Estimating the Unmeasured Output of Nonlinear SISO System under Uncertainty

Abstract

Nonlinear single-channel control plant with affine unmached external disturbances are considered. Their mathematical model has the so-called triangular (based on the composition of the arguments of the functions in each equation) “input-output” form, which has the following structural properties. If there are no external disturbances, then this form is controllable and observable in terms of output. If external disturbances are smooth, then the control plant model is representable in the canonical “input-output” form with respect to mixed variables (functions of state variables, external disturbances and their derivatives). In the new mixed variable basis, the system remains controllable, observable, and has the same relative degree as the original system. If the output variable is measured, then an observer of mixed variables can be constructed based on the canonical system and, using suitable feedback, ensure the desired behavior of the output variable. In this case, there is no need to detail external disturbances and design individual observers for them, which greatly simplifies the structure of the controller. This paper discusses the problem of implementing the specified synthesis procedure in the case when the output variable is not measured. Motivating examples are given and conditions are formulated under which it is possible to first restore the output variable from the measurement of other state variables invariantly with respect to the action of external disturbances. Methods for estimating external disturbances using observers with piecewise linear corrective actions, which do not require the introduction of dynamic disturbance models, constitute the methodological basis for solving this problem. Using the example of various mathematical models of single-link manipulators, the fulfillment/failure of the conditions necessary to restore an unmeasured output variable is demonstrated. The proposed approach can be extended to multichannel nonlinear control plants without loss of generality.