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In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

In this article, the analysis and implementation of an alternative Flat Filtering Control for a class of partially known fourth order flat systems is given. The Flat filtering control uses the cascade property of the system, which leads to a simplified control design in which high order time derivatives are algebraically simplified in terms of low order measurable states and the subsequent integral compensation. The control proposal is implemented and validated experimentally in a fourth order mechanical system (rotatory flexible joint) with accurate tracking results.

In the present contribution, the problem of establishing tuning rules to proportional retarded controller for LTI systems is addressed. Based on the D-decomposition methodology and σ-stability analysis, analytic conditions are determined on the parameters of a delayed controller that guarantee us that the system response reaches the maximal decay rate. The conditions presented in this paper are tested experimentally in tracking tasks of a flexible joint robotic arm.

This article deals with the control of a class of robotic systems with constant input time delay through the Active Disturbance Rejection paradigm, by means of Generalized Proportional Integral observers. The system is represented as a linear perturbed system, whose lumped disturbance input is estimated and then compensated by an Extended State Observer-Based Control, which is implemented on a predictor scheme for the time delay compensation. A complete Lyapunov Krasovskii functional was used to perform the stability analysis, leading to an ultimate bound trajectory tracking error. The proposal is tested and validated on a two degrees of freedom robotic manipulator.

This paper is concerned with the design and experimental assessment of, both, feedback linearization and sliding mode control techniques to the tracking trajectory problem of a flexible-joint robotic arm for a smooth rest to rest maneuver. The robust improvement of these controllers is analyzed by means of additional integral compensation, in which an alternative sliding surface was proposed for the control of the flexible arm. A feedback linearization of the nonlinear dynamic equation of the robot arm is computed in order to get a full-state non-linear feedback control law. On the other hand, it is proposed a second order sliding mode control with an integral term in the sliding surface, which improves the robustness of the controller sliding surface. Some experimental evaluations that include the addition of external unmodeled perturbations to test the enhancement of the robustness property show the improvements and effectiveness of the proposed control laws in disturbance rejection tasks. The controllers were implemented using exclusively position measurements and time derivatives approximations.