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The Design of the LQR ControllerThe Observer Design

2.2.5 The Controller Design Using Constrained Feedback Stabilization

Selected for further experiments is a controller in the middle of the list lqcontrollers that adequately improves the damping factor and yet avoids extremely large feedback gains. In effect, this choice provides a reasonable compromise between the settling time of the system and the sensitivity of the feedback to the noise.

This selects the controller in the middle of the list.

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This is a norm of the feedback gains.

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This provides a measure of the noise sensitivity of the feedback.

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These are the closed-loop poles for the selected feedback matrix.

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This is a measure of the damping factor of the closed-loop system.

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This uses the partial Lyapunov feedback stabilization to construct a state feedback controller that provides a comparable damping factor.

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The norm of the feedback gain matrix is somewhat smaller than the one provided by the LQR design.

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The noise sensitivity of the feedback is also smaller.

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Here are the closed-loop poles. Note that the partial Lyapunov stabilization shifted the only noncompliant pole (the one at the origin) into the chosen region.

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The Design of the LQR ControllerThe Observer Design