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La respuesta en frecuencia de sistemas lineales es una popular herramienta utilizada en el análisis y diseño de sistemas de control automático. La forma común de obtener la respuesta en frecuencia es a partir de la representación entrada-salida (función de transferencia) de un sistema. En este trabajo se presenta una manera novedosa para obtener la respuesta en frecuencia partiendo de la representación en el espacio de estados. El resultado es obtenido mediante la caracterización de la señal de entrada (función senoidal) mediante un sistema externo adicional, así como la evaluación del estado estacionario. La determinación de la fase y magnitud se obtiene de la solución a una ecuación de Sylvester reiteradamente para diferentes valores de la frecuencia en un intervalo específico junto con algunas manipulaciones algebraicas y uso de identidades trigonométricas. El procedimiento es mostrado mediante ejemplos y comparado con las maneras clásicas de obtener la respuesta en frecuencia.

A novel approach to tracking control of a differential robot is proposed. Based on a Port-Hamiltonian representation of a differential robot, canonical transformations are used to obtain a controller that guarantees the tracking of a reference. The control law is inspired by a well-known controller taken from the literature and the Port-Hamiltonian version of the control law is derived. The performance of the algorithm as well as some of the robustness properties are tested using simulations under different scenarios.

The presence of faults in dynamic systems causes the potential loss of some of the control objectives. For that reason, a fault-tolerant controller is required to ensure a proper operation, as well as to reduce the risk of accidents. The present work proposes a passive fault-tolerant controller that is based on robust techniques, which are utilized to adjust a proportional-derivative scheme through a linear matrix inequality. In addition, a nonlinear term is included to improve the accuracy of the control task. The proposed methodology is implemented in the control of a two degrees of a freedom robotic helicopter in a simulation environment, where abrupt faults in the actuators are considered. Finally, the proposed scheme is also tested experimentally in the Quanser® 2-DOF Helicopter, highlighting the effectiveness of the proposed controller.

This paper considers a general approach to fault diagnosis using a generalized Hamiltonian system representation. It can be considered that, in general, nonlinear systems still represent a problem in fault diagnosis because there are results only for a specific class of them. Therefore, fault diagnosis remains a challenging research area despite the maturity of some of the available results. In this work, a type of nonlinear system that admits a generalized Hamiltonian representation is considered, in practice, there are many systems that have this kind of representation. Thereupon, an approach for fault detection and isolation based on the Hamiltonian representation is proposed. First, following the classic approach, the original system is decoupled in different subsystems so that each subsystem is sensitive to one particular fault. Then, taking advantage of the structure, a simple way to design the residuals is presented. Finally, the proposed scheme is validated at the two-degree of freedom (DOF) helicopter of Quanser&reg, where the presence of faults in sensors and actuators were considered. The results show the efficacy of the proposed scheme.

En este trabajo se propone un algoritmo para el diseño de un controlador de sistemas lineales con incertidumbre paramétrica. El punto de partida es una herramienta matemática para la solución de problemas de positividad de funciones multivariables polinómicas. El algoritmo propuesto está basado en un resultado para la estabilidad de sistemas lineales invariantes en el tiempo (Linear Time Invariant, LTI) con incertidumbre en sus parámetros. El algoritmo permite encontrar una familia de controladores que garantizan estabilidad robustamente. La solución propuesta, así como sus ventajas, son mostradas mediante un ejemplo.

In this document, a data-driven algorithm to continuous-time observer-based fault isolation from sampled input-output data is considered. The core of the proposed algorithm is to show the advantages with respect previous results such as fault isolation and the capability of consider a special class of nonlinear systems. An example is shown using the algorithm to prove its efficiency as well as a justification of the results.

The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.

Fault diagnosis in nonlinear systems is a challenging and very active research area. One of the difficulties to detect and isolate faults in nonlinear systems via observer-based methods is the design of a residual generator. In this work an integrated procedure combining conventional decoupling methods and Fuzzy Takagi-Sugeno observers for fault diagnosis in nonlinear systems is proposed. The advantage of the proposed AI based approach is that the design condition for the observers is relaxed in contrast with conventional approaches. Furthermore the potential use of decoupling techniques is reinforced. The design methodology is shown using a three tank system.

