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An integral and MRAC-based approach to the adaptive stabilisation of a class of linear time-delay systems with unknown parameters

Ramírez Jerónimo Luis Felipe, Saldivar Belem, Aguilar-Ibañez Carlos, Acosta José Ángel

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 1

81--91

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.

A new control algorithm for a nonholonomic mobile robot

Kozłowski K., Majchrzak J.

Archives of Control Sciences

2002

Vol. 12, no. 1/2

37-69

In this paper a trajectory tracking control problem for a nonholonomic mobile robot by making use of a kinematic oscillator has been solved. Firstly - time varying oscillator is axamined to control nonholomic mobile robot based only on its kinematics. Secondly - backstepping procedure is proposed to include robot dynamics and servo loop. It is shown that overall multilevel controller is asymptotically globally stable to a amall error different from zero. A wide range of simulation results are presented which illustrate behaviour of the controller with respect to tuning its parameters. Some preliminary experiments are reported too.