Feedback Linearization 

Feedback linearization is an exact linearization process that computes state and feedback transformations to linearize a nonlinear system and allows for the design of nonlinear controllers using linear techniques. Compare controller designs based on exact and approximate linearizations for a magnetically levitated system.

The affine model can be obtained directly from the governing equations.

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It is completely feedback linearizable, since there are no residual dynamics.

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Compute the stabilizing feedback gains using the exactly linearized system.

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Simulate the closed-loop system for given initial conditions.

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Compute stabilizing feedback gains using the approximately linearized system.

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The design based on exact linearization has a better response.

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The nonlinear controller used in the exact linearization design.

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The control effort expended.

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The effort expended for the exact case is much lower than that of the approximate.

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An animation of the ball being levitated using the nonlinear controller.

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