Hebertt Sira-Ramirez

• PhD
• Cinvestav IPN at Center for Research and Advanced Studies of the National Polytechnic Institute

In this paper, the problem of transporting an inverted or a suspended pendulum on a quadrotor, subject to external crosswind disturbances is addressed. The proposed solution is based on the flatness property of the tangent linearisation model, obtained around a stationary equilibrium point of the system; such an approach allows to define auxiliary...

In this article, a Geometric Algebra (GA) and Geometric Calculus (GC) based exposition is carried out dealing with the formal characterization of sliding regimes for general Single-Input-Single-Output (SISO) nonlinear switched controlled Hamiltonian systems. Necessary and sufficient conditions for the local existence of a sliding regime on a given...

In control system design, managing measurement noise is a critical challenge, requiring a balance between responsiveness and noise suppression. Traditional methods often involve trade-offs, compromising either aspect. This paper proposes a novel solution by integrating a Finite Impulse Response (FIR) filter within the discrete controller transfer f...

From the Guest Editors: Announcing yet another special issue on ADRC Since its introduction, the Active Disturbance Rejection Control (ADRC) philosophy has attracted worldwide attention from academic and industrial communities. Although most ADRC contributors come from Asia, a growing control community in Ibero-America has adopted ADRC as a control...

1st INTERNATIONAL WORKSHOP ON ACTIVE DISTURBANCE REJECTION CONTROL July 3-5, 2024, 9:00 a 16:00 hours México City at the Universidad Iberoamericana Ciudad de México On behalf of the organizing committee, we extend a warm invitation to join us at the 1st International Workshop on Active Disturbance Rejection Control, July 3-5, 2024, which will be...

https://www.diplomados-ibero-blog.com.mx/1st-international-workshop-on-active-disturbance-rejection/

The regulation of switched power converters is a very active area of research both in power electronics and automatic control theory. A typical example, and one that captures the essence of the research problem, is the boost DC–DC converter. This circuit is described by a bilinear second order model with a binary input. The control task is further...

This article addresses the problem of balancing an inverted spherical pendulum on a quadrotor. The full dynamic model is obtained via the Euler-Lagrange formalism, where the dynamics of the pendulum is coupled to the dynamics of the quadrotor, taking as control inputs the torques associated with the yaw, roll, and pitch dynamics, and a control inpu...

Within a Geometric Algebra (GA) framework, this article presents a general method for synthesis of sliding mode (SM) controllers in Single Input Single Output (SISO) switched nonlinear systems. The method, addressed as the invariance control method, rests on a reinterpretation of the necessary and sufficient conditions for the local existence of a...

Lyapunov stability theory for smooth nonlinear autonomous dynamical systems is presented in terms of Geometric Algebra. The system is described by a smooth nonlinear state vector differential equation, driven by a vector field in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \us...

In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems...

We explore the incremental flatness based control of single input under-actuated nonlinear Hamiltonian systems exhibiting a controllable tangent linearization model around a given equilibrium point. General properties of controllable linearized Hamiltonian systems are presented, which significantly ease the stabilizing, or output reference trajecto...

In this article, an Extended State Observer (ESO) based Active Disturbance Rejection Control (ADRC) scheme is applied to the Pendubot system for a trajectory tracking tasks. The tangent linearization of the system allows to implement the control scheme taking advantage of the differential flatness property, while including a cascade configuration....

The flexible transmission system benchmark was proposed to evaluate the robustness of digital controllers. The multi-model uncertainty coupled with the non-minimum phase (NMP) zero is a challenging issue for the controller design. Therefore, a flatness-based discrete active disturbance rejection control (ADRC) scheme is formulated in this work, con...

With sight on maximizing the amount of energy that can be extracted, by a wind turbine, from the wind, this article solves the maximum power point tracking problem for a permanent magnet synchronous generator-based horizontal wind turbine connected to the electrical grid. A three-phase back-to-back converter, which allows a decoupling between the e...

