Estimation of valve stiction in control loops using separable least-squares and global search algorithms

This contribution presents a new procedure for quantifying valve stiction in control loops based on global optimisation. Measurements of the controlled variable (PV) and controller output (OP) are used to estimate the parameters of a Hammerstein system, consisting of a connection of a two-parameter stiction model and a linear low-order process model. As the objective function is non-smooth, gradient-free optimisation algorithms, i.e., pattern search (PS) methods or genetic algorithms (GA), are used for fixing the global minimum of the parameters of the stiction model, subordinated with a least-squares estimator for identifying the linear model parameters. Some approaches for selecting the model structure of the linear model part are discussed. Results show that this novel optimisation-based technique recovers accurate and reliable estimates of the stiction model parameters, dead-band plus stick band (S) and slip jump (J), from normal (closed-loop) operating data for self-regulating and integrating processes. The robustness of the proposed approach was proven considering a range of test conditions including different process types, controller settings and measurement noise. Numerous simulation and industrial case studies are described to demonstrate the applicability of the presented techniques for different loops and for different amounts of stiction.     

一种多输入单输出Hammerstein系统的集成辨识方法

针对多输入单输出(MISO)Hammerstein系统提出了一种稳态与动态辨识相结合的集成辨识方法.该方法利用稳态信息获取稳态模型的强一致性估计,并通过稳态模型以神经网络获得其非线性逼近函数,再利用动态信息辨识获取多输入单输出(MISO)Hammerstein系统的线性子系统未知参数的一致性估计.仿真结果表明了该方法的有效性和实用性.     

System identification applied to stiction quantification in industrial control loops: A comparative study

A comparative study of different models and identification techniques applied to the quantification of valve stiction in industrial control loops is presented in this paper, with the objective of taking into account for the presence of external disturbances. A Hammerstein system is used to model the controlled process (linear block) and the sticky valve (nonlinear block): five different candidates for the linear block and two different candidates for the nonlinear block are evaluated and compared. Two of the five linear models include a nonstationary disturbance term that is estimated along with the input-to-output model, and these extended models are meant to cope with situations in which significant nonzero mean disturbances affect the collected data. The comparison of the different models and identification methods is carried out thoroughly in three steps: simulation, application to pilot plant data and application to industrial loops. In the first two cases (simulation and pilot plant) the specific source of fault (stiction with/without external disturbances) is known and hence a validation of each candidate can be carried out more easily. Nonetheless, each fault case considered in the previous two steps has been found in the application to a large number of datasets collected from industrial loops, and hence the merits and limitations of each candidate have been confirmed. As a result of this study, extended models are proved to be effective when large, time varying disturbances affect the system, whereas conventional (stationary) noise models are more effective elsewhere.     

控制阀粘滞特性的频域检测方法研究

控制阀粘滞特性是导致控制回路振荡的主要原因之一,对控制阀粘滞特性进行了详细分析,在此基础上使用离散傅里叶变换分析振荡的偏差信号,提出了一种频域分析、适用范围较广的控制阀粘滞特性检测方法。通过仿真研究,表明了该方法的有效性。     

A simple method for detecting valve stiction in oscillating control loops

This paper presents a simple and new method for detecting valve stiction in an oscillating control loop. The method is based on the calculation of areas before and after the peak of an oscillating signal. The proposed method is intuitive, requires very little computational effort, and is easy to implement online. Analytical results are derived to show the theoretical basis of the new method and field results are presented to show its effectiveness on real world control loops.     

Iterative identification of Hammerstein systems

Convergences of iterative algorithms have been established for identification of Hammerstein systems in the case that the unknown nonlinearities are odd. Then, the results are further extended to nonsmooth nonlinearities.     

Detection and diagnosis of plant-wide oscillations from industrial data using the spectral envelope method

Plant-wide oscillations are common in many processes. Their effects propagate to many units and may impact the overall process performance. It is important to detect and diagnose the cause of such oscillations in order to rectify the situation. This paper proposes a new procedure to detect and diagnose plant-wide oscillations using routine operating data. A technique called spectral envelope is used to detect oscillations. The variables that have common oscillations are identified and categorized accurately by a statistical hypothesis test. A new index called the oscillation contribution index (OCI) is proposed to isolate the key variables as the potential root cause candidates of the common oscillation(s). Two industrial case studies are presented to demonstrate the utility and practicality of the proposed procedure.     

A noniterative neuro-fuzzy based identification method for Hammerstein processes

In this paper, a noniterative identification procedure for neuro-fuzzy based Hammerstein model is presented. The proposed method not only avoids the inevitable restrictions on static nonlinear function encountered by using the polynomial approach, but also overcomes the problems of initialization and convergence of the model parameters, which are usually resorted to trial and error procedure in the existing iterative algorithms used for the identification of Hammerstein model. To construct the neuro-fuzzy based model, a clustering algorithm is presented to estimate the centers and widths of the model, and an analytical solution is developed to calculate the weights of the model in a noniterative manner. Examples are used to illustrate the applicability of the proposed method and a comparison with polynomial approach is made.     

