Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only

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 purpose...

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Bibliographic Details
Published in:Automation (Basel) 2021-12, Vol.2 (4), p.266-277
Main Authors: Delpoux, Romain, Floquet, Thierry, Sira-Ramírez, Hebertt
Format: Article
Language:English
Subjects:
Acceleration measurement
Accelerometers
Algebra
algebraic state estimation
Algorithms
Automatic Control Engineering
Computer Science
Control theory
Feedback control
finite-time acceleration feedback
Integrals
Mathematical analysis
Mechanical systems
Methods
Mode tracking
Noise
Parameter estimation
Parameter identification
Position errors
Sliding mode control
State estimation
Tracking control
Variables
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Summary: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.
ISSN:2673-4052
2673-4052
DOI:10.3390/automation2040017