The paper considers nonlinear single-channel control plants with affinely uncoordinated external disturbances and an unmeasured output variable. It is shown that the model can be represented in the canonical "input-output" form with respect to mixed variables (functions of state variables, external disturbances and their derivatives). It is important that in the new coordinate basis of mixed variables the system remains controllable, observable and has the same relative degree as the original system. Based on the obtained form, it is possible to construct an observer of mixed variables and further construct a controller. The paper uses observers with piecewise linear corrective actions that do not require the introduction of dynamic disturbance models. Using various mathematical models of single-link manipulators as an example, the fulfillment/non-fulfillment of the conditions necessary for restoring the unmeasured output variable is demonstrated. The proposed approach can be extended in future to multichannel nonlinear control plants.