Abstract
This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.
Highlights
In the last 3 decades, there has been increasing interest in the control of underactuated mechanical systems
This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system
We are interested in the output feedback asymptotic stabilization and the output feedback trajectory control problems of the uncertain ball and rigid triangle (BRT) system
Summary
In the last 3 decades, there has been increasing interest in the control of underactuated mechanical systems. We can propose two decoupled extended linear observers, assuming that only the position variables of this system are available These observers allow us to simultaneously estimate the time derivatives of the nonavailable flat output and recover the uncertain underlying nonlinear dynamics. These estimations, together with the ADRC approach, allow us to propose a control scheme to solve the aforementioned control problems. Given the system model described in (8), the objective of this work consists of two goals: (1) designing a linear stabilizing controller to simultaneously bring the rigid triangle and the cart to the zero position (x1 = x2 = 0), assuming that all variables are initialized within a small vicinity of the origin, and (2) solving locally the output feedback trajectory tracking problem. The proof of this theorem can be found in Appendix
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