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In this article, the problem of designing Active Disturbance Rejection Control (ADRC) for a class of second-order mechanical systems, expressed with Euler-Lagrange equations, is studied. A specific and practically motivated case is considered here, namely trajectory tracking task without the use of signal time-derivatives in the tracking controller. A general solution is proposed showing how to synthesize and tune the observer and the controller parts of the ADRC scheme. A special Extended State Observer is used in the design and here it takes the form of a Generalized Proportional Integral Observer (GPIO), which uses a Taylor series approximation of the total disturbance. A set of experimental results, obtained using a two degree-of-freedom robotic manipulator, shows the effectiveness of the proposed governing scheme in terms of trajectory realization and disturbance rejection without the use of signal time-derivatives in the controller.

In this article, an Active Disturbance Rejection Control (ADRC) scheme is tested on a non-differentially flat system, with controllable linearization, to solve the problem of trajectory tracking for the inverted pendulum on a cart. Differential Flatness allows to design a control law that simultaneously achieves the trajectory tracking for the cart while regulating the inverted pendulum so that it remains near the unstable equilibrium point in spite of large perturbations. The proposed method assumes a limited knowledge of the system and relies on linear disturbance observation using linear feedback control techniques. Internal and external disturbance inputs are estimated by an Extended State Observers (ESO), which delivers these estimates to the controller for an on-line disturbance cancellation. Experiments on a laboratory prototype allowed to evaluate the proposed scheme with effective results in the presence of external disturbances.

This paper presents a linear, decoupled, robust output trajectory tracking controller, addressed as flat filtering controller (FFC), for a multiple input multiple output (MIMO) nonlinear differentialy flat systems. The flat filter only requires the outputs to be regulated with the help of a well tuned filter and a suitable linear combinations of the internal states of such filter. To illustrate the proposal, the Permanent Magnet Synchronous Motor (PMSM), which is a flat MIMO system with the angular position and the $i_{d}$ current as flat outputs, is considered. Although the control inputs are coupled, the controller is designed on the basis of a drastic simplification to a first and third order pure integration systems respectively with additive disturbances to be compensated. The robustness of the proposed scheme, with respect to ignored nonlinear state-dependent, endogenous, disturbances and, also, to independent unstructured exogenous disturbances, is verified via computer simulations as well as experimental results.

This study presents a solution to design an automatic controller that forces the trajectory tracking of a tomographic robotic system. The methodology to design the controller was the Active Disturbance Rejection Control (ADRC). A pseudo-adaptive version of ADRC enforces a smooth trajectory tracking with a small ultimate bound for the tracking error. The control solution used the estimation of velocity that was estimated by an extended adaptive state observer included in the ADRC solution. A set of numerical evaluations over a tomographic robotic system proved the efficiency of the proposal in terms of a performance index.

The aim of this study was to design and evaluate an output based adaptive rejection controller (ADRC) for a biped robot. The controller considers the application of an extended state observer which serves for either estimate the velocity of the legs articulation angles as well as to estimate the disturbances affecting the robot dynamics. The observer design considered the angles constrains which naturally appear in the movement of a biped robot. A class of hybrid observer appeared as solution for the estimation of angles values and their positions. The control design (proposed in a distributed structure) used the constrained estimation of velocity to solve the tracking trajectory problem associated to the gait cycle of the biped robot. A set of numerical evaluations over a simulated biped robotic system proved that active disturbance rejection controller using the estimated state constrains tracked the reference angles of articulation. The comparison of the controller proposed in this study overcame the tracking results attained by the classical ADRC where the estimated velocities were freely estimated without taking into account the angles constrains.

The present work shows the design and implementation of a position control by artificial vision for the focus system of a desalination robot by solar distillation, in order to provide conditions of operation, safety and monitoring to carry out the process Of distillation. In such a way that the limits of displacement and the position of the container are established in real time by crossing two permissible curves, one defined in relation to the process temperature and another in terms of safety. The control is validated through experimental tests.

In this article, a bilateral output feedback controller to solve the trajectory tracking problem of a Master-Slave mechanical system is designed. A robust disturbance rejection scheme was implemented to regulate the slave trajectory. A Linear Extended State Observer of GPI class was used to, both, estimate the non-measurable states of the mechanical systems as well as the global disturbance input, which was assumed to be a lumped signal from non-modelled dynamics and external forces in the slave side. The bilateral controller was synthesised by means of two feedback strategies: estimation of disturbances and impedance based control. Experimental results show the effectiveness of the control scheme in a manipulation task.

