In this paper, we show numerical and experimental results obtained when a new PWM-digital control technique is applied to DC-DC converters. The controller combines Zero Average Dynamics (ZAD) and Fixed Point Inducting Controller (FPIC)... more
In this paper, we show numerical and experimental results obtained when a new PWM-digital control technique is applied to DC-DC converters. The controller combines Zero Average Dynamics (ZAD) and Fixed Point Inducting Controller (FPIC) strategies. The first one has been reported in the literature in the last years and the second one is still in experimental phase. The design has been tested in an experimental way in low power DC-DC converters, using dSPACE platform. Numerical and experimental bifurcation diagrams agree. When the system is working in a stable range it has very good performance, showing low error.
Este libro ha sido pensado principalmente para ingenieros dedicados al control de procesos, que deseen conocer los fundamentos teóricos del control ZAD, y quieran profundizar en la aplicación de esta estrategia. Esta técnica de control... more
Este libro ha sido pensado principalmente para ingenieros dedicados al control de procesos, que deseen conocer los fundamentos teóricos del control ZAD, y quieran profundizar en la aplicación de esta estrategia. Esta técnica de control puede ser pensada como una forma débil de la técnica de control basada en modos deslizantes. En el ZAD se fuerza a una función de error a tener promedio cero en cada iteración. El libro incluye dos grandes componentes, por un lado contempla una componente teórica, en la cual se incluyen análisis de estabilidad y diagramas de bifurcaciones entre otros; y una componente experimental, donde se explica la manera como se desarrolló el experimento, y la forma como se determinaron algunos elementos necesarios para definir nuevos modelos. Finalmente se presenta la comparación entre los resultados numéricos -con los nuevos modelos obtenidos- y experimentales, los cuales tienen una alta concordancia. El principal objeto de aplicación del ZAD en este texto es el...
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ABSTRACT This paper focuses on the dynamical response of the ZAD-controlled buck converter under the variation of the PWM structure. Numerical analysis shows that the system can exhibit supercritical and subcritical period-doubling... more
ABSTRACT This paper focuses on the dynamical response of the ZAD-controlled buck converter under the variation of the PWM structure. Numerical analysis shows that the system can exhibit supercritical and subcritical period-doubling bifurcations, depending on the parameter values. This indicates that the ZAD technique can be highly dependent on the PWM composition.
ABSTRACT In this work an adaptive strategy for state dependent switching systems in Brunovsky form is presented. Lyapunov direct method is used to derive the adaptive control law to track a given reference signal. The resulting controller... more
ABSTRACT In this work an adaptive strategy for state dependent switching systems in Brunovsky form is presented. Lyapunov direct method is used to derive the adaptive control law to track a given reference signal. The resulting controller is equipped with a set of adaptive gains able to tackle plant commutations. Control gains are adapted through a feedback law depending on the state space region visited by the system trajectories. A consistent proof of convergence of the tracking error is given and a numerical example is used to illustrate the analytical result.
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We show in this document two mathematical models of development. Namely, we state two systems of nonlinear differential equations with state variables which regard to ecosystem, social and economic dimensions. We analyze nonlinear... more
We show in this document two mathematical models of development. Namely, we state two systems of nonlinear differential equations with state variables which regard to ecosystem, social and economic dimensions. We analyze nonlinear dynamics through bifurcation theory and state space simulations. Complex nonlinear systems including variables from ecosystem, social and economic dimensions show that, depending on the parameter values and
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In this paper we present the use of a control technique based on state feedback linearization, and the considerations that must keep in mind in agreement with the nonlinearity of model inherent saturation, at the time of inducing desired... more
In this paper we present the use of a control technique based on state feedback linearization, and the considerations that must keep in mind in agreement with the nonlinearity of model inherent saturation, at the time of inducing desired linear dynamics. The particular case of a parallel motor DC has studied, considering torque as the output. It has been analyzed
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In this paper, we discuss the occurrence of Hopf-like transitions in nonsmooth dynamical systems. Namely, we examine the nonstandard bifurcation scenario caused by the interaction of an equilibrium of a nonsmooth system with its... more
In this paper, we discuss the occurrence of Hopf-like transitions in nonsmooth dynamical systems. Namely, we examine the nonstandard bifurcation scenario caused by the interaction of an equilibrium of a nonsmooth system with its discontinuity boundary. We discuss two examples of non-smooth bifurcations, where the nonsmooth transition from an equilibrium to a stable limit cycle is observed.
