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2 International Journal of Applied Mathematics and Computer Science

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Algebraic active disturbance rejection to control a generalized uncertain second-order flat system

Aguilar-Ibanez Carlos, Suarez-Castanon Miguel S., Saldivar Belem, Jimenez-Lizarraga Manuel A., de Jesus Rubio Jose, Mendoza-Mendoza Julio

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 2

185--198

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.

A trajectory planning based controller to regulate an uncertain 3D overhead crane system

Aguilar-Ibanez Carlos, Suarez-Castanon Miguel S.

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 4

693--702

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.