In this article, the ball and beam trajectory tracking problem is tackled using a robust Generalized Proportional Integral (GPI) Controller. The controller is developed on the basis of the tangent linearized system model around the equilibrium point. The approximate linearized system is differentially flat, and hence, controllable. Flatness reveals that the resulting linearized system has an interesting cascade property which allows the simplification of the controller design. Experimental results are included to show the effectiveness of the controller in trajectory tracking and disturbance rejection control.

Flat filtering constitutes a reinterpretation of Generalized Proportional Integral Control (GPIC) in the form of robust Classical Compensation Networks (CCN). Roughly speaking, any linear controllable system can be output regulated with the help of a well tuned filter and a suitable cascaded linear combinations of the internal states of such filter. Here, it is shown that such classical tool is also capable of efficiently handling control tasks on perturbed nonlinear systems, including unknown nonlinearities and un-modeled dynamics.

In unknown environment, path planning of multiagent systems is difficult. The popular methods for the path planning, such as reinforcement learning (RL), do not work for these two cases: unknown environment and multi-agent.

In this article, an Active Disturbance Rejection Control (ADRC) scheme, using a Generalized PI disturbance observer based control is applied to the stabilization problem of the Inertia wheel pendulum. The control scheme assumes a limited knowledge of the underactuated system and relies on a simplified model regarded as a perturbed chain of two integrators with a stable zero dynamics. The control scheme is experimentally tested, showing good performance. A comparison study with respect to a linear control scheme is also carried out.

A possible limitation of differentially flat systems stems from the possibility of gain singularities on open or closed regions of the flat output phase space. The evasion of control gain singularity poses an important theoretical problem even under the scope of Active Disturbance Rejection Control. In this article, we illustrate an interesting example of controlling a singular flat system, the inertia wheel pendulum, using the combined benefits of ADR control and flatness as applied to a carefully chosen flat tangent linearization model of the singular system.

In this article, the problem of parameter identification and state estimation for synchronous motors is tackled by means of the combination of algebraic techniques, in the context of a step by step approach. The step by step procedure consists in separating the estimation problem in three subsequent steps, in such a manner that it is possible to carry out each identification (estimation) step. The first one estimates a set of electrical parameters, then a state estimation based on the algebraic derivative approach is performed. The results of the proposed algebraic techniques are used to make possible the last step, in which the mechanical parameters are estimated. Numerical results are used to illustrate the effectiveness of the proposed methodology.

This article studies, an Active Disturbance Rejection Control scheme, using a Generalized PI disturbance observer based control applied to the stabilization problem of the Furuta pendulum. The control scheme assumes a limited knowledge of the system and uses a simplified model of the Furuta pendulum modeled as a disturbed chain of two integrators. The control scheme is experimentally tested, showing good performance. A comparison study with respect to a linear control scheme is also carried out.

This article addresses the problem of Linear Active Disturbance Rejection Control for a class of nonlinear mechanical input time delayed systems. To solve the problem, it is necessary to obtain a set of predictive lumped disturbance estimations, which is carried out by a purely linear high gain observer of Extended Luenberger type, denoted as a Generalized Proportional Integral (GPI) Observer. This task is performed using an approximation of the predictive disturbance using a truncated Taylor series expansion, where the set of necessary values for the estimation are provided by the observer. Once the (approximate) disturbance canceling is made, the control task is reduced to a simple linear Smith Predictor PD control, using the simplified model of the mechanical system. Some experimental results show the effectiveness of the strategy in a trajectory tracking task for a perturbed flywheel.

In this article, a model matching controller for the stabilization of the Two Wheels Inverted Pendulum is present. The stabilization strategy consists in forcing the closed-loop system to behave as another nonlinear target system with some stability properties. To this end, we solve two matching conditions that allow us to shape a suitable target system and we obtain the stabilizing controller. The resulting closed-loop system is locally asymptotically exponentially stable, with a very large domain of attraction.

In this article, we address an active disturbance rejection controller design for the output reference trajectory tracking problem in a 3 degree of freedom (DOF) Delta Robot. The proposed method relies on purely linear high gain disturbance observation and linear feedback control techniques. The estimation tasks are carried out with the help of Generalized Proportional Integral (GPI) observers, endowed with output integral injection to counteract zero mean measurement noise effects. As the lumped exogenous and endogenous disturbance inputs are estimated, the observers deliver them to the controllers for on-line disturbance cancelation, while simultaneously the phase variables, related to the measured flat outputs, are being estimated by the same GPI observer. The gathered values of the phase variables are used to complete a linear multivariable output feedback control scheme. The proposed control scheme avoids the traditional computed torque method, reducing the computation time and bypassing the need for explicit, accurate, knowledge of the plant. The estimation and control method is only approximate as small as desired reconstruction, or tracking, errors are guaranteed. The reported results, including laboratory experiments, are significantly better than the results provided by the classical model-based techniques, when the system is subject to endogenous and exogenous uncertainties.

