An EM-based identification algorithm for a class of hybrid systems with application to power electronics

In this paper we present an identification algorithm for a class of continuous-time hybrid systems. In such systems, both continuous-time and discrete-time dynamics are involved. We apply the expectation-maximisation algorithm to obtain the maximum likelihood estimate of the parameters of a discrete-time model expressed in incremental form. The main advantage of this approach is that the continuous-time parameters can directly be recovered. The technique is particularly well suited to fast-sampling rates. As an application, we focus on a standard identification problem in power electronics. In this field, our proposed algorithm is of importance since accurate modelling of power converters is required in high- performance applications and for fault diagnosis. As an illustrative example, and to verify the performance of our proposed algorithm, we apply our results to a flying capacitor multicell converter.     

Continuous-time model identification from sampled data: Implementation issues and performance evaluation

This paper deals with equation error methods that fit continuous-time transfer function models to discrete-time data recently included in the CONTSID (CONtinuous-Time System IDentification) Matlab toolbox. An overview of the methods is first given where implementation issues are highlighted. The performances of the methods are then evaluated on simulated examples by Monte Carlo simulations. The experiments have been carried out to study the sensitivity of each approach to the design parameters, sampling period, signal-to-noise ratio, noise power spectral density and type of input signal. The effectiveness of the CONTSID toolbox techniques is also briefly compared with indirect methods in which discrete-time models are first estimated and then transformed into continuous-time models. The paper does not consider iterative or recursive algorithms for continuous-time transfer function model identification.     

Augmented hybrid method for continuous process identification from sampled data with coloured noise

The identification of a linear continuous-time model for a multivariable dynamic system from sampled input-output observations is considered. An augmented hybrid parametric method is proposed to overcome the interference of the coloured output noise in the sampled output. The parameters of the continuous-time process model are estimated from an augmented input-output realization which utilizes the dynamic information of the discrete-time noise model. Numerical examples are presented to illustrate how to obtain an adequate dynamic process model, considering the coloured output noise, by using a discrete-time noise model.     

Digital sliding mode controller design for multiple time-delay continuous-time transfer function matrices with a long input–output delay

This paper extends the dominant eigenvector-based sliding mode control (SMC) design methodology, which was originally developed for delay-free continuous-time processes with known parameters, to the case of multiple time-delay continuous-time processes with known/unknown parameters. In addition, this paper presents a new prediction-based Chebyshev quadrature digital redesign methodology for indirect design of the digital counterpart of the analog sliding mode controller (ASMC) for multiple time-delay continuous-time transfer function matrices with either a long input delay or a long output delay. An approximated discrete-time model and its corresponding continuous-time model are constructed for multiple time-delay continuous-time stable/unstable dynamical processes with known/unknown parameters, using first the conventional observer/Kalman filter identification (OKID) method. Then, an optimal ASMC is developed using the linear quadratic regulator (LQR) approach, in which the corresponding sliding surface is designed using the user-specified eigenvectors and the scalar sign function. For digital implementation of the proposed non-augmented low-dimensional ASMC, a digital counterpart is designed based on the existing prediction-based digital redesign method and the newly developed prediction-based Chebyshev quadrature digital redesign method. Finally, a non-augmented low dimensional digital observer with a long input or output dead time is constructed for the implementation of the digitally redesigned sliding mode controller, to improve the performances of multiple time-delay dynamical processes. The effectiveness of the proposed method has been verified by means of two illustrative examples.     

关于《Identification of Multi-variable Continuous Time System From Samples of Input-output Data》的注记

关于利用采样数据辨识连续时间系统,本文提出了用插值拟合手段将连续时间模型离散化的思想,并从理论的角度,对几种典型的离散模型进行了精度分析,给文[1]的结果,提供了进一步的解释和补充,预示了提高辨识精度的可能途径。     

Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems

A continuous-time system cannot be recovered solely from its uniformly sampled discrete-time model through the zero-order hold discretization or step-invariant transformation, but our studies indicate that it can be recovered uniquely from its non-uniformly sampled discrete-time model. In this paper, we discuss some related issues of non-uniformly sampled systems, including model derivation, controllability and observability, computation of single-rate models with different sampling periods, reconstruction of continuous-time systems, and parameter identification of non-uniformly sampled discrete-time systems. A numerical example is also given for illustration.     

