Sampled-data Model Research Articles

Control of bifurcation in the one-cycle controlled Cuk converter

One-cycle controlled Cuk converter is a piecewise smooth nonlinear system. In this paper, sampled-data model is applied to analyze the dynamics of this converter. The results show that the four eigenvalues of the converter can be two pairs of complex conjugates, and that one pair may move out of the unit circle as some parameters are varied. This causes occurrence of slow-scale oscillation as a result of the Neimark–Sacker bifurcation in the input stage of the converter. Bifurcation may jeopardize the performance of the converter by decreasing the efficiency. A washout filter is used to control the bifurcation so as to stabilize the converter, and the effects of parameters of the filter on the stability of the converter are analyzed. Experimental measurements are provided to verify the analytical results.

Identification of continuous-time state-space models from non-uniform fast-sampled data

In this study, we apply the expectation-maximisation (EM) algorithm to identify continuous-time state-space models from non-uniformly fast-sampled data. The sampling intervals are assumed to be small and uniformly bounded. The authors use a parameterisation of the sampled-data model in incremental form in order to modify the standard formulation of the EM algorithm for discrete-time models. The parameters of the incremental model converge to the parameter of the continuous-time system description as the sampling period goes to zero. The benefits of the proposed algorithm are successfully demonstrated via simulation studies.

Frequency domain accuracy of approximate sampled-data models

AbstractAccurate sampled-data models are required when a digital device interacts with a continuous-time system. Even though exact sampled models can be obtained for linear systems, simple approximate models are sometimes preferred in applications to reduce computational load or to preserve the role of physical parameters. In this paper we quantify the frequency domain relative error of three kinds of approximate sampled models: (i) simple models obtained by derivative approximations, (ii) models obtained including the asymptotic sampling zeros, and (iii) models obtained by a truncated Taylor expansion of the system state equations. In particular, we characterize the bandwidth where each of the proposed models provides the highest accuracy.

LQ Optimal Control Synthesis for a Class of Pulse Frequency Modulated Systems

AbstractWe consider linear quadratic optimal control for a class of pulse frequency modulated systems. The problem is motivated from a practical application — digital control of a new type of twin-buck switching power converters. The pulse frequency modulated technique is deemed necessary in order to achieve the so-called “zero current switching”. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the at-sampling behavior into account.

Intervention in Biological Phenomena Modeled by S-Systems

Recent years have witnessed extensive research activity in modeling biological phenomena as well as in developing intervention strategies for such phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. In this paper, two different intervention strategies, namely direct and indirect, are proposed for the S-system model. In the indirect approach, the prespecified desired values for the target variables are used to compute the reference values for the control inputs, and two control algorithms, namely simple sampled-data control and model predictive control (MPC), are developed for transferring the control variables from their initial values to the computed reference ones. In the direct approach, a MPC algorithm is developed that directly guides the target variables to their desired values. The proposed intervention strategies are applied to the glycolytic-glycogenolytic pathway and the simulation results presented demonstrate the effectiveness of the proposed schemes.

Sampled-data models for affine nonlinear systems using a fractional-order hold and their zero dynamics

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin proposed a more accurate model than the simple Euler model in the case of a zero-order hold. This article derives a sampled-data model for nonlinear systems using a fractional-order hold, and analyzes the zero dynamics of the sampled-data model.

MLS TESTING OF VRLA BATTERIES USING PSEUDO RANDOM BINARY SEQUENCES (PRBS)

Non-intrusive methods of establishing battery state offer distinct advantages to systems where complex charge and discharge profiles make implementation of conventional battery state reporting difficult. Furthermore, examination of equivalent circuit parameters for batteries and cells offers potential opportunities for State-of-Charge (SoC) and State-of-Health (SoH) reporting, irrespective of historic charge and discharge events. This paper expands the use of maximum length sequences as tools for parameter estimation within electrochemical cells, to seek to identify performance indicators within batteries. In order to facilitate this identification, Randles' model is used with Pseudo Random Binary Sequences (PRBS) as the excitation signal within the test system for the batteries being examined. Design of these sequences for experimental analysis is discussed, leading to application in the described test system, employing a monopolar current signal in order to apply the perturbation to the subject battery. Battery impedance is investigated using a frequency domain approach, leading to characteristic impedance spectra being produced for the test batteries. The experimental results obtained allow parameters to be established, and verification against conventional battery test methods, and a sampled data model, is carried out.This analysis is used to present characteristics which can be subsequently used to inform the design of SoC and SoH algorithms, in order to develop online systems for evaluating these batteries.

