maryam alizadeh april 27 th 2011 1. contents: quick review proportional controller results ...
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VISUAL SERVOING USING 2-DOF HELICOPTER
Maryam AlizadehApril 27th 2011
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Contents:
Quick Review Proportional Controller Results Proportional + Derivative Controller Conclusion Future Works
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Quick Review
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Considered Parameters
Initial position of ball Camera location Sampling rate of camera ECG
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This system is considered as a second-order system
By finding poles of this system, that system would be a known system and its response to different situations can be predictable.
The following plots show pole trajectory by changing one the considered parameters (Sampling rate of Camera and ECG)
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Pole Trajectory by changing sampling rate of camera
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Pole Trajectory by changing ECG
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Comparison between Pole Trajectory by changing sampling rate of camera & ECG
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Proportional Controller
(Kp)Plant
ECG performs as Proportional controller gain
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Proportional + Derivative Controller
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Derivative Controller
(Kd)
Proportional Controller
(Kp)Plant
PD controller
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14Pole trajectory by changing Kd in Yaw controller, ECG=0.1
Kd=0.1
Kd=0.1
Kd=0.01
Kd=0.01
Kd=0.05
Kd=0.05
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15Pole trajectory by changing Kd in Pitch controller, ECG=0.1
Kd=0.1
Kd=0.1
Kd=0.01
Kd=0.01
Kd=0.05
Kd=0.05
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These two trajectories show that there is an optimum value for kd
(≈0.05). With this proportional controller gain,
controller is more stable. By increasing the gain, the system is
going toward unstability. Next figures show how unstable the
system is for kd=0.12
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Ball trajectory in X direction(Yaw), Kd=0.12
Ball trajectory in Y direction(pitch), Kd=0.12
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Comparison between P & PD controllers:
In next step, Kd is chosen equals to 0.05 and ECG is changed.
The purpose is finding the effect of adding a derivative controller to the system
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Comparison between pole trajectories in P & PD controller by changing ECG , Kd=0.05
ECG=0.1
ECG=0.1
ECG=0.1ECG=0.
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ECG=0.01
ECG=0.1
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Conclusion:
Above plot illustrates the effect of adding a derivative controller to our system.
As it is expected , PD controller’s poles are further away from imaginary axis .It confirms that PD controller is more stable than a proportional controller in the same situations.
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Future Work
Changing ECG & Kd in a wider range to collect more information about system behaviour in different situations.
Applying a more systematic approach instead of ECG in order to define a trajectory and precisely track that.
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