A field oriented armature input voltage output feedback control approach is proposed for the robust linear controller design on an induction motor. The scheme simultaneously solves an angular velocity reference trajectory tracking task, and a flux magnitude regulation in the presence of arbitrary time varying load torques and unknown nonlinearities. The field oriented input voltage scheme is combined with linear high gain asymptotic observers, of the Generalized Proportional Integral (GPI) type, and linear, active disturbance rejection, output feedback controllers. The linear observers on-line estimate, in a simultaneous manner, the output phase variables and the lumped effects of a) unknown time-varying load torques and unmodeled frictions and b) rather complex state-dependent nonlinearities present in the electric and magnetic circuits. The field oriented part of the scheme uses the classical flux observer, or simulator. The proposed control laws naturally decouple, while linearizing, the extended second order dynamics for the angular velocity and for the squared flux magnitude. The proposed control scheme is here tested on an experimental induction motor set up.

This article proposes the use of a high gain, Generalized Proportional Integral (GPI), observer for the accurate linear estimation of nonlinear endogenous, and exogenous, disturbance inputs affecting the creation of local sliding regimes, on a given sliding manifold, for Single-Input Single-Output (SISO) systems with limited control authority. Active, online, estimation, and cancelation, of state dependent and time-dependent disturbances, significantly contribute to reducing the required switching control amplitude needed to sustain a sliding regime. This method results in enhanced performance on the controlled variable. Illustrative simulation examples are presented which validate the proposed approach.

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a suitable external control input channel guided by a) the induction of the flatness property on a measurable output signal of the circuit and b) the physical viability of the control input. A linear active disturbance rejection control, based on a high gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear, high-gain, observer, called a Generalized Proportional Integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.

In this article, we propose a fast, on-line, algebraic identification scheme for the determination of some relevant induction motor parameters. The estimated values, given by the algebraic identification methodology, are here tested in a self-tuning output feedback control, subject to constant perturbation load torques while solving a reference trajectory tracking task. An output feedback controller of the classical, Field Oriented, Proportional Integral (PI) type, is proposed for the perturbed output trajectory tracking problem. Experimental results validate the effectiveness of the proposed approach.

In this paper, the process of developing a Flight Control System (FCS) by using an economical Commercial-Off-The-Shelf (COTS) solution will be discussed. The approaches and methods of incorporating advanced features onto an inexpensive but fundamental FCS will be evaluated.

In this article, we propose a new discontinuous feedback controller design approach for the asymptotic sliding mode control of a large class of linear switched systems. The method is devoid of state measurements and efficiently extends the sliding mode control methodology to traditional input-output descriptions of the plant. The approach is based on regarding the average Generalized Proportional Integral (GPI) output feedback controller design as a guide for defining the sliding mode features. Throughout, it is assumed that the available output signal coincides with the system's flat output, an output capable of completely differentially parameterizing all the variables in the system (inputs, original outputs and state variables) and exhibits no zero dynamics. Encouraging simulation results are presented in connection with a tutorial example. Experimental results are also presented for the trajectory tracking problem on a popular DC-to-DC switched power converter of the “buck” type.

The problem of controlling load perturbed induction motors is tackled by means of an observer based robust discrete-time control. In this scheme, model uncertainties and external disturbances are included in a general additive disturbance input which is to be on-line estimated and subsequently rejected via the controller actions. The observer carries out the disturbance estimation, thus reducing the complexity of the controller design. The controller efficiency is tested via some numerical simulations, performing a trajectory tracking task under severe load variations.

An algebraic parameter identification method for, high rate, sampled linear systems is proposed for the output feedback control of a completely unknown DC motor. The parameter estimation method is based on the algebraic methodology (introduced by Fliess and Sira-Ramirez in [1]) for continuous time systems. In this article, we adapt the algebraic parameter identification methodology so that it takes into account sampling effects. We apply the algebraic identification method within the delta operator framework developed by Middleton and Goodwin in [2]. Delta operators constitute an effective alternative, over the Z-transform, for working with fast sampled systems. One of its advantages ensures a smooth transition between a continuous and a high sampled discrete sampled system. We use a delta operator-based algebraic identification scheme for the construction of the involved linear regressor in combination with a special invariant filtering to improve the identifier against additive noise effects. Our invariant filtering coincides with the least squares solution of the linear regressor equation. A delta-operator based output feedback controller of the Generalized Proportional Integral (GPI) type is also proposed for the solution of the output trajectory tracking problem, for the DC-motor, as a certainty equivalence controller. The fast identification of all system parameters is used in the certainty equivalent feedback control law design. Some experimental results are presented which validate the effectiveness of the proposed approach.