A delay system approach to networked control systems with limited communication capacity

This paper addresses the problem of quantized feedback control for networked control systems (NCSs). Firstly, with consideration of the effect of network conditions, such as network-induced delays, data packet dropouts and signal quantization, the sampled-data model of closed-loop feedback system based on the updating sequence of the event-driven holder is formulated, from which a continuous system with two additive delay components in the state is developed. Subsequently, by making use of a novel interval delay system approach, the stability analysis and control synthesis for NCSs with two/one static quantizer are solved accordingly. Finally, two illustrative examples are given to show the effectiveness and advantage of the method.

Improvement on Sampled-data Model of High-voltage Direct Current Converter and Its Validation in Subsynchronous Oscillation Studies

This article presents an improved sampled-data model of a 12-pulse high-voltage direct current converter that is suited for linearized analyses of power systems using frequency domain methods. The applications of this model of converter with pure equidistant firing control and phase-locked loop control are discussed, respectively. Under small perturbations, the process of igniting is considered in detail. Therefore, the accuracy of the model is improved. The model is validated by time domain simulations in PSCAD/EMTDC. The results from the presented model, the quasi-steady model, and the former sampled-data model are compared by eigenvalue analysis and the complex torque coefficient method. The investigations show that the presented model is accurate and valuable in studying subsynchronous oscillations.

Relative Error Issues in Sampled Data Models

Abstract Most real world systems operate in continuous time. However, to store, analyze or transmit data from such systems the signals must first be sampled. Consequently there has been on-going interest in sampled data models for continuous time systems. The emphasis in the literature to-date has been on three main issues namely the impact of folding, sampled zero dynamics and the associated model error quantification. Existing error analyses have almost exclusively focused on unnormalized performance. However, in many applications relative errors are more important. For example, high performance controllers tend to invert the system dynamics and consequently relative errors underpin closed loop performance issues including robustness and stability. This motivates us to examine the relative errors associated with several common sampled data model types. This analysis reveals that the inclusion of appropriate zero dynamics is essential to ensure that the relative error converges to zero as the sampling period is reduced.

Stability of Zero Dynamics of Sampled-Data Nonlinear Systems

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate approximate model which includes extra zero dynamics corresponding to the relative degree of the continuous-time nonlinear system. Such extra zero dynamics are called sampling zero dynamics. A more accurate sampled-data model is, however, required when the relative degree of a continuous-time nonlinear plant is two. The reason is that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics and a controller design method based on cancellation of the zero dynamics is applied. This paper derives the sampling zero dynamics of the more accurate sampled-data model and shows a condition which assures the stability of the sampling zero dynamics of the model. Further, it is shown that this extends a well-known result for the stability condition of linear systems to the nonlinear case.

Stability Analysis of a Class of PWM Systems

This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-dc converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

LQ optimal control for a class of pulse width modulated systems

We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application—digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.

Passivity and Passification for Networked Control Systems

This paper investigates the problems of passivity analysis and passification for network-based linear control systems. A new sampled-data model is first formulated based on the updating instants of the ZOH (zeroth order hold), where the physical plant and the controller are, respectively, in continuous time and discrete time. In this model, network-induced delays, data packet dropouts, and signal measurement quantization have been taken into account. The measurement quantizer is assumed to be logarithmic, and the network-induced delays are assumed to have both a lower bound and an upper bound, which is more general than those assumptions used in the literature. The key idea is to transform the sampled-data model into a linear system with two successive delay components in the state. Then, by using a Lyapunov–Krasovskii approach plus the free weighting matrix technique, a passivity performance condition is formulated in the form of linear matrix inequalities (LMIs). Based on this condition, two procedures are proposed for designing passification controllers, which guarantee that the closed-loop networked control system (NCS) is passive. Finally, two illustrative examples are presented: one shows the advantage of introducing the lower bound of transmission delays and shows how much the quantization behavior affects the passivity performance; the other illustrates the applicability and effectiveness of the proposed passification results.

