Flat output characterization for linear systems using polynomial matrices

This paper is devoted to the study of linear flat outputs for linear controllable time-invariant systems in polynomial matrix form. We characterize the transformations expressing the system variables in terms of a linear flat output and derivatives, called defining matrices, as the kernel of a polynomial matrix. An application to trajectory planning is presented, showing the usefulness of the present characterization.     

Identification of linear time varying systems by Haar wavelet

This study addresses the identification of linear time varying systems. The identification is based on the expansion of all time functions in the state equations by Haar wavelets. The unknown time function can thus be identified in terms of Haar wavelets. A Haar wavelet is a set of complete, orthogonal basis and is easy to use computations. Several good properties of Haar wavelets are utilized in the algorithm. Both numerical and experimental results verify the analysis.     

Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can be substantially reduced by means of post-filtering of the frequency estimates. The modified (debiased) algorithm has better tracking capabilities than the original algorithm.     

Fractional representations of linear systems

A fractional representation of an arbitrary linear system is obtained that can be viewed as a generalization of a classical fractional representation of a transfer function. Conversely, a state-space model, not necessarily observable or controllable, can be assigned to any such fractional model. It is then shown that the categories of state-space and fractional representations of a linear system are equivalent.     

Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on time-varying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimensional frequency features can be visualised in a low-dimensional time–frequency space.     

On the equivalence of time and frequency domain maximum likelihood estimation

Maximum likelihood estimation has a rich history. It has been successfully applied to many problems including dynamical system identification. Different approaches have been proposed in the time and frequency domains. In this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data. A key point in this context is how initial (and final) conditions are considered and how they are introduced in the likelihood function.     

Feature detection using the general linear model

The detection of simple features using position-invariant filters constructed by the use of the matched filter theorem is extended to the general case of features with more than one free parameter.     

含积分环节过程对象模型的频域辨识方法

由于考虑系统的安全性和经济性无法进行开环实验,而目前最常用的闭环继电反馈辨识方法需要进行数次的继电反馈实验,并且该方法只能辨识固定结构的低阶模型,无法满足实际工业的需要。针对这一情况,提出了一种新的含积分环节过程对象的频域模型辨识方法,其能快速找到对象模型的主要频率段,分析频率段内的频率特性,从而准确的辨识出含积分环节对象的模型。仿真实验的结果表明该辨识方法能够高效且准确的辨识出含积分加环节的对象。     

非整数阶系统的频率辨识

使用频响数据对非整数阶系统作频域模拟和辨识.首先,定义了非整数阶微分器的频率特性,进而给出了非整数阶系统的余奎斯特曲线的绘制方法.然后,运用方程式误差的辅助变量法,根据实部和虚部频率数据进行非整数阶系统的频率辨识.最后,通过两个数字仿真来验证这种辨识方法.     

复杂多变量过程模型的闭环频域辨识

针对模型预测控制中模型辨识存在的问题,提出一种多变量过程闭环辨识方法.首先通过对多变量闭环系统正常运行产生的输入输出信号进行信号分解和频谱分析,得出多变量过程对象在重要频率段上的频率响应特性矩阵;然后采用最小二乘法,在幅值和相位两方面拟合一个二阶加纯滞后模型结构;最终获得一个多变量传递函数模型矩阵.仿真实验表明,该闭环辨识方法适用于广泛的多变量过程对象,具有很好的鲁棒性和精确性.     

Boundary control of hyperbolic conservation laws using a frequency domain approach

The paper uses a frequency domain method for the boundary control of hyperbolic conservation laws. We show that the transfer function of the hyperbolic system belongs to the Callier-Desoer algebra, which opens the way of sound results, and in particular to the existence of a necessary and sufficient condition for the closed loop stability and the use of Nyquist type test. We examine the link between input-output stability and exponential stability of the state. Specific results are then derived for the case of proportional diagonal boundary controllers. The results are illustrated in the case of diagonal boundary control of open channel flow.     

Computing the frequency response of linear systems with parametric perturbation

The problem of computing the frequency response of linear systems with parametric perturbation is addressed. Under the assumption that the coefficients of the system transfer function depend on the perturbation parameters in a linear manner, we provide results for plotting the frequency response of the perturbed transfer function. These results are useful in determining the H∞ norm, gain margin and phase margin and in improving the diagonal dominance of multi-input multi-out-put uncertain systems. An illustrative example is provided to demonstrate the results.     

Impulse response function identification of linear mechanical systems based on Kautz basis expansion with multiple poles

The impulse response function (IRF) identification of linear mechanical systems is important in many engineering applications. This paper proposes a novel IRF identification method of linear systems based on Kautz basis expansion with multiple poles. In order to reduce the parameters to be identified, the IRF is expanded in terms of orthogonal Kautz functions with multiple poles, and the poles in Kautz functions should be optimised. This allows the identification of IRF for linear mechanical systems operated under more than one mode, such as systems under the white noise excitation or the swept frequency excitation with a wide range of frequency, and can improve the identification accuracy. Furthermore, based on the backpropagation through-time technique and the expectation maximisation algorithm, a pole optimisation algorithm is presented in this paper. The simulation studies verify the effectiveness of the proposed IRF identification method.     

On state estimation and control in discrete-time systems of linear type

This note contains recurrence state estimation and control algorithms for general time-delay, discrete linear systems with the noises correlated on time intervals whose lengths change in time.     

Identification of switched linear systems via sparse optimization

The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we present here a sparse optimization approach inspired by very recent developments from the community of compressed sensing. We formally pose the problem of identifying each submodel as a combinatorial ?₀ optimization problem. This is indeed an NP-hard problem which can interestingly, as shown by the recent literature, be relaxed into a (convex) ?₁-norm minimization problem. We present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating-submodels. Some simulation results are included to support the potentialities of the proposed method.     

On the frequency domain accuracy of closed-loop estimates

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed-loop data is largely invariant to whether direct or indirect approaches are used. The analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order, and hence are approximations when either of these are finite. However, recent work has provided variance expressions that are exact for finite (possibly low) model order, and hence can potentially deliver more accurate quantification of estimation accuracy. This paper, and a companion one, revisits the study of identification from closed-loop data in light of these new quantifications and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates. These discrepencies are established here and in the companion paper to be dependent on what type of direct, indirect or joint input-output identification strategy is pursued.     

Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

This paper combines polynomial chaos theory with maximum likelihood estimation for a novel approach to recursive parameter estimation in state-space systems. A simulation study compares the proposed approach with the extended Kalman filter to estimate the value of an unknown damping coefficient of a nonlinear Van der Pol oscillator. The results of the simulation study suggest that the proposed polynomial chaos estimator gives comparable results to the filtering method but may be less sensitive to user-defined tuning parameters. Because this recursive estimator is applicable to linear and nonlinear dynamic systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.     

用MATLAB求取线性系统的时域性能指标

采用MATLAB编程求取线性系统的时域性能指标,用户只需从键盘上输入线性系统的传递函数的分子,分母多项式系数,就可以获得该系统的时域性能指标和阶跃响应图,使得时域性能指标的求取变得简单、容易、准确、应用实例验证了所设计的程序的有效性,该程序可用于线性系统的分析和设计。