Weighted Recursive Least Squares Research Articles

An Adaptive PID Control System for the Attitude and Altitude Control of a Quadcopter

Abstract In adaptive model-based control systems, determining the appropriate controller gain is a complex and time-consuming task due to noise and external disturbances. Changes in the controller parameters were assumed to be dependent on the quadcopter mass, which was the process variable. A nonlinear model of the plant was used to identify the mass, employing the weighted recursive least squares (WRLS) method for online identification. The identification and control processes involved filtration using differential filters, which provided appropriate derivatives of signals. Proportional integral derivative (PID) controller tuning was performed using the Gauss–Newton optimisation procedure on the plant. Differential filters played a crucial role in all the developed control systems by significantly reducing measurement noise. The results showed that the performance of classical PID controllers can be improved by using differential filters and gain scheduling. The control and identification algorithms were implemented in an National Instruments (NI) myRIO-1900 controller. The nonlinear model of the plant was built based on Newton’s equations.

An Improvement of DV-Hop Localization Algorithm Based on Cyclotomic Method in Wireless Sensor Networks

Location information is one of the crucial and essential elements for monitoring data in wireless sensor networks. The distance vector-hop (DV-Hop) localization algorithm is of practical importance in improving its localization performance. To achieve global optimization, a DV-Hop algorithm based on the cyclotomic method and weighted normalization, also known as CMWN-DV-Hop, is nominated in this paper. Therefore, the segmentation and weighting factors are introduced and normalized. The weighted recursive least-squares (WRLS) algorithm is chosen to compute the coordinates of the unknown nodes. The effects of various factors on this algorithm are tested, including the number of nodes, the anchor node ratio, and the communication radius. The simulation results show that the proposed algorithm has a super performance in reducing the localization error.

Stochastic configuration network based cascade generalized predictive control of main steam temperature in power plants

The main steam temperature (MST) in power plants suffers from nonlinearity and large time delay, which cause large overshoot and long settling time under widely used cascade proportion integration differentiation (PID) controller. In order to cope with the negative effects, we propose a stochastic configuration network (SCN) based cascade generalized predictive control (GPC) scheme to improve the performance of the MST. A three-layer SCN is employed to model the MST process. The SCN is constructed by two phases, i.e., initial phase and real-time phase. The initial phase determines the structure and primary parameters of the learner model using the stochastic configuration algorithm. The real-time phase employs weighted recursive least squares (WRLS) for building the real-time MST process model for GPC design. Taking into account some constraints of the MST process, Karush–Kuhn–Tucker (KKT) conditions are applied for solving the constrained receding-horizon optimization problem. The derived explicit solutions of GPC avoid the implicit form which usually has to be solved iteratively. Comparative simulations demonstrate the superiority of the proposed SCN based cascade GPC (SCN-CGPC). