Download Loop Transfer Function - Energy Power Systems - Exam and more Exams Energy Efficiency in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 200 11 / 12
Module Title: Energy Systems Control
Module Code: MECH
School: Engineering (Mechanical Engineering Department)
Programme Title: Bachelor of Science (Honours) in Sustainable Energy Technology – Year 4
Programme Code: ESENT_8_Y
External Examiner(s): Mr C. Buckley, Mr P. Kenny Internal Examiner(s): Mr. Conor O’Farrell
Instructions: Answer any 4 from 6. All questions carry equal marks. 25 Marks per question
Duration: 2 Hours
Sitting: Autumn 2012
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Question 1:
(a) Write down the control equation for proportional + integral + derivative control making sure you define any variables used. List one advantage and one disadvantage of this type of control. [5 Marks]
(b) Using the error signal shown in figure 1, calculate the PID controller output and draw the plot when: Kp = 5 1/Ti = 0.7s- Td = 0.5s And Nominal Load = 20%
Figure 1 [20 Marks]
Time (s)
Error (%)
Question 3:
(a) Describe, giving appropriate equations the operation of a resistance thermometer. [4 Marks]
(b) Discuss the role that “the temperature coefficient of resistance” has when making temperature measurements over large ranges. [3 Marks]
(c) The temperature in a control process has a range of 400 to 670 Kelvin and a setpoint of 610
Kelvin. Find the percentage of span error when the temperature is 620 Kelvin. [5 Marks]
(d) Explain the concept and rationale behind the 4 methods listed below for measuring level.
- Direct Level Measurement
- Indirect Level Measurement
- Continuous Level Measurement
- Point to Point Level Measurement [8 Marks]
(e) A liquid-level control system linearly converts a displacement of 3-3.5m into a 4-20mA control signal. A relay serves as the two-position controller to open or close the inlet valve. The relay closes at 14mA and opens at 8mA. Find
i. The relationship between displacement level and current ii. The neutral zone or displacement gap in meters. [5 Marks]
Question 4:
(a) Determine the following for the feedback system in figure 3 in which K 1 and K 2 are constants i. Open loop Transfer Function ii. Closed loop Transfer Function iii. Error Ratio iv. Primary feedback Ratio v. Characteristic Equation
Figure 3 [10 Marks]
(b) Show that the RC electrical system shown in figure 2 obeys first order dynamics and calculate its
transfer function. The input voltage is vi t , vo t is the voltage across the capacitor C and i t
is the current in the circuit.
vo t
Figure 2 [10 Marks]
(c) Consider a first order process represented by the transfer function
s
G s kss (^) p. What do the symbols kss and represent? Sketch the typical response curve obtained from a first order
process given that kss 1. 2 and 1. 5 s
[5 Marks]
K 1 K 2
S(S +P)
R +
E C
K 1 K 2 S
R
i(t) C
Question 6:
(a) Figure 3 shows the response of a second order underdamped system. Determine the transfer function parameters for this second order system.
Figure 3 [10 Marks]
(b) A critically damped second order process has a steady state gain of 1 and a natural radiancy of 20 rad/s. It is controlled by a P-Only controller with gain kp using negative feedback. Derive the closed loop transfer function for the system. [10 Marks]
(c) Using the answer from question 6 (b), determine the value of kp if the closed-loop response is to have a maximum percentage overshoot of 10% [5 Marks]
Laplace Transform of common functions
Time-domain function Laplace domain function f(t) F(s)
0 0 ( )^10 t ut t s
1
C s
C
f ( t d ) e s^ dF ( s ) t 2
1 s
dt
df sF^ (^ s ) f (^0 )
0
( )
t ^ f^^ ^ d
(^1) F s ( ) s e at s a
1
te at ( )^2
1 s a t (^) e at 2
2 ( )^3
1 s a
t e 1 ( 1 )
1 s s sin t (^2) 2
s cos t s^2 ^2
s
e at sin t ( )^2 ^2
s a e at cos t ( )^2 ^2
s a
s a
