Refined Instrumental Variable Research Articles

A Robust Data-Driven Approach for Adaptive Dynamic Load Modeling

With the power system operating close to its stability margin, the increased penetration of renewable resources and loads with diverse characteristics, appropriate stability studies, and control decisions have become crucial. Due to the importance of accurate representation of aggregate loads in such studies, research interests for load modeling have increased. This paper puts forward a novel measurement-based load modeling approach that adapts itself based on the complex dynamics exhibited by the installed aggregate loads. The proposed approach primarily utilizes the collected measurements to gain insight regarding the dynamic trend in the measurements and subsequently determines the optimal order of an equivalent system or load model capable of effectively representing the aggregate load dynamics. An advanced signal pre-processing technique is employed, which effectively suppresses the noise and also preserves the transients present in the measurements. Afterward, an adaptive dynamic load model (ADLM) accurately represents the installed aggregate load. Lastly, the Refined Instrumental Variable (RIV) approach estimates the equivalent dynamic load model parameters. The results on a 2 bus and the IEEE 118 bus networks in DIgSILENT Powerfactory and a 7 bus network in Real-Time Digital Simulator (RTDS) reveal the efficacy of the proposed approach.

Online Parameter Identification of the Lithium-Ion Battery with Refined Instrumental Variable Estimation

Refined Instrumental Variable (RIV) estimation is applied to online identify the parameters of the Equivalent Circuit Model (ECM) for Lithium-ion (Li-ion) battery in this paper, which enables accurate parameters estimation with the measurement noise. Since the traditional Recursive Least Squares (RLS) estimation is extremely sensitive to the noise, the parameters in the ECM may fail to converge to their true values under the measurement noise. The RIV estimation is implemented in a bootstrap form, which alternates between the estimation in the system model and the noise model. The Box-Jenkins model of the Li-ion battery transformed from the two RC ECM is selected as the transfer function model for the RIV estimation in this paper. The errors of the two RC ECM are independently generated by the residual of high-order Auto Regressive (AR) model estimation. With the benefit of a series of auxiliary models, the data filtering technology can prefilter the measurement and increase the robustness of the parameters against the noise. Reasonable parameters are possible to be obtained regardless of the noise in the measurement by RIV. Simulation and experimental tests on a LiFePO4 battery validate the efficiency of RIV for parameter online identification compared with traditional RLS.

Data-Driven Modeling of Wireless Power Transfer Systems With Slowly Time-Varying Parameters

This article considers the data-driven modeling of a class of phase-controlled wireless power transfer (WPT) systems, where the load may vary slowly with respect to time. The dominant mode analysis suggests that a model of the Hammerstein type, which consists of a static nonlinearity function, followed by a linear time-varying model with a pure time delay, is the best structure to describe the input–output relationship of the system. On this basis, we derive a small-signal model that is linear in the variables in order to aid control design and allow the associated model parameters to be estimated from sampled input–output data using the standard refined instrumental variable (RIV) method. In the presence of a time-varying load, however, the plant model parameters may not be correctly estimated if the load response is not removed. In order to address this problem, a new recursive RIV method is proposed, in which an effective technique is introduced to track the load response, so allowing the parameters and time delay of the time-varying model to be accurately estimated. The effectiveness of the proposed method is verified by applying it to both a simulation model and a laboratory system.

A New control structure for tert-amyl methyl ether production using reactive distillation

The aim of this paper is to introduce new control structures in both centralized and decentralized scheme for tert-amyl methyl ether (TAME) production unit using reactive distillation which developed as a benchmark by Luyben (2005). Steady state and dynamic simulation was performed based on the case study data using Aspen® simulator. Dynamic simulation shows that control performance of the plant has oscillatory behavior using conventional PI controllers. Hence, a proper modification on the process flow sheet was carried out in order to remove oscillatory behavior of the process. Although, the new structure has better dynamic performance than the previous one using PI controller, it is not capable of eliminating the oscillations completely. Non-minimal state space with proportional integral plus controller (NMSS–PIP) controller was applied to dynamic model of the modified process. In this way, the system identification was carried out using refined instrumental variable (RIV) method and state matrices was obtained as left matrix fraction description (LMFD). The control performance of the PI and PIP controller for the modified structure revealed that the NMSS–PIP, completely eliminates the process oscillations while it has smoother responses with better settling time than the PI configuration. Furthermore, comparison of the ITAE criterion between main case and modified process indicates that the ITAE for PI and PIP control decreased by about 20% and 88%, respectively.

An improved instrumental variable method for industrial robot model identification

Industrial robots are electro-mechanical systems with double integrator behaviour, necessitating operation and model identification under closed-loop control conditions. The Inverse Dynamic Identification Model (IDIM) is a mechanical model based on Newton’s laws that has the advantage of being linear with respect to the parameters. Existing Instrumental Variable (IDIM-IV) estimation provides a robust solution to this estimation problem and the paper introduces an improved IDIM-PIV method that takes account of the additive noise characteristics by adding prefilters that provide lower variance estimates of the IDIM parameters. Inspired by the prefiltering approach used in optimal Refined Instrumental Variable (RIV) estimation, the IDIM-PIV method identifies the nonlinear physical model of the robot, as well as the noise model resulting from the feedback control system. It also has the advantage of providing a systematic prefiltering process, in contrast to that required for the previous IDIM-IV method. The issue of an unknown controller is also considered and resolved using existing parametric identification. The evaluation of the new estimation algorithms on a six degrees-of-freedom rigid robot shows that they improve statistical efficiency, with the controller either known or identified as an intrinsic part of the IDIM-PIV algorithm.

