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This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (ψ), given by the z axis, is in free form, while the pitch angle (θ), which results from rotation about the y axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index.

This paper presents a linear robust output reference trajectory tracking controller, addressed here as a flat filtering controller (FFC), for nonlinear differentially flat systems. Here, we illustrate the controller's performance, via digital computer simulations and, also, via laboratory experiments, carried out on a single link-direct current (DC) motor driven robot manipulator undergoing a reference trajectory tracking task. The proposed linear FFC only requires the output to be regulated of the composite system and none of the internal states of the resulting third-order nonlinear system. The controller is designed on the basis of a drastic simplification of the combined single link-DC motor dynamics to a, perturbed, third-order pure integration system. This demonstrates the robustness of the proposed scheme with respect to ignored nonlinear state-dependent, endogenous, disturbances and, also, to independent unstructured exogenous disturbances inevitable in an experimental setup. Simulation and experimental results, as well as comparisons with other controllers, are presented. [ABSTRACT FROM AUTHOR]

The development of an autotuning mechanism for robotic manipulators, inspired by the success of autotuners in industrial systems, aims to reduce the time and cost of tuning robotic manipulators. This paper introduces an auto‐tuning method for PID controllers in robotic manipulators using the Modified Relay Feedback Test (MRFT) and the Optimization Under Uncertainty (OUU) principle. The mechanism is versatile, suitable for manipulators of varying scales and motor power capacities. It incorporates actuator dynamics and a combined model of Brushless DC motors with an n‐link manipulator for TR development. Various manipulator models, including commercial and open‐source types were used to refine and test the TR. An algorithm is also proposed for tuning commercial manipulators' controllers without changing the existing closed‐loop system structure. Experimental and simulation tests demonstrate the method's effectiveness, showing better performance than traditional approaches, particularly in reducing overshoot and settling time. [ABSTRACT FROM AUTHOR]

In this work, the problem of governing systems subjected to harmonic uncertainties is addressed. An active disturbance rejection control (ADRC) framework is proposed here with a key component being a novel resonant extended state observer (RESO). In contrary to the conventional ADRC-based solutions, the introduced one gives the ability to directly estimate and mitigate the influence of harmonic uncertainties. By structuring the whole observer-centred control topology into one degree-of-freedom, compact, feedback error-form (similar to industry-proven PID), the proposed approach can be straightforwardly implemented and commissioned across popular industrial control platforms. Its effectiveness is systematically analysed in terms of tracking accuracy, disturbance rejection and noise sensitivity. The new technique is generalised for the class of nonlinear control-affine systems and expressed with three special forms, each one providing certain advantages to control design. Additionally, an experimental case study is conducted, showing superior performance of the proposed solution against a conventional one. Finally, the stability of the developed approach is rigorously proved using singular perturbation theory. [ABSTRACT FROM AUTHOR]

We explore the equivalence among flat filters, dirty derivative-based proportional integral derivative (PID) controllers, active disturbance rejection control, and integral reconstructor-based sliding mode control, in the context of SISO second-order, perturbed, pure integration systems. This is the prevailing paradigmatic class of differentially flat systems or feedback linearizable systems. The equivalence is valid beyond the second-order pure integration systems. However, PID controllers of such plants do not make much sense without imposing assumptions that will move the considerations out of the pure integration systems case. The equivalence among the rest of the controllers is valid for any finite order pure integration system. [ABSTRACT FROM AUTHOR]

Summary: We address the sliding mode control design problem for output reference trajectory tracking problems in the special class of MIMO flat systems known as static feedback linearizable systems. We assume unavailable system state components but rely on available inputs and measurable flat outputs. Each controller will largely ignore state and control input couplings by adopting a standard sliding mode controller scheme derived from the SISO case and used this as decoupled input‐to‐flat‐output model. The standard controller arises from a vastly simplified pure integration, additively perturbed, system. The simplified pure integration system controlled trajectories are shown to be time‐scale homotopically equivalent to those of the nonlinear flat system. The basic sliding surface coordinate function design is approached from the perspective of structural integral reconstructors requiring only the inputs and the flat outputs of the system. Integral structural reconstructors were introduced by Fliess et al for the control of linear SISO and MIMO systems, giving rise to the generalized proportional integral control method. Simulations are presented for SISO and MIMO systems and experimental results are reported for a two‐degree‐of‐freedom fully actuated robotic manipulator. [ABSTRACT FROM AUTHOR]

The need for observers, or other means of state- or phase variables-on-line computations, is revisited from the perspective of structural integral reconstructors. The problem addressed is the regulation, via simplified pure integration dynamics, of the large class of static, or dynamic, feedback linearisable systems (i.e. differentially flat systems), subject to additive exogenous disturbances and where nonlinearities are purposefully neglected. Integral reconstructors of the simplified input-to-flat output dynamics, directly lead to generalised proportional integral controllers, which are also shown to be equivalent to classical compensation networks. Their robust version, addressed here as flat filters, are found to be quite useful in the approximate (i.e. practical) control of perturbed differentially flat systems. The controller design is based on their simplified, perturbed, and pure integration dynamics. Flat filters evade for the need of nonlinear asymptotic observers and other, on-line, explicit output time derivatives computations. Simulation and challenging experimental examples are provided to validate this linear approach to the control of nonlinear flat systems. [ABSTRACT FROM AUTHOR]