wind turbine control matlab simulations pid
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Control Systems Lab Project
(WIND TURBINE CONTROL)
Section:
G (H)
Project Team:
KHURUM HASHMI……………………………L2F08BSEE0660
NAJAM UD DIN…………………….…………L2F08BSEE0688
Session 2008-2012
FACULTY OF ENGINEERING UNIVERSITY OF CENTRAL PUNJAB LAHORE,
PAKISTAN
WIND TURBINE CONTROL ABSTRACT
The following system describes a wind turbine running an induction generator through a gear
train with the transformation ratio N. The following calculations are made in order to Control the
Closed Loop output bringing it to Near idea. The intrinsic constraints involved with varying the
parameters such as increased overshoot for quicker rise time have been dealt with accordiongly.
MAIN TRANSFER FUNCTION
Where N is the Gear Train Ratio
Substituting typical numerical values in above equation yields result
Putting N=1; we have
Gdt(s)=
1.023*1016
*s
------------------------------------------------------------------------------------------------
1.864*1011
*s5 + 9.32*10
12 *s
4 + 1.611*10
16 *s
3 + 7.211*10
17 *s
2 + 2.609*10
15 *s
Simplifying
Gdt(s)=
10228490495999998*s
--------------------------------------------------------------------------------------------------------------------
7840*s*(23776543*s4+1188827150*s
3+2054688049000*s
2+1972388250000*s+332820000000)
STATE SPACE
A=
B=
C= D= [0]
Time Response
The system attains its peak value in a very large time Span. Even though system is stable Peak
amplitude appears only at the termination of the response time
So Rise time, Peak time, Settling time all parameters are crowded at the end of the response
Rise Time 123 seconds
Settling time 220 seconds
%age Overshoot 0
Peak time > 1*10^3 seconds
Peak mag (closed loop) 0.796
Steady State error 21 %
Stability Stable
ROOT LOCUS
System Has two poles on real
axis and two on the imaginary
axis
One zero at origin
Intuitively from the position of
the poles the system appears to
be marginally stable
Effect of Varying N positively increasing
Figure shows Step
response for
Transfer functions
with Values of N
from1 to 10
The greater the
value of N. Closer
the response to
Ideal and System
Attains stability
much Quicker
We choose N at 10
substituting N=10
Gdt(s)=
1.023*1018
*s
-----------------------------------------------------------------------------------------------
6.17*1011
*s5 + 3.085*10
13 *s
4 + 2.004*10
16 *s
3 + 7.225*10
17* s
2 + 2.609*10
17* s
Simplified
Gdt(s)=
10228490495999998*N2*s
--------------------------------------------------------------------------------------------------------------------
2395512000000*s2*(688*s+(
*(
)+301000*N
2*(190120*s
2+12600000)*(688*s+(1
9*s2*(
))
STATE SPACE
A=
B=
C= D= [0]
TIME RESPONSE
System response has modified to
be nearer to the ideal. Still, Peak
amplitude occurs at the very End
and so with the rest of the
parameters
Rise Time 1.17 seconds
Settling time 2.12 seconds
%age Overshoot 0
Peak time >14 seconds
Peak mag
(closed loop)
0.796
Steady State
error
21 %
Stability Stable
ROOT LOCUS
As in case of N=1
System Has two poles on real axis and
two on the imaginary axis
One zero at origin
Intuitively from the position of the poles
the system appears to be marginally
stable
Frequency Response
For N=1
Showing Frequency Response and Phase angle
For varying
values of N from
1 to 10
With increase in
N
Corner frequency
occurs further on
at greater
frequencies
SIMULINK
Gear Ratio N=1 Original system
Controlling through PID chosen system of Gear Ratio N=10
State Space model
PID Controller GUI
Auto Tuning GUI
CONTROLLING OUTPUT
We have worked with the system with Gearing Ratio (N) =10 so less tuning has to be effected to
bring the system nearer to the ideal response
Original transfer function with N=10
Gdt(s)=
1.023*1018
*s
-----------------------------------------------------------------------------------------------
6.171*1011
s5 + 3.085*10
13 s
4 + 2.004*10
16*s
3 + 7.225*10
17*s
2 + 2.609*10
17*s
The Proportional Integral Derivative (P I D) method is used
Controller(s) =
1
Kp + Ki * --- + Kd *s
s
Auto tuning followed by limited trial and error leads to the following
Kp = 3.39008930751897
Ki = 1.4346893216856
Kd = -0.47
Multiplying this with the given transfer function yields
Gdt(s)=
-4.807*1017
*s3 + 3.468*10
18* s
2 + 1.467*10
18*s
---------------------------------------------------------------------------------------------------
6.17*1011
* s6 + 3.085*10
13*s
5 + 2.004*10
16*s
4 + 7.225*10
17*s
3 + 2.609*10
17*s
2
Solving in Feedback
Tf(s)=
-4.807*1017
*s3 + 3.468*10
18*s
2 + 1.467*10
18*s
------------------------------------------------------------------------------
6.17*1011
*s6 + 3.085*10
13*s
5 + 2.004*10
16*s
4 + 2.418*10
17*s
3 + 3.728*10
18*s
2+ 1.467*10
18*s
Which is the required transfer function
STATE SPACE
A=
B=
C= D= [0]
TIME RESPONSE
Seen in LTI view. Peak response occurs at17.7 seconds. Steady state error is zero the overshoot
is so ignorable that does not appear here and system is very close to ideal
Rise Time 0.379 seconds
Settling time 0.649 seconds
%age Overshoot 0.757
Peak time 1.34 seconds
Peak mag (closed loop) 1.01
Steady state error 1%
Stability Stable
ROOT LOCUS
Zoomed in
BODE PLOT
COMPARING PARAMETERS:
N=1 N=10 Tuned Output
Rise Time 123 seconds 1.17 seconds 0.379 seconds
Settling time 220 seconds 2.12 seconds 0.649 seconds
%age Overshoot 0 0 0.757
Peak time > 1*10^3
seconds
>14 seconds 1.34 seconds
Peak mag (closed
loop)
0.796 0.796 1.01
Steady State
error
21 % 21 % 1%
Stability Stable Stable Stable
Increasing the gear ratio Response nears ideal. In addition Propotional Derivative Integrator
Controller is used to control peak time and bring it nearer to the beginning of the response
References: Control Systems Engineering by Norman.S.Nise 6
th edition
www. Mathworks.com
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