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DC-DC power electronic converters are usually modelled by switching systems, that means discontinuous systems of Filippov type. These systems are piecewise linear, and simulation is straightforward since analytical solutions are available... more
DC-DC power electronic converters are usually modelled by switching systems, that means discontinuous systems of Filippov type. These systems are piecewise linear, and simulation is straightforward since analytical solutions are available in each linear topology. Recently, it has been shown that they can undergo some nonstandard bifurcations. In this report, we show that a DC-DC Buck converter can undergo a
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ABSTRACT In this work, an adaptive controller for bioreactors, using the measurement of output gas flow rate to handle the uncertainty on biomass concentration and kinetic rate is developed. A mass–balance model based on an unique... more
ABSTRACT In this work, an adaptive controller for bioreactors, using the measurement of output gas flow rate to handle the uncertainty on biomass concentration and kinetic rate is developed. A mass–balance model based on an unique reaction pathway to represent the input–output behavior is considered. Time-varying and unknown but bounded behavior of plant parameters, including the substrate concentration at the inflow and the yield coefficients are taken into account in the controller. The Lyapunov-like function method to develop the controller is used. A new method to handle the unknown time-varying behavior of the control gain is developed; with this method it is assured that the output tracks the desired reference with a user-defined tolerance and parameter drifting is avoided. The main contributions of the scheme with respect to closely related works are: (i) the exact values of the plant parameters are not required to be known; (ii) upper or lower bound related to the plant parameters are not required to be known; (iii) the time-varying behavior of plant parameters in the control design and in the convergence analysis are considered.
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Abstract In this paper an adaptive controller for bioreactors is developed, using a mass balance model based on an unique biological reaction pathway. The control scheme is constructed from Lyapunov-like function method and an extended... more
Abstract In this paper an adaptive controller for bioreactors is developed, using a mass balance model based on an unique biological reaction pathway. The control scheme is constructed from Lyapunov-like function method and an extended Luenberger observer ...
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ZAD strategy has been widely analyzed in the last decade to control buck power converters. The first models were ideals; as consequence of these numerical and experimental results did not agree. The discrepancy between both of the results... more
ZAD strategy has been widely analyzed in the last decade to control buck power converters. The first models were ideals; as consequence of these numerical and experimental results did not agree. The discrepancy between both of the results is probably due to the sensitivity of the ZAD strategy to compute the duty cycle. In the present work the inductor internal
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ABSTRACT In this work an adaptive controller for an anaerobic digester is developed taking into account the input constraints. The following assumptions are considered: (i) the biomass and chemical oxygen demand concentrations are... more
ABSTRACT In this work an adaptive controller for an anaerobic digester is developed taking into account the input constraints. The following assumptions are considered: (i) the biomass and chemical oxygen demand concentrations are unknown, (ii) the model parameters are unknown and vary but they are bounded, and (iii) the upper or lower bounds of model parameters are unknown. The Lyapunov-like function method is used to derive the controller. A state observer is employed to handle the saturation of the control input, and updated parameters are used to handle the unknown bounds of the plant parameters. Some features of the control design are: (i) discontinuous signals are avoided, (ii) the boundedness of the updated parameters is ensured despite input saturation, in order to avoid parameter drifting, and (iii) the convergence of the observer error to a residual set of user-defined size is ensured despite input saturation.
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ABSTRACT In this work a two-valued state feedback control is developed for a plant of second order with known constant coefficients and no disturbance, and for a plant with unknown varying coefficients and additive disturbance with known... more
ABSTRACT In this work a two-valued state feedback control is developed for a plant of second order with known constant coefficients and no disturbance, and for a plant with unknown varying coefficients and additive disturbance with known upper and lower bounds. A reference model is used in order to avoid large commutation rate of the control input. In the first part of the present work, the controller is developed by means of the Lyapunov-like function method achieving the convergence of the tracking error to a residual set whose size is user-defined. In the second part, the Lyapunov function at zero time is inside a predefined set and the developed controller forces the Lyapunov function to dwell inside such set. The size of this set is chosen such that the tracking error asymptotically converges to a residual set of user-defined size.
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ABSTRACT SUMMARY The response of a digital Zero Average Dynamics (ZAD)-controlled buck converter under the variation of its intrinsic parameters as well as the pulse-width modulation signal is studied in detail. The multiparameter... more
ABSTRACT SUMMARY The response of a digital Zero Average Dynamics (ZAD)-controlled buck converter under the variation of its intrinsic parameters as well as the pulse-width modulation signal is studied in detail. The multiparameter analysis presented here leads to a complete knowledge of the different dynamical scenarios exhibited by the system. Numerical results indicate that the success of the ZAD-strategy is highly dependent on the parameter and pulse-width modulation (PWM) combinations. Experiments are included to validate the performance inside the so-called optimum region. Copyright © 2013 John Wiley & Sons, Ltd.