In this paper, a discrete active disturbance rejection control (DADRC) scheme is proposed to manipulate linear input–output systems with zero dynamics. The DADRC is formulated according to the relative degree of the system output and is designed to track a reference and cancel both internal uncertainties and external disturbances. A parameter tunin...

This article deals with a linear classical approach for the robust output reference trajectory tracking control of nonlinear SISO Lagrangian systems with a controllable (flat) tangent linearization around an operating equilibrium point. An endogenous injections and exogenous feedback (EIEF) approach is proposed, which is naturally equivalent to the...

An equivalence is established between Extended State Observer (ESO) based Active Disturbance Rejection Control (ADRC) and Flat Filter (FF) controllers in the context of perturbed pure integration systems. These are known to constitute a most convenient paradigm for the control of SISO flat nonlinear systems. It is shown that a Reduced Order ESO (RO...

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...

In this article, a highly oscillatory 3 degrees of freedom (DOF) torsional plant is used to demonstrate the effectiveness of the combined differential flatness property and active disturbance rejection control (ADRC) methodology in the output tracking of fast reference trajectory and vibration suppression problems. The controller design is synthesi...

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...

A procedure is described for direct tangent linearization, around a given equilibrium point, of non-linear multivariable Lagrangian systems, in terms of second order variational expansions of the Lagrangian function. When the linearized model is controllable (i.e., it exhibits the flatness property), we present an Active Disturbance Rejection Contr...

A new Disturbance Observer Based (DOB) controller design procedure is here obtained via a reinterpretation of the disturbance estimation scheme, present in the Extended State Observer (ESO) based Active Disturbance Rejection (ADR) control scheme. If the reinterpreted disturbance estimation process is explicitly used, now, in combination with an ADR...

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 f...

An algebra based active disturbance rejection control approach for uncertain second-order flat systems, perturbed by a matching perturbation, is presented. This approach consists of proposing an online algebraic estimator for the uncertain system, together with an algebraic reconstructor for the unknown velocity. To assess the efficiency of the app...

A flatness based approach is proposed for the linear Active Disturbance Rejection Control (ADRC) stabilization of a nonlinear inertia wheel pendulum (IWP) around its unstable equilibrium point, subject to unmodelled dynamics and disturbances. The approach exploits the cascade structure, provided by the flatness property, of the tangent linearizatio...

In this article, we establish the route taken by the author, and his research group, to bring differential flatness to the realm of active disturbance rejection control (ADRC). This avenue entitled: 1) generalized proportional integral observers (GPIO), as natural state and disturbance observers for flat systems, 2) generalized proportional integra...

The book contains theoretical and practical aspects of ADRC in the context of differentially flat systems. Relations are established with Generalized Proportional Integral control based on Integral Reconstructors of phase variables and with Sliding Mode Control. Numerous laboratroy application examples are included throughout the book, complemented...

CONTENIDO: Algunos modelos de sistemas no lineales - Linealización aproximada - Realimentación del vector de estados - Observadores dinámicos de estado - Síntesis de compensadores clásicos - Realimentación no lineal del vector de estado - Diseño de observadores dinámicos no lineales basados en linealización extendida - Síntesis de compensadores no...

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 in...

This paper documents the design and implementation of a controller for DC/DC Buck-Parallel Converter under the perspective of differential flatness and active disturbance rejection control approach based on GPI extended state observer. The main objectives of the proposed controller are to regulate the output voltage and a balance of currents for pa...

This work proposes a robust controller to solve the trajectory-tracking control problem of planar vertical take-off and landing (PVTOL) aircraft under crosswind. The controller combines input-output feedback linearization and active disturbance rejection control techniques. The former linearizes the PVTOL dynamics and the latter actively estimates...

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 linearizable systems (i.e., differentially flat syste...

An input-output approach is presented for sliding mode control of linear and nonlinear switched systems of the differentially flat type. Two sliding mode control design options are presented: (1) a Delta-Sigma modulation implementation of a robust continuous output feedback controller design, such as the Active Disturbance Rejection Control scheme...

