Closed-Loop Performance Analysis of Algebraic Estimators

Abstract

The closed-loop behavior of algebraic estimators is studied in this work via the simulation of an example. The algebraic estimators can be implemented as time-varying filters that gives an estimation of derivatives of the input signal. One considers here the inverted pendulum over a car as a representant of a class of systems with state \(x= (y^{\top }, {\dot{y}}^{\top })^{\top }\), where \(y \in \mathbb {R}^m\) is the output and \(\dot{y} \in \mathbb {R}^m\) is its time derivative. For this class of systems, which includes several important mechanical systems, the estimation of the state relies on the determination of the derivative of the output. The case study that is presented in this paper indicates many interesting properties of those estimators and allows one to state many conjectures that can be considered in a future research. This work includes also a theoretical contribution that allows to compute a bound of the error of the second-order algebraic estimator. Furthermore, it is shown that all estimators that respects this bound will assure closed-loop stability in the context of the separation principle for this particular class of systems.