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  "body": "\n## Summary\n\nFeedback linearization transforms a nonlinear [[control system|ZPDTVZQN5K]] into a linear one by a change of state coordinates and a feedback law that cancels the nonlinearities.\nAfter the transformation, the tools of linear control, such as eigenvalue placement, can be used to design a controller.\nExact conditions for it are given in terms of [[Lie brackets|68FGQEBD6J]] of the vector fields of the system.\n\n## Explanations\n\n### L1 human\n\nMany machines obey nonlinear equations, which are hard to control directly.\nIf the input enters the equations in the right place, one can choose the input to cancel the nonlinear terms exactly.\nWhat is left is a linear system, which is well understood.\nFor a pendulum $x_1' = x_2$, $x_2' = -\\sin x_1 + u$, the choice $u = \\sin x_1 + v$ gives $x_1' = x_2$, $x_2' = v$, a linear system in the new input $v$.\n",
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