A receding horizon control approach to sampled-data implementation of continuous-time controllers

We propose a novel way for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller. Our approach exploits a model predictive control (MPC) strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We propose a control law and present conditions under which stability and sub-optimality of the closed loop can be proved. We only consider the case of unconstrained MPC. We show that the recent results in [G. Grimm, M.J. Messina, A.R. Teel, S. Tuna, Model predictive control: for want of a local control Lyapunov function, all is not lost, IEEE Trans. Automat. Control 2004, to appear] can be directly used for analysis of stability of our closed-loop system.

SAMPLED-DATA MODELS FOR STOCHASTIC NONLINEAR SYSTEMS

To carry out identification of continuous-time models one inevitably needs to work with a sampled-data description of a system. In this paper a sampled-data model to represent continuous-time stochastic nonlinear systems is proposed. The model is simple to obtain and accurate in a well defined sense. It is based on numerical solution of stochastic differential equations, and shows some connections to the linear case. The results here extend previous work by the authors for the (nonlinear) deterministic case.

On sampled-data models for nonlinear systems

Models for deterministic continuous-time nonlinear systems typically take the form of ordinary differential equations. To utilize these models in practice invariably requires discretization. In this paper, we show how an approximate sampled-data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order /spl Delta//sup r+1/, where /spl Delta/ is the sampling period and r is the system relative degree. The resulting model includes extra zero dynamics which have no counterpart in the underlying continuous-time system. The ideas presented here generalize well-known results for the linear case. We also explore the implications of these results in nonlinear system identification.

EXPERIMENTAL VERIFICATION OF BORDER COLLISION BIFURCATION DUE TO MODE TRANSITION IN A CURRENT MODE CONTROLLED BUCK CONVERTER

The bifurcation phenomena occurring in a current mode controlled buck converter when it shifts from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) have been reported. A sampled data model has been developed considering CCM as well as DCM. The bifurcation phenomena observed in such converters have been verified experimentally.

Speed Sensorless Stator Flux-Oriented Control of Induction Motor in the Field Weakening Region Using Luenberger Observer

In a conventional speed sensorless stator flux-oriented (SFO) induction motor drive, when the estimated speed is transformed into the sampled-data model using the first-forward difference approximation, the sampled-data model has a modeling error which, in turn, produces an error in the rotor speed estimation. The error included in the estimated speed is removed by the use of a low pass filter (LPF). As the result, the delay of the estimated speed occurs in transients by the use of the LPF. This paper investigates the problem of a conventional speed sensorless SFO system due to the delay of the estimated speed in the field weakening region. In addition, this paper proposes a method to estimate exactly speed by using Luenberger observer. The proposed method is verified by the simulation and experiment with a 5-hp induction motor drive.

Modeling and Analysis of a Digitally Controlled High Power Switch-Mode Rectifier

A recently proposed high power switch-mode rectifier topology offers advantages over the conventional line-commutated thyristor rectifiers in terms of size and cost. This paper presents modeling and analysis of the high power switch-mode rectifier configuration, operated under a newly developed digital control strategy. The developed strategy provides a fast transient response to disturbances and achieves equal current sharing between the buck converter modules which are paralleled within the switch-mode rectifier. A continuous-time state-space model of the switch-mode rectifier and analyses of both the steady-state and the transient operation modes of the digitally controlled rectifier are presented. The continuous-time model is used as a basis for time-domain simulations of the rectifier's behavior in the MATLAB/Simulink environment. The validity of the presented model is demonstrated based on comparison between the simulation results and the corresponding experimental results. The experimental results are obtained from a 2-kW scaled-down laboratory setup of the rectifier. The stability of the digitally controlled rectifier system is also examined based on an overall small-signal sampled-data model of the rectifier system including the controls.