Derivative controller has 0.4 to 2.0 V input measurement range and 0 to 5
V
output, KP = 5 % / % and KD =0.08% per (%/min). The period of the fastest expected signal
changes is 1.5 sec. Implement this controller with an op amp circuit.
21. A temperature control system inputs the controlled variables as a range from 0 to 4 V.
The output is a heater requiring 0 to 8 V. A PI is to be used with KP = 2.4 (% / %) and
TI= 9 %/% min Develop the PID circuit.
