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We introduce an algebraically active disturbance rejection-based control solution for the trajectory tracking problem of an uncertain second-order flat system with unknown external disturbances. To this end, we first algebraically identify the system’s unknown dynamics and the external disturbances with a linear set of time-varying integral expressions for the output and the control signal. We use the identified dynamics on an online feedback cancellation scheme to linearize the second-order system and cancel the uncertainties. With a proportional-integral controller we stabilize the linearized system without the need to estimate the velocity and have feedback from it. We carry out the stability analysis using linear systems theory. Finally, we evaluate the effectiveness of the proposed controller in a partially known 2-DOF manipulator.

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.