Revisiting Hammerstein system identification through the Two-Stage Algorithm for bilinear parameter estimation

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.     

Convergence of the iterative algorithm for a general Hammerstein system identification

The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters.     

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.     

Identification of Hammerstein systems with asymmetric dead-zone nonlinearities using canonical parameterized model

A non-iterative identification method with parameterization of the unknown dead-zone is proposed for Hammerstein systems in presence of asymmetric dead-zone nonlinearities.The canonical parameterized model which is a single expression without segmentation is utilized to describe the dead-zone,based on which a universal-type parametric model can be established to approximate the entire system.This model can be established without separating the nonlinear part from the linear part.The dead-zone parameters and the coefficients in the linear transfer function can be estimated simultaneously according to the proposed algorithm.Numerical experiments are presented to illustrate the effectiveness of the proposed scheme.     

Identification and control of Hammerstein systems via wireless networks

This article investigates a systematic approach for the identification and control of Hammerstein systems over a physical IEEE 802.11b wireless channel. Three major factors which may affect system stability and stabilisation are concerned: wireless network-induced delays, nonlinearity and model mismatch. First the network-induced delays are characterised by an inverse Gaussian distribution model according to IEEE 802.11b protocol and a model-based compensation method is used to estimate the delayed samples. Then an inverse function of nonlinear part of the identified model is used to attenuate the influence of nonlinearity, while the model mismatch is regarded as disturbance which is then dealt with by H _∞ control approach. A sufficient condition for mean-square asymptotic stability is obtained and expressed by a set of linear matrix inequalities, enabling direct controller design. Finally, numerical simulation examples are used to confirm the efficacy of the proposed approach.     

一类多变量Hammerstein模型的参数辨识方法

通过对系统输入信号的设计,使Hammerstein系统输出只反映系统的线性动态,并将非线性部分的静态影响有效地分离掉.利用最小二乘辨识得到系统的线性动态模型.基于此模型并依据系统的测量输出重构系统的中间输入,进而可估计出非线性部分的参数,据此给出了多变量Hammerstein系统辨识的动态分离方法.仿真结果表明所提出的方法是有效的.     

Recursive identification of Hammerstein systems with application to electrically stimulated muscle

Modeling of electrically stimulated muscle is considered in this paper where a Hammerstein structure is selected to represent the isometric response. Motivated by the slowly time-varying properties of the muscle system, recursive identification of Hammerstein structures is investigated. A recursive algorithm is then developed to address limitations in the approaches currently available. The linear and nonlinear parameters are separated and estimated recursively in a parallel manner, with each updating algorithm using the most up-to-date estimation produced by the other algorithm at each time instant. Hence the procedure is termed the alternately recursive least square (ARLS) algorithm. When compared with the leading approach in this application area, ARLS exhibits superior performance in both numerical simulations and experimental tests with electrically stimulated muscle.     

On identification of Hammerstein and Wiener model with application to virtualised software system

This paper proposes a system identification method for estimating virtualised software system dynamics within the framework of a Hammerstein–Wiener model. Building on the authors’ previous work in identification and control of the software systems, the approach utilises frequency sampling filter structure to describe the linear dynamics and B-spline curve functions for the inverse static output nonlinearity. Furthermore, the issue on parameter selection for B-spline model approximation of scatter data is addressed by using a data clustering method. An experimental test-bed of virtualised software system is established to generate real observational data which are used to confirm the performance of the proposed approach. The identification results have shown that the model efficacy is increased with the proposed approach because the dimension of the nonlinear model can be significantly reduced while maintaining the desired accuracy.     

Hammerstein system identification through best linear approximation inversion and regularisation

Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.     

Identification of an additive nonlinear system and its applications in generalized Hammerstein models

An identification algorithm is developed for a class of nonlinear systems that are multi-input and multi-output in an additive form. The convergence results are achieved and its applications to identification of a generalized Hammerstein system is also discussed.     

Recursive identification of Hammerstein systems with dead-zone nonlinearity in the presence of bounded noise

The existing identification algorithms for Hammerstein systems with dead-zone nonlinearity are restricted by the noise-free condition or the stochastic noise assumption. Inspired by the practical bounded noise assumption, an improved recursive identification algorithm for Hammerstein systems with dead-zone nonlinearity is proposed. Based on the system parametric model, the algorithm is derived by minimising the feasible parameter membership set. The convergence conditions are analysed, and the adaptive weighting factor and the adaptive covariance matrix are introduced to improve the convergence. The validity of this algorithm is demonstrated by two numerical examples, including a practical DC motor case.     

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.