Abstract
In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.
Highlights
In many practical applications of automatic control, the fast and accurate stabilization or tracking of a second-order system from acceleration measurements only constitutes an important task
In many mechanical systems, accelerometers are the only available sensing devices for feedback control such as in the control of some unmanned vehicles used in aerospace, some positioning control applications or rotor-dynamics problems
The observability analysis of the system considered in this paper shows that any suitable differentiator of the output and the input could be used for completing the finite-time estimation-based feedback control scheme
Summary
In many practical applications of automatic control, the fast and accurate stabilization or tracking of a second-order system from acceleration measurements only constitutes an important task. This article (based on the paper [4] with significant improvements) is concerned with the finite-time (or non-asymptotic) feedback control of second-order systems where only the highest-order time derivative of the output is available for stabilization or tracking purposes. This objective is fulfilled in two steps. Sira-Ramírez in [6] for the finite time of state and parameters estimation This procedure mainly consists of differentiating, in the frequency domain, with respect to the complex variable s, as many times as required, the Laplace transformed expression of either the system equation or of a significantly related equations.
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