Frequency-domain identification of continuous-time ARMA models from sampled data

The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.     

Brazilian Society of Simulation

Estimation of the parameters of a reducible (inflated common denominator) model for the transfer function matrix of MIMO systems is well known. However, the reduction of the model to the minimal form by pole-zero cancellation is possible only in the noise-free case. This paper presents an algorithm for the estimation of the minimal continuous-time transfer function matrix model. Monte Carlo simulation results are presented for discrete-time and continuous-time models. Least-squares and generalized least-squares methods have been used in both cases. An asymptotic analysis of convergence has also been provided for these models in the noise-free case. The computation times and space complexities of different variants of the algorithm are compared. The results show that in noisy situations, obtaining a discrete-time model by discretizing an estimated continuous-time model may be a viable proposition     

Identification of MIMO continuous-time models by indirect methods

The problem of using indirect methods to identify a linear MIMO continuous-time model from sampled input–output records of a multivariable process is discussed. In the indirect identification methods, a discrete-time model is first found by any existing standard methods; next a continuous-time model as an equivalent to the discrete-time one is determined. Three algorithms, each employing state-conversion, moment-matching and frequency-response matching methods, are proposed to carry out the second step of the indirect identification methods. Numerical examples are included to illustrate the applicability of the proposed methods.     

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.     

Identification of time delays in linear stochastic systems

This paper presents a new approach to the explicit identification of an input time delay in continuous-time linear systems. The system model is converted to a discrete-time version, assuming that a digital computer is to be used for time delay estimation and control. A recursive identification algorithm based on parallel Kalman filtering and Bayes' estimation is developed. The sampling rate is adapted during the time delay estimation process using the most recent estimate of the time delay. This method assures that the estimate of the time delay approaches the true value with each successive iteration. The proposed method also has the advantage of a fast convergence rate because prior knowledge of the delay, if available, can be effectively utilized.     

A Kalman filter type of extension to a deterministic gradient technique for parameter estimation

It is shown that a method for the identification of deterministic systems derived from the Kalman filter is related to a gradient technique of parameter estimation and that the range of problems to which the gradient method may be applied is thereby extended. Various versions of the discrete-time algorithm are compared from theoretical and computational points of view and also contrasted with the continuous-time algorithm. An important outcome is that the system containing unknown parameters and the identification algorithm may be formulated with one in discrete-time and the other in continuous-time.     

A variational integrators approach to second order modeling and identification of linear mechanical systems

The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures. We discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete-time identified model. We test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous-time parameters of second-order mechanical systems starting from discrete measured data.     

Approximated modeling and minimal realization of transfer function matrices with multiple time delays

The modeling and minimal realization techniques for a specific multiple time-delay continuous-time transfer function matrix with a delay-free denominator and a multiple (integer/fractional) time-delay numerator matrix have been developed in the literature. However, this is not the case for a general multiple time-delay continuous-time transfer function matrix with multiple (integer/fractional) time delays in both the denominator and the numerator matrix. This paper presents a new approximated modeling and minimal realization technique for the general multiple time-delay transfer function matrices. According to the proposed technique, an approximated discrete-time state-space model and its corresponding discrete-time transfer function matrix are first determined, by utilizing the balanced realization and model reduction methods with the sampled unit-step response data of the afore-mentioned multiple time-delay (known/unknown) continuous-time systems. Then, the modified Z-transform method is applied to the obtained discrete-time transfer function matrix to find an equivalent specific multiple time-delay continuous-time transfer function matrix with multiple time delays in only the inputs and outputs, for which the existing control and design methodologies and minimal realization techniques can be effectively applied. Illustrative examples are given to demonstrate the effectiveness of the proposed method.     

