Dependence on Time Derivatives of the Input in the Nonlinear Controller Canonical Form

Introducing time derivatives of the input in the nonlinear controller canonical form, it is possible to enlarge the class of systems transformable into such a form. Exact linearization of this form is possible using dynamic feedback. On the other hand, this approach does not linearize the whole closed loop since the dynamics of the feedback is nonlinear. The dimension of this nonlinear dynamics is determined by the order of input time derivatives occuring in the canonical form. Relations are derived which allow the calculation of the transformation into canonical coordinates with minimal order of time derivatives of the input. A nonlinear third order example is considered.