Non‐minimal state‐space polynomial form of the Kalman filter for a general noise model

The optimal refined instrumental variable (RIV) method for the estimation of the Box-Jenkins (BJ) model is modified so that it functions as an optimal filter and state-estimation algorithm. In contrast to the previously developed minimal and non-minimal state space (NMSS) forms for an Auto-Regressive Moving Average with eXogenous variables (ARMAX) model, the new algorithm requires the introduction of a novel extended NMSS form. This facilitates representation of the more general noise component of the BJ model. The approach can be used for adaptive filtering and state variable feedback control.

New developments in the CAPTAIN Toolbox for Matlab with case study examples

The CAPTAIN Toolbox is a collection of Matlab algorithmic routines for time series analysis, forecasting and control. It is intended for system identification, signal extraction, interpolation, forecasting and control of a wide range of linear and non-linear stochastic systems across science, engineering and the social sciences. This article briefly reviews the main features of the Toolbox, outlines some recent developments and presents a number of examples that demonstrate the performance of these new routines. The examples range from consideration of global climate data, through to electro-mechanical systems and broiler chicken growth rates. The new version of the Toolbox consists of the following three modules that can be installed independently or together: off-line, time-varying parameter estimation routines for Unobserved Component (UC) modelling and forecasting; Refined Instrumental Variable (RIV) algorithms for the identification and estimation of both discrete and ‘hybrid’ continuous-time transfer function models; and various routines for Non-Minimal State Space (NMSS) feedback control system design. This new segmented approach is designed to provide new users with a gentler introduction to Toolbox functionality; one that focuses on their preferred application area. It will also facilitate more straightforward incorporation of novel algorithms in the future.

Refined instrumental variable estimation: Maximum likelihood optimization of a unified Box–Jenkins model

For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab™. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.

Practical experience with unified discrete and continuous–time, multi–input identification for control system design

The paper is concerned with the practical aspects of a unified approach to the identification and estimation of multiple–input, single–output (MISO) transfer function models for both continuous and discrete–time systems. The estimation algorithms considered in the paper are based on the Refined Instrumental Variable (RIV) approach to identification and estimation, where the MISO model denominator polynomials are normally constrained to be equal. Unconstrained RIV estimation presents a more difficult problem and it is necessary to exploit an iterative, back–fitting routine to handle this more general situation. The paper focuses on the practical realization of this back–fitting algorithm, including its initiation from either common denominator MISO or repeated SISO estimation. The rivcdd algorithm for continuous–time model estimation, as implemented in the CAPTAIN Toolbox for Matlab™, is then used in three practical examples: first, the modelling of solute transport and dispersion in a water body; secondly, modelling for two control problems, namely a pair of connected laboratory DC motors and a nonlinear wind turbine simulation.

Discussion on: “Why Is Resorting to Fate Wise? A Critical Look at Randomized Algorithms in Systems and Control”

For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab™. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.

A REFINED IV METHOD FOR CLOSED-LOOP SYSTEM IDENTIFICATION

This paper describes an optimal instrumental variable method for identifying discrete-time transfer function models of the Box-Jenkins transfer function form in the closed-loop situation. This method is based on the Refined Instrumental Variable (RIV) algorithm which, because of an appropriate choice of particular design variables, achieves minimum variance estimation of the model parameters. The Box-Jenkins model is the most natural since it does not constrain the process and the noise models to have common polynomials. The performance of the proposed approach is evaluated by Monte Carlo analysis in comparison with other alternative closed loop estimation methods.

AN INSTRUMENTAL VARIABLE APPROACH TO ARMA MODEL IDENTIFICATION AND ESTIMATION

The paper describes an optimal Instrumental Variable (IV) algorithm for estimating an AutoRegressive Moving Average model of a time series. This IVARMA method is based on a modification of a previous algorithm and utilizes the Simplified Refined Instrumental Variable (SRIV) algorithm to estimate the ARMA model from the results of initial, high order, AutoRegressive (AR) model estimation. Using Monte Carlo simulation, the new algorithm is compared with the maximum likelihood method of ARMA estimation, using the well known PEM algorithm, and shown to produce parameter estimates with similar, statistically efficient properties. It is also incorporated in the Refined Instrumental Variable (RIV) algorithm to produce a new implementation of RIV for the full Box-Jenkins TF model form. Once again, MCS analysis confirms that this performs in a similar, statistically optimal manner to PEM, without the need for gradient-type optimization and with less sensitivity to the choice of initial conditions.

Adaptive True Digital Control (TDC) of Continuous-Time Systems Using

The paper outlines a general approach to the digital identification, estimation and control of linear continuous-time systems based on the True Digital Control (TDC) design philosophy using δ operator models. The Refined Instrumental Variable (RIV) identification and estimation procedures, which provide the modelling basis for the implementation of these δ operator TDC concepts, are seen to be a theoretically inspired generalisation of earlier continuous-time techniques proposed in the 1960's.

Recursive-Iterative IV Estimation of Multiple-Input Transfer Function Models

The refined instrumental variable (RIV) approach to the identification and estimation of multiple input transfer function models has some deficiencies when applied to short time-series obtained from impulse-response-type experiments of the kind used in Diomedical and environmental science. This paper proposes a modifica-tion of the RIV method which corrects these deficiencies by a novel application of the Kalman filter. The practical utility of the method is demonstrated through its application to the analysis of time-series data obtained from experiments on the glucose insulin system in humans and dogs.