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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