Design parameters and uncertainty bound estimation functions for adaptive-robust control of robot manipulators

In this paper, a parameter and uncertainty bound estimation functions for adaptive-robust control of robot manipulators are developed. A Lyapunov function is defined and parameters and uncertainty bound estimation functions are developed based on the Lyapunov function. Thus, stability of an uncertain system is guaranteed and uniform boundedness of the tracking error is achieved. As distinct from previous parameter and bound estimation laws, the parameters and uncertainty bounds are updated as a function of a combination of trigonometric function depending on robot parameters and tracking error. Based on the same Lyapunov function, a robust control law is also defined and the stability of the uncertain system is proved under the same set of conditions. Simulation results are given to illustrate the tracking performance of the proposed adaptive-robust controller.

Anahtar Kelimeler:

Robust control, adaptive control, robot manipulators, parameter uncertainty, adaptive-robust control, stability analysis

Design parameters and uncertainty bound estimation functions for adaptive-robust control of robot manipulators

Keywords:

Robust control, adaptive control, robot manipulators, parameter uncertainty, adaptive-robust control, stability analysis,

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the most appropriate values of ˆπ and ˆρ(t) in order to reduce the tracking error. Computer simulation results illustrated that proper estimation of ˆπ and ˆρ(t) were achieved, tracking performance was improved, and, as a result, proper estimation of ˆπ and ˆρ(t) improved the tracking performance.
In order to guarantee stability of an uncertain system, a Lyapunov function was deŞned, including 2 novel functions such as Φ1and Φ2. There may be some sort of functions Φ1and Φ2for control inputs u(t)1and u(t)2that satisfy the stability of the uncertain system. However, there is no certain rule for the determination of Φ1and Φ2for control inputs u(t)
and u(t)2that satisŞes ˙V≤ 0 in Eq. (15). We used system state parameters and mathematical insight and found the appropriate novel functions Φ1and Φ2for control inputs u(t)1and u(t)
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