FINAL
Exam review answers Name:____________________________
BAE 3023
SPRING 2006
Work
6 of the following 8 problems:
- Determine an appropriate transfer
function relating guidance error to steering input based on the guidance
system performance in the following plot.
Use MATLAB to test and assure you have a
reasonable model.
kp=2/15 process gain = (delta out ss / deltin in ss)
t=10.75-5.5 - period = peak to peak time
os=0.6/2 overshoot = overshoot output / delta out ss
z=1/sqrt(1+(3.14/log(os))^2) formula for calculating damping ratio
tau=t*sqrt(1-z^2)/(2*3.14) formula for calculating time constant
[n,d]=pade(3,4) calculate numerator and denominator for dead time of 3 sec. (might as well use 4th order pade)
gd=tf(n,d) calculate dead time transfer function
g1=tf([kp,],[tau^2 2*z*tau 1]) calculate transfer function without dead time using standard form
g=gd*g1 calculate transfer function with dead time
g=g*15 set-up for a step test with a step of 15
step(g) calculate step response and compare with above
- For the
system in problem 1, draw a block diagram of a closed loop feedback system that has a process as shown,
a position measuring element with a 1 sec time constant and a gain of 1,
and a proportional controller.
- A
closed loop feedback control system with a PID controller is proposed to
control vehicle position. The plot in problem 1 shows how the
vehicle position responds to Steering input. Determine
initial PID controller settings that could be used with the system that
would produce Ό amplitude decay response.
If this was first order, I could use the
tables. Since it is not, I will use
MATLAB and field tuning. I will test the
TF to determine max gain with td and ti off.
Kc
ultimate = 5.6
Tultimate
= 7.3 sec
From 7-1.1 in Smith and Corripio
Kc = 5.6/1.7 = 3.3
ti
= 7.3/2 = 3.65
td= 7.3/8 = .9
Tested with MATLAB
kc=3.3
ti=3.65
td=.9
gc=tf([ti*td ti 1],[ti 0])
gc=gc*kc
g=gd*g1 calculate transfer function with dead time from
problem 1
sisotool
Result looked OK, approximately Ό
amplitude decay.
- The
following chart was produced from a test of a pressure control
system. A PID controller was being
used and had the differential and integral actions turned OFF. The proportional band of the controller
was set at 30%. Estimate the
controller settings for Kc, Ti, and Td that
would produce a quarter decay response.
Tu = .18
s
Kcu =
100/30 = 3.33
Kc = .6*3.33 = 2
ti = Tu/2 = .18/2=.09
td= Tu/8 = .18/8 = 0.0225
|
Zeigler-Nichols Settings
for 1/4 Amplitude Decay |
|||
|
controller |
Kc |
tI |
tD |
|
P |
0.5 KCU |
- |
- |
|
PI |
0.45 KCU |
PU/1.2 |
- |
|
PID |
0.6 KCU |
PU/2 |
PU/8 |
- The
chart below shows discharge head at the gate for a pressure controller
used in an irrigation control system.
A pnuematic controller is being used to
control head and the pneumatic pressure that manipulates the valve was
stepped at time zero from 10 to 5 psi to produce
the chart. Propose a transfer
function to represent the ratio of discharge head to pneumatic control
pressure.
Kp = (57-14)/(5-10)
= - 8.6
Tau = 41-10 = 31 s
TauD = 10 s
- The
displacement, x, at the end of the armature that the solenoid pictured
below can develop has been modeled as:
Where
m0 is free space permeability (4px107 H/m)
N is the number of turns in
the coil (2400)
I is the
current in the coil
A is the crossectional area of the coil core (0.0018 m2)
Ks is the spring constant (0.001 N/m)
Determine a linear
form of the equation relating current to displacement.
Use a root locus analysis to
determine if the system described in the following block diagram: 1) Could become unstable?
and 2)
Could ever have an oscillatory response? (Show your diagram and explaination.)
|
|
- The
following ladder logic diagram describes the control wiring of a
combustion system which uses an electric igniter to initiate
combustion. Describe how and in
what sequence the blower, fuel valve, and igniter are energized. You may use PICO Soft to examine the
system.
Press Start
Blower (Q1) energized.
Contact (Q1) closed
Timer, Time Delay #1 started
Release Start
Blower continues to run
Time delay #1 times out
Time Delay #1 contact (T1) closes
If blower (Q1) is running then Fuel Valve (Q2) is started and Time delay #2 is started
If Fuel valve is running and blower is running and Time Delay #2 has not timed out, Igniter is started
Time Delay #2 times out
Time Delay #2 normally closed contact(T2) opens
Igniter is stopped
Press Stop
Blower stops
Time delay #1 stops
Fuel valve and time delay #2 is stopped
Igniter is stopped