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Feedback Linearization.md

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Feedback Linearization Technique

Let image be the FBL state of the controller and image be the linear FBL control input

The next step is to construct the second order linear system as

Based on the equation, it can be easily depicted that the linear control input is defined as an acceleration vector state of the vessel in the global frame

A_FSF = [0 1 0 0 0 0;
        0 0 0 0 0 0;
        0 0 0 1 0 0;
        0 0 0 0 0 0;
        0 0 0 0 0 1;
        0 0 0 0 0 0];
B_FSF = [0 0 0;
        1 0 0;
        0 0 0;
        0 1 0;
        0 0 0;
        0 0 1];
pole_FSF = [-1 -0.35 -1.2 -0.55 -1.3 -0.6];
K_FSF_MATRIX = place(A_FSF,B_FSF,pole_FSF);