Robust and early detection of oscillatory failures in the electrical flight control system of an aircraft is a crucial issue. Oscillatory failures, if not detected and passivated in time, can lead to strong interactions with loads and aeroelasticity and may potentially lead to structural damages. A nonlinear observer-based solution to detect such failures with small amplitude at a very early stage is presented. The stability and convergence proofs are given and experimental results with real A380 flight data are presented.

This paper presents the development of a process control interface system (PCIS) for a distillation pilot plant that is based on the communication protocol called MODBUS. MODBUS communicates the computer (used as a control unit) with the process because it allows an efficient, flexible, and reliable system. The interface system is presented in an operator-friendly application, which has the capability to monitor the variables, manipulate actuators, and tune the controllers in the distillation process.

In this paper, we address the problem of Oscillatory failure Case (OFC) detection in A380 aircraft. The importance of OFC detection is well known in the literature because of natural mode excitation and the structural loads they can provoke. A novel nonlinear observer-based approach, which has two different gains is proposed in this paper to solve the problem. The main advantage of the proposed residual generator is that, by an adequate selection of observer gains, the residual generator has a kind selective (frequency dependent) attenuation property: disturbances and unmodelled dynamics effects on the residual are reduced while the effect of the fault is slightly amplified in a specific fault frequency range. Further, if the gains are chosen to be zero, the particular case of the technique implemented on A380 Airbus is obtained. A test based on real measurements of an A380 airplane is presented to show the efficiency of the proposed residual over the existing techniques.

Internal transformer faults could cause severe damage to electrical networks and also deteriorate the energy quality standard. Most of existing approaches for fault detection in transformers are based on signal processing methods or a static parity check of functionality. Two analytical redundancy approaches one based on dynamic parity checs and a second using a receding horizon observer, to internal fault detection in transformers are proposed in this paper. The main advantage of our proposal is that explicit knowledge of the Lipschitz constant of the transformer nonlinearities is not required and the considered algorithms has a high degree of portability. Furthermore, the effect of load and external faults on the residual are decoupled. Stability properties of the model are demonstrated. Some simulations shown the efficiency of the proposed detection method and highlight the reliability of the considered approach.

Abstract This work is concerning with the problem of determinate if a fault has been originated in a subsystem of a electric network or in somewhere else. This problem is motivated for the legal aspect related to co-generation systems. To solve the problem an approach based on analytical redundancy is proposed. An electrical part of a co-generation system is used to show (via simulations) the success of the proposed approach.

Abstract The problem of threshold selection for fault detection in nonlinear systems is considered. For the linear case the existing result requires of factorization of transfer function from perturbations to the output. In the nonlinear case a different approach is proposed in this work. Using ideas based on the concept of uniform ultimate boundedness a procedure to construct a residual generation is considered. The residual obtained is defined in such a way that a corresponding threshold can be defined in a natural form, in fact, as term in the residual equation. The proposed threshold can reduce the size of detectable faults and in this way the result is comparable to the existing for linear systems. The benefits of the approach are discussed.

La representación Hamiltoniana generalizada de sistemas brinda una estructura que puede ser utilizada con ventaja en muchas ´areas, entre las cuales se puede mencionar el diseño de observadores y el diagnóstico de fallas basado en modelos. Muchos de los trabajos en estos temas tienen como punto de partida al sistema en forma Hamiltoniana generalizada y, en general, se omite la explicación de como llegar a esta representación, por ejemplo, a partir de un modelo no lineal basado en las ecuaciones de Euler-Lagrange. En este trabajo se presenta un análisis detallado de como es que se obtiene la representación Hamiltoniana generalizada de un sistema a partir de las n ecuaciones diferenciales de segundo orden obtenidas con el formalismo Euler-Lagrange. Con la finalidad de mostrar en lo particular, después del caso general, cómo se obtiene la representación Hamiltoniana generalizada, se presentan algunos casos de estudio.

In this work it is proposed an extension to the Greenhouse climate model given by (Tap, 2000). The extension considers the effect of humidity in the air temperature as well as some terms related to the use of fogs, shade cloth and fan. The introduced modification is validated using measurements of a greenhouse in north west Mexico. The results show that the proposed model is adequate to simulate the climate behavior of the Greenhouse.

