Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

[EN] The problem of output stabilization and disturbance rejection for input-delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov-Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed-loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.PROMETEOII/2013/004; Conselleria d'Educacio; Generalitat Valenciana, Grant/Award Number: TIN2014-56158-C4-4-P-AR; Ministerio de Economia y Competitividad, Grant/Award Number: FPI-UPV 2014; Universitat Politecnica de ValenciaSanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control. 28(6):2457-2467. https://doi.org/10.1002/rnc.4027S24572467286Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Watanabe, K., & Ito, M. (1981). A process-model control for linear systems with delay. 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Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust control strategies for unstable systems with input/output delays

Los sistemas con retardo temporal aparecen con frecuencia en el ámbito de la ingeniería, por ejemplo en transmisiones hidráulicas o mecánicas, procesos metalúrgicos o sistemas de control en red. Los retardos temporales han despertado el interés de los investigadores en el ámbito del control desde finales de los años 50. Se ha desarrollado una amplia gama de herramientas para el análisis de su estabilidad y prestaciones, especialmente durante las dos últimas décadas. Esta tesis se centra en la estabilización de sistemas afectados por retardos temporales en la actuación y/o la medida. Concretamente, las contribuciones que aquí se incluyen tienen por objetivo mejorar las prestaciones de los controladores existentes en presencia de perturbaciones. Los retardos temporales degradan, inevitablemente, el desempeño de un bucle de control. No es de extrañar que el rechazo de perturbaciones haya sido motivo de estudio desde que emergieron los primeros controladores predictivos para sistemas con retardo. Las estrategias presentadas en esta tesis se basan en la combinación de controladores predictivos y observadores de perturbaciones. Estos últimos han sido aplicados con éxito para mejorar el rechazo de perturbaciones de controladores convencionales. Sin embargo, la aplicación de esta metodología a sistemas con retardo es poco frecuente en la literatura, la cual se investiga exhaustivamente en esta tesis. Otro inconveniente de los controladores predictivos está relacionado con su implementación, que puede llevar a la inestabilidad si no se realiza cuidadosamente. Este fenómeno está relacionado con el hecho de que las leyes de control predictivas se expresan mediante una ecuación integral. En esta tesis se presenta una estructura de control alternativa que evita este problema, la cual utiliza un observador de dimensión infinita, gobernado por una ecuación en derivadas parciales de tipo hiperbólico.Time-delay systems are ubiquitous in many engineering applications, such as mechanical or fluid transmissions, metallurgical processes or networked control systems. Time-delay systems have attracted the interest of control researchers since the late 50's. A wide variety of tools for stability and performance analysis has been developed, specially over the past two decades. This thesis is focused on the problem of stabilizing systems that are affected by delays on the actuator and/or sensing paths. More specifically, the contributions herein reported aim at improving the performance of existing controllers in the presence of external disturbances. Time delays unavoidably degrade the control loop performance. Disturbance rejection has been a matter of concern since the first predictive controllers for time-delay systems emerged. The key idea of the strategies presented in this thesis is the combination of predictive controllers and disturbance observers. The latter have been successfully applied to improve the disturbance rejection capabilities of conventional controllers. However, the application of this methodology to time-delay systems is rarely found in the literature. This combination is extensively investigated in this thesis. Another handicap of predictive controllers has to do with their implementation, which can induce instability if not done carefully. This issue is related to the fact that predictive control laws take the form of integral equations. An alternative control structure that avoids this problem is also reported in this thesis, which employs an infinite-dimensional observer, governed by a hyperbolic partial differential equation.Sanz Díaz, R. (2018). Robust control strategies for unstable systems with input/output delays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/111830TESI

Prediction-Based Super Twisting Sliding Mode Load Frequency Control for Multi Area Interconnected Power Systems with State and Input Time Delays using Disturbance Observer

International audienceA shift in paradigm from dedicated to open communication channels in power systems have made them prone to constant and time varying delays. This paper tackles a novel load frequency control (LFC) problem in the presence of constant and time varying delays in state and control input under load disturbances. The presence of time delays can deteriorate the performance of the controller or even destabilize the system. The above problem is addressed through a prediction-based super twisting sliding mode control (ST-SMC) using a state and disturbance observer. The proposed design achieves finite time convergence of frequency and tie line power deviation. The said design is validated under ramp and random step disturbance, with nonlinearities like generation rate constraints and governor deadband, with an integration of renewable energy and also with IEEE 39 bus power system. The closed loop stability is proven thanks to candidate Lyapunov function and verified by simulations

Variable domain transformation for linear PAC analysis of mixed-signal systems

This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly