Recursive Extended Least Squares Research Articles

Dynamic Model Identification of the Main Steam Temperature for Supercritical Once-through Boiler

In this paper the dynamic model of single-input and single-output (SISO) is established, which take the coal feed as the input and the main steam temperature as the output. Recursive extended least squares (RELS) was used to identify the system model, and the ideal identification results were achieved. The results showed that the output of identification and actual output in good agreement by usage of the recorded data to verify the accuracy of model further.

Implementation of electrohydraulic shaking table controllers with a combined adaptive inverse control and minimal control synthesis algorithm

This study presents a combined control strategy for electrohydraulic shaking table (EST) systems. The position frequency bandwidth of the EST system is so low that it results in a worse tracking accuracy during seismic tests, particularly when the frequency bandwidth of the desired position signal exceeds the frequency bandwidth of the EST position closed-loop system. In order to improve the position tracking accuracy, a combined control strategy is proposed, which utilises a recursive extended least square (RELS) algorithm to offline or online estimate the position closed-loop transfer function of the EST system, then uses the estimated transfer function to offline or online yield a feedforward inverse controller for extending the position frequency bandwidth, finally, employs a minimal control synthesis (MCS) algorithm to further improve the tracking performance of the EST position system. The proposed control strategy combines the merits of offline or online feedforward inverse compensation and adaptive control. The procedure of the proposed control strategy is programmed in MATLAB/Simulink, and is then compiled to a real-time PC with Microsoft Visual Studio.NET for implementation. A better tracking performance for the proposed control strategy is achieved in experiments by using actual EST.

Modelling and Validation of Automotive Engine Fuelled with Palm Oil Biodiesel

This paper presents the Black-box modelling of automotive diesel engine fuelled with palm oil biodiesel (Palm Oil Methyl Ester). The aim of the work described in this paper is to obtain linear dynamic model of the palm oil biodiesel from test data. Assuming a discrete time form for the system model, an Autoregressive Moving Average with eXogenous input (ARMAX) model structures was selected in this work. A Pseudo-Random Binary Sequence (PRBS) with maximum lengths sequence of 31 has been used as the test input signal to the engine at the speed range around 2100 rpm. The input and output signals were interfaced to the plant via Matlab programming. Recursive estimation algorithm, Recursive Extended Least Squares (RELS), is used to estimate the model parameters. Finally, model validation was done by comparing the output predicted by the model against the measured output and also by error analysis. The mathematical model developed in this study present an analysis and simulation tools of engine dynamic system that forms the foundation for a systematic approach to the analysis, simulation and synthesis of the automotive palm oil biodiesel engine control systems. The model derived in this work is intended for the development of self-tuning engine speed controller in future work. Index Terms—Identification; Modeling; Biodiesel; Palm oil biodiesel

Self-tuning fusion Wiener filter for multisensor multi-channel AR signals with common disturbance noise

For the multisensor multi-channel autoregressive (AR) signals with common disturbance noise, when model parameters and noise variances are unknown, the estimates of model parameters and noise variances can be obtained based on the multi-dimension recursive extended least squares (RELS) algorithm and the correlation method. Further, a self-tuning fusion Wiener filter is presented based on the modern time series analysis method by substituting the estimates for the true values. A simulation example shows the consistence of the estimates of the model parameters and noise variances, and the tracking characteristics of the self-tuning fusion Wiener filter.

Auxiliary model-based RELS and MI-ELS algorithm for Hammerstein OEMA systems

This paper considers the identification problem for Hammerstein output error moving average (OEMA) systems. An auxiliary model-based recursive extended least-squares (RELS) algorithm and an auxiliary model-based multi-innovation extended least-squares (MI-ELS) algorithm are presented using the multi-innovation identification theory. The basic idea is to express the system output as a linear combination of the parameters by using the key-term separation principle and auxiliary model method. The proposed algorithms can give highly accurate parameter estimates. The simulation results show the effectiveness of the proposed algorithms.

A Recursive Blind Adaptive Equalizer for IIR Channels with Common Zeros

This paper considers the problem of blind adaptive equalization of infinite impulse response (IIR) channels without requiring the channel diversity condition. That is, the subchannels in the fractionally sampled model can have common factors. We analyze the case of two parallel channels, and develop an equalizer based on IIR prediction of the received signal. The predictor parameters are estimated by using the recursive extended least squares (RELS) algorithm. It is proved that with probability one the adaptive equalizer is globally stable, the parameter estimates are consistent, and the prediction error converges toward a scalar multiple of the input symbol sequence.