This paper considers an observer-based approach for detection and isolation of actuator and component faults in a Fluid Catalytic Cracking (FCC) unit. Model based analytical redundancy is used on an augmented linearised model of the non-linear FCC unit to the isolation of faults. Some component faults are modelled and implemented in a software package to show the considered approach. The proposed design is tested using a non-linear simulation of the FCC unit model. The results show that the linear observer-based approach applied to an augmented state of the FCC to actuator and component fault detection and isolation can be used with success even if the non-linear behaviour of the FCC has some effect on the residuals.

Climate control is one of the principal reasons to use a Greenhouse. The control task requires of a dynamic model of the climate variables in the Greenhouse. There are different Greenhouse climate models in the literature, some of them include not only the air temperature, soil temperature but also the effect of the crop, CO2 concentration and humidity (Tap, 2000). In order to improve the existing dynamic climate models an approach to consider non constant air density in the climate model of a Greenhouse is proposed. The effect of variations in the air density, due to humidity, is modeled and included in a version of the climate model of (Tap, 2000). The effect of the proposed modification on the Greenhouse climate variables is shown via simulations. A comparison between the proposed approach and one with constant air density is discussed.

This work is concerned with the design of a fault detection and isolation (FDI) system to monitor malfunctions in sensors and actuators of a fluid catalytic cracking (FCC) unit model predictive control (MPC) system. The control system is based on an infinite-horizon MPC algorithm. The fault detection scheme is developed based on two banks of robust observers, while the fault isolation task is done employing a structured residual approach. The models used in the control and in the FDI of the FCC unit are obtained by using subspace identification methods. The effectiveness of the proposed strategy is verified through numerical simulations carried out on a dynamical model of an industrial FCC unit under abrupt fault in its control devices.

Fault tolerant control (FTC) seeks to avoid the deterioration of the system at the time that there is a change of one or more parameters outside the limits of tolerance. There is in the literature a set of approaches based on the idea of tracking the nominal trajectory, which have been proved to be effective. However, some of them do not maintain the nominal controller, others, even if they keep it, require meet very demanding existence conditions. This paper proposes a fault recovery using a cascade control structure. The proposed design is based on the nominal trajectory tracking as well, but keeps intact the original control while existence conditions are relaxed. The resulting equivalent controller can be changed according to the performance needs of the system's response to faults. The controller could be defined by using stability regions and LMI tools.

This paper presents a fatness based active fault tolerant control technique. This approach is based on flat systems theory and on the non-uniqueness property of these to flat outputs. This property allows to develop an accurate fault detection and isolation technique, in addition, it allows to generate non-faulty analytically redundant measures. These signals can be used to reconfgure the system after a fault. This approach is applied to a three tank system.

"Se resuelve el problema de detección y aislamiento de fallas para una planta piloto no lineal, orientada a desarrollar algoritmos de tolerancia a las fallas, auspiciada por la Unión Europea. Se retoma una forma novedosa de modelar las fa- llas de los sensores, de manera que cada falla física sea aso- ciada a un conjunto adecuado de fallas matemáticas. Ello permite, mediante geometría diferencial, diseñar un FDI no lineal ligeramente extendido para tomar en cuenta la estruc- tura del sistema. Se describen las técnicas del modelado, el diseño de los generadores de los residuales, la matriz de residuales y se termina con la simulación de sistema térmico de tres tanques del proyecto europeo IFATIS."

The characterization of frequency response functions for convergent systems is considered in this paper. Besides a couple of approaches available in the literature, this paper is focused on the frequency response function proposed recently for a class of non-linear systems which are called convergent. Using some properties of convergent systems a characterization of a frequency response function based on Fourier series is obtained. This result expands a known result from linear to nonlinear systems and complements the existing results about frequency response functions of nonlinear systems. An example is utilized to show the proposed approach.

A novel non-linear observer for detection of oscillatory faults in commercial airplanes is proposed in this work. Oscillatory Failure detection in airplanes is an important problem because of natural mode excitation and the structural loads they can provoke. A simple and novel non-linear observer with two correction terms is developed. Formal proof of stability and convergence of the observer in the fault free case is provided. The proposed approach satisfies technical requirements of no false alarm, small detection time, detectability of small faults while keeping a simple structure. A test with real measurements is presented to show the efficiency of the proposed observer over the existing techniques.