Due to the nature of the equilibrium point, located at the origin of the state space, the incremental variables coincide with the actual variables.

An Extended State Observer-based linear output feedback controller is developed for trajectory tracking problems defined on a class of disturbed differentially flat systems. A linear active disturbance rejection control based on a high-gain linear disturbance observer is proposed and implemented on a variety of challenging cases of study. We show t...

For interpretation of the references to color in this and the following figures, the reader is referred to the web version of this chapter.

For interpretation of the references to color in this and the following figures, the reader is referred to the web version of this chapter.

In this article, the output reference trajectory tracking control of a non-differentially flat, underactuated, system is approached from the perspective of Active Disturbance Rejection Control (ADRC) including a suitable Extended State Observer (ESO). The class of underactuated systems, which are non-differentially flat, constitutes the most challe...

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...

This article presents an input-output approach to sliding mode control (SMC) using integral reconstructors for the sliding surface specification in trajectory tracking tasks associated with a full non-linear link-DC motor system. These integral reconstructors are based on input errors, output tracking errors, and linear combinations of iterated int...

We solve consensus problems for networks of identical linear agents whose dynamics is unknown except for the order. We estimate the unknown dynamics via an “extended state-observer” and cancel it with a suitably designed control. The agent dynamics is thus approximated by that of an n-integrator, and standard protocols for networks of such type can...

This paper proposes a feedback method for the control of uncertain systems with unknown external disturbances, which includes an algebraic estimator and relies on the Active Disturbance Rejection Control (ADRC) approach. The proposed estimator considers a generalized disturbance in order to deal with systems which may simultaneously present time va...

In this article, the local trajectory tracking control problems ascribed to two interacting plants, considered as agents, are formulated as adaptive control problems, which involve online interaction estimation and interaction elimination. This approach gives rise to a robust decentralized collaborative control, with virtually no information, on th...

The article deals with the design and implementation of a flat filter tracking digital controller for a boost dc-dc power converter. A highly perturbed switched boost converter circuit is shown to be efficiently controlled, in a trajectory tracking task for its non-minimum phase output, by means of a suitable linear filter, here addressed as a flat...

This paper presents a rotor position sensorless control for the permanent magnet synchronous motor (PMSM), based on an active disturbance rejection control technique and an integral reconstructor for the rotor position estimation. The control law uses a generalized proportional integral observer (GPIO) for estimating and compensating the unknown un...

An on-linealgebraic filtering scheme, based on the recently introduced algebraic approach to parameter and state estimation, is presented along with successful experimental results. The proposed filtering algorithm is based on the connections between a time derivative estimator and an algebraically based signal filtering option.The main advan- tage...

In this article, a systematic procedure for controller design is proposed for a class of nonlinear under-actuated systems which are non feedback linearizable but exhibit a con-trollable (flat) tangent linearization around an equilibrium point. Linear Extended State Observer (LESO) based Active Disturbance Rejection Control (ADRC) is shown to allow...

En este trabajo se presenta el diseño de un controlador lineal robusto para el seguimiento simultáneo de posición y fuerza de robots manipuladores completamente actuados. Las no linealidades aditivas, posiblemente dependientes del estado, se modelan como una perturbación variante en el tiempo absolutamente acotada. Los observadores Proporcionales I...

This paper presents the design and simulation of robust control for DC/DC multi-converter based on terms like differential flatness and active disturbance rejection. The main goal of the control law is to obtain a regulated output voltage for each converter in cascade, and a balance of currents for parallel converters. The controller must actively...

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization o...

This paper is concerned with the design and implementation of a robust position backstepping tracking controller for a permanent magnet synchronous motor (PMSM). The information on the angular position and velocity, provided by a classical resolver-to-digital converter, additionally employs a phase lock loop (PLL) circuit. A backstepping control la...