Multiple ARMAX modeling scheme for forecasting air conditioning system performance

System identification is a procedure to characterize the dynamic behavior of a system, subsystem or individual component from measured data. This paper presents a study on the modeling and parameter identification of air conditioning processes by using the mathematical black box modeling technique, autoregressive moving average exogeneous (ARMAX) structure. A generic multiple input multiple output (MIMO) ARMAX structure of typical air conditioning systems is developed, whose parameters are identified by using the recursive extended least squares (RELS) method. The performance of the model is compared with that of a single input single output (SISO) ARMAX model. A significant component of the determination of an ARMAX model is the selection of an appropriate model order. Models of different orders and the effects of properties are evaluated. Site measurements from an air conditioning system in a building are used for the testing and validation of the models in the study.

A fast method for online closed-loop system identification

In the modern control schemes broadly applied presently in the servo drive system of machine tools, the sampling frequency has been growing larger and larger becomes higher and higher, so it is important to keep up-to-date with the variance of the actual system parameters. As a solution to the problem, a novel method developed from the recursive extended least squares (RELS) algorithm in terms of the computation of functions, operates in such a way that the parameters of the system model are revised only when several proper new groups of data are obtained. The simulation and experimentation of online direct closed-loop system identification indicate that, by selecting the updating step, this method is able to effectively cut down the identifying cost time while obtaining satisfactory accuracy of estimation.

Modelling and prediction of machining errors using ARMAX and NARMAX structures

Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.

Roundness error compensation in lathe turning through 2-D ARMAX model based FCC

This paper describes the design, simulation, and implementation of a two-dimensional (2-D) exogenous autoregressive moving average (ARMAX) model-based forecasting compensatory control (FCC) system for a lathe turning machine. The 2-D ARMAX model is used to represent the relative motion errors between the workpiece and the cutting tool in the longitudinal and radial directions. Here, the formulation of recursive ARMAX models is necessary to account for the variation of the cutting force, which is the exogenous input to this process. The parameters are estimated online by means of the recursive extended least square (RELS) method. The predicted motion errors, which will adversely affect the workpiece roundness, are compensated by means of a two-axis piezoactuator. An offline simulation model has been developed to find the most suitable model order and parameters. The application of the proposed system to both simulated and actual cutting data has confirmed the effectiveness of the proposed strategy. Experiments revealed that the maximum roundness improvement achieved could be as high as 66% while the average roundness improvement is found to be 52%, which proved the effectiveness of the proposed FCC system.

High-performance speed control of electric machine using low-precision shaft encoder

For a high-performance servo drive system, it is important to estimate and control the motor speed precisely over a wide-speed range. Therefore, the disturbance-rejection ability and the robustness to variations of the mechanical parameters such as inertia should be considered. This paper shows that the adaptive state estimator and self-tuning regulator based on the recursive extended least squares (RELS) parameter identification method can achieve high-performance speed control over a wide-speed range. The RELS method identifies the variations of mechanical parameters, and the estimated mechanical parameters are used to replace the role of manual tuning by adjusting the gain of the speed controller automatically for good dynamic response. Also, these estimated parameters are used to adapt the Kalman filter, which is an optimal state estimator, to provide good estimation performance for the rotor speed, rotor position and disturbance torque even in a noisy environment. Simulation and experimental results show an improved speed control performance in the wide-speed range.

Improving fault handling in marine vehicle course-keeping systems

Proposes a FDI algorithm that is tested by simulation of the rudder servosystem in the closed-loop course-keeping system for a Mariner Class vessel. A properly adjusted recursive extended least-squares (RELS) identification algorithm is utilized for fault-detection purposes, since hardly detectable faults (also called multiplicative faults) are handled. The rudder subsystem model, as a part of the overall closed-loop course-keeping system, is presented, and the three main parts of the proposed FDI module, which are configured on the basis of a RELS algorithm, are described. We show simulation results and provide comments for both linear and nonlinear (complete 3 degree-of-freedom model) Mariner Class vessel dynamics. We also discuss the connection to some other approaches and provide possible improvements for the suggested algorithm.

