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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)
Pole Trajectory by changing sampling rate of camera
Pole Trajectory by changing ECG
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
Derivative Controller
(Kd)
Proportional Controller
(Kp)Plant
PD controller
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
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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