基于混杂系统方法的一类采样数据系统鲁棒故障检测

针对具有连续时间过程噪声和离散时间测量噪声的采样数据系统, 提出了一种新的鲁棒故障检测直接设计方法. 首先利用具有有限跳变的线性系统作为残差产生器, 采样数据系统的鲁棒故障检测设计问题被描述成采样数据滤波问题, 然后给出有限跳变线性系统有界实引理的线性矩阵不等式(LMI)表达形式, 基于此, 推导出采样数据系统鲁棒故障检测滤波器的存在条件及设计参数, 并将所提方法推广到具有结构不确定性的采样数据系统上. 所设计的滤波器能够保证残差与故障之间误差最小, 并对过程噪声、测量噪声、结构不确定性等因素鲁棒. 最后, 通过数值仿真对所提方法的可行性进行了验证.     

基于即时交货的离散时间模型及其在炼油过程调度优化中的应用

针对炼油过程调度优化的离散时间与连续时间建模方法在应用中的局限性,提出一种基于即时交货的离散时间建模方法.该方法总体上采用离散时间表示,通过对成品油交货环节相关部分更加细致的描述,使得交货活动能够在时间片段内部发生,既可保证对实际问题的准确刻画,又能实现对模型规模的有效控制.以华北地区某炼油厂的改质及调合过程为例,分别建立离散时间模型、连续时间模型以及所提出的基于即时交货的离散时间模型,并结合对3个案例的求解,从不同的角度对3种模型进行对比研究.研究结果表明,所提出的模型兼具原离散时间模型和连续时间模型的优势,能够在不同的情形下保持稳定且优良的性能.     

Stability analysis and synthesis of fuzzy singularly perturbed systems

In this paper, we investigate the stability analysis and synthesis problems for both continuous-time and discrete-time fuzzy singularly perturbed systems. For continuous-time case, both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities (LMIs). For discrete-time case, only the analysis problem can be cast in LMIs, while the derived stability conditions for controller design are nonlinear matrix inequalities (NMIs). Furthermore, a two-stage algorithm based on LMI and iterative LMI (ILMI) techniques is developed to solve the resulting NMIs and the stabilizing feedback controller gains can be obtained. For both continuous-time and discrete-time cases, the reduced-control law, which is only dependent on the slow variables, is also discussed. Finally, an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures.     

Singular perturbational approximations for discrete-time balanced systems

A new zero-order singular perturbational type approximation is developed for model reduction of discrete-time linear systems. This approximation is also suitable for model reduction of systems which have fast subsystems and which are represented in the internally balanced format. Subsystem elimination as suggested by Moore for continuous-time systems does not generalize for the discrete-time case, and the singular perturbational approximation gives a particular solution to the discrete-time internally balanced model reduction problem.     

Robust stability of discrete-time systems under parametricperturbations

Stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable. In this paper, two methods are presented to estimate the stability robustness region of a linear, time-invariant, discrete-time system under multiparameter additive perturbations. An inherent difficulty, which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region, is resolved by transforming the problem to stability of a higher order continuous-time system. This allows for application of the available results on stability robustness of continuous-time systems to discrete-time systems. The results are also applied to stability analysis of discrete-time interconnected systems, where the interconnections are treated as perturbations on decoupled stable subsystems     

Limiting sampling results for continuous-time ARMA systems

The objective of this paper is to present some general properties of discrete-time systems originating from fast sampled continuous-time autoregressive moving average (CARMA) systems. In particular, some results concerning the zero locations and the innovations variance of fast sampled CARMA systems will be stated. Knowledge of these properties is of importance in various fast sampling applications, such as discrete-time simulation of continuous-time systems and identification of continuous-time systems using discrete-time measurements. The main contribution, however, is to provide a mean to evaluate limiting properties for various problems. For example, how to determine the accuracy of approximate sampling schemes, how to describe the characteristics of different estimators, and how to examine the behaviour of the dynamics of a fast sampled system. The results are illustrated by an extensive set of examples.