DSP-based self-tuning IP speed controller with load torque compensation for rolling mill DC drive

This paper describes the design and the implementation of a self-tuning integral-proportional (IP) speed controller for a rolling mill DC motor drive system, based on a 32-bit floating point digital signal processor (DSP)-TMS 320C30. To get a better transient response than conventional proportional-integral (PI) and/or integral-proportional (IP) speed control in the presence of transient disturbance and/or parameter variations, an adaptive self-tuning IP speed control with load torque feedforward compensation was used. The model parameters, related to motor and load inertia and damping coefficient, were estimated online by using recursive extended least squares (RELS) estimation algorithm. On the basis of the estimated model parameters and a pole-placement design, a control signal was calculated. Digital simulation and experimental results showed that the proposed controller possesses excellent adaptation capability under parameter change and a better transient recovery characteristic than a conventional PI/IP controller under load change. >

Sidestepping the positive real condition in RELS via multiple RLS identifiers

A recursive ARMA identifier based on multi-step prediction error minimization is considered so as to sidestep the positive real condition of recursive extended least squares (RELS). For a single step prediction horizon the algorithm reduces to RELS while, as is shown by local convergence analysis, it tends to be a local approximation of the recursive maximum likelihood (RML) algorithm as the prediction horizon increases.

Estimating lung mechanics of dogs with unilateral lung injury.

Extended least-squares algorithms using transpulmonary pressure and airway flow data from ventilatory waveforms were studied for their ability to track parameters of one- and two-compartment models of lung mechanics. A recursive extended least-squares algorithm with discounted measures estimated parameters of discrete-time models during synchronized intermittent mandatory ventilation. In tests on seven dogs developing oleic acid-induced unilateral hemorrhagic pulmonary edema, the one-compartment estimator responded rapidly and appropriately to changes in mechanics: compliance fell to 0.55 +/- 0.15 of its initial value and resistance rose by a factor of 1.8 +/- 0.5 in 3 h following injection of oleic acid. One-compartment parameter estimates revealed a difference between the airway resistance of inspiration and expiration. Two-compartment estimates were seldom physiologically plausible. The difference between inspiratory and expiratory resistance may have caused the two-compartment estimator to fail when applied to data from the entire respiratory cycle; when only expiratory data were used for estimation, the two-compartment estimates were meaningful. These estimates demonstrated increasing lung inhomogeneity after oleic acid was injected; at the end of 3 h, the ratio of the time constants of the two compartments ranged from 5 to 20 in six of the seven dogs. We conclude that the one- and two-compartment estimates may be combined to provide a meaningful assessment of lung mechanics.

Application of an adaptive filter for criticality surveillance systems

Applicability of the adaptive filter for an on-line criticality surveillance system has been discussed through numerical simulations and analysis of real data from a subcritical reactor, based on the fact that the break frequency in the higher frequency region of the PSD of the neutron signal fluctuation has a one-to-one correspondence to subcriticality within the framework of a point reactor kinetics. The recursive extended least squares (RELS) algorithm, a modified RELS algorithm, and the recursive maximum likelihood (RML) algorithm have been examined and it was found that: 1. 1. The model parameters estimated by the adaptive filters do not converge to the theoretical values, however, the PSD of the model agrees well with that of the theoretical one in a higher frequency region. 2. 2. The modified RELS method is best for ARMA model identification of the neutron signal fluctuation from the viewpoint of parameter convergence when the sampling frequency, an anti-aliasing filter and a high-pass filter are appropriately selected. 3. 3. The order of ARMA model is best at (2,2) for subcriticality resolution. 4. 4. The break frequency of the first-order high-pass filter should be set within the range 1/10-1/100 of the break frequency of the PSD of the neutron signal in a higher frequency region. These results indicate that: this approach cannot provide the absolute value of subcriticality without criticality measurement in contrast to Mihalczo's method, however, it can be applicable to an inexpensive on-line monitoring system of reactivity change with a relatively small amount of numerical calculations.

A recursive (on-line) identification of bilinear systems

A recursive identification of a discrete dynamical system is presented in this paper. Two methods of recursive identification, namely the recursive extended least-squares method and the recursive maximum likelihood method, are described and analysed. The techniques are illustrated numerically with simulations.

Lattice implementation of some recursive parameter-estimation algorithms†

Linear dynamic models of plants are usually parametrized by the coefficients of difference equations. Lattice structures and their reflection coefficients provide an alternative parametrization that offers several advantages, including numerical robustness, computational efficiency and ease of hardware implementation. The recursive square-root normalized lattice versions of the following well-known parameter-estimation algorithms are presented ; recursive least-squares, recursive instrumental variable, extended least-squares, and recursive maximum-likelihood