A linearizing robust dynamic output feedback control scheme is proposed for earth coordinate position variables trajectory tracking tasks in a hovercraft vessel model. The controller design is carried out using only position and orientation measurements. A highly simplified model obtained from flatness considerations is proposed which vastly simpli...

A flatness based decentralized Active Disturbance Rejection Control (ADRC) approach is here proposed as a means to deal with the fully nonlinear, exogenously perturbed, version, of the four-tank benchmark process problem under non-minimum phase behavior for the traditionally chosen system outputs. The liquid level control task, related to the two l...

Global ultra-models are introduced as a paradigm for vastly simplifying the design of observer-based linear output feedback control laws in output trajectory tracking problems for a large class of uncertain nonlinear flat systems. An ultra-model simply lumps, as an unknown time-varying disturbance, the combined effects of all uncertain state-depend...

A flatness-based active disturbance rejection control approach is proposed to deal with the linear systems with unknown time-varying coefficients and external disturbances. By selecting appropriate nominal values for the parameters of the system, all the deviation between the nominal and actual dynamics of the controlled process, as well as all the...

In this paper a nonlinear algorithm for adaptive control of a fed-batch bioreactor for high density cultures is proposed. The control of these processes is difficult due to parameter variations and process disturbances. The control scheme is based on a reduced model used to estimate the uncertainties with adaptive techniques. Convergence of estimat...

In this article, a multivariable control design scheme is proposed for the reference trajectory tracking task in a kinematic model of a mobile robot. The control scheme leads to time-varying linear controllers accomplishing the reference trajectory tracking task. The proposed controller design is crucially based on the flatness property of the syst...

In this artilce we propose an output feedback control scheme for the robust stabilization, through sliding mode creation, of nonlinear discrete-time systems described in Fliess' Generalized Observability Canonical Form. The results are applied to the regulation of a discretized model of a nonlinear DC motor.

In this article we present a tutorial introduction to Generalized Proportional-Integral-Derivative Control (GPID). We particularly emphasize the links between flatness and GPID control, in the context of linear dynamic systems. We present several illustrative design examples, some of them of physical flavor. The performance of the controlled system...

In this paper, the sliding mode control of a permanent magnet (PM) stepper motor is addressed from the perspective of differentially flat systems. A static and a dynamic discontinuous feedback control schemes are proposed. Implementation results of these control schemes on an experimental set-up are given to illustrate the developments. Both, the r...

A feedback regulation scheme is presented which allows for a wide range of displacement maneuvers on a simplified longitudinal model of a helicopter system which is underactuated and nondifferentially flat. The system, nevertheless, is shown to be of the 'Liouvillian' type. An off-line, open loop, trajectory planning procedure is proposed, based on...

In this article, the problem of robust trajectory tracking, for a parallel robot is tackled via an observer-based active disturbance rejection controller. The proposed design method is based on purely linear disturbance observation and linear feedback control techniques modulo nonlinear input gain injections and cancellations. The estimations are c...

A system is said to be differentially flat if there exists a set of independent differential functions of the state (i.e., they do not satisfy any differential equations and, additionally, they are functions of the state and of a finite number of their time derivatives), called the flat outputs. The set of flat outputs exhibits the same number of e...

In this chapter we formalize, in a rather direct, and elementary, mathematical language, the ideas presented in the previous chapter. We introduce all the previously discussed elements of sliding mode control theory and illustrate, through several design examples mainly drawn from the switched power electronics area, the use and features of this im...

Delta modulation was actively developed for communication purposes in the sixties and seventies. It has also had applications in consumer audio equipment, industrial electronics devices, and precision measurement devices (see Jarman [14]). It consisted in an underlying analog-to-fixed sampling frequency pulse-width-modulation encoding transformatio...

One of the disadvantages of classical sliding mode control resides in the need to feedback the entire state to synthesize the controller. Traditionally, state observers are used for this requirement. However, the lack of a separation principle in nonlinear systems makes it difficult to assess the closed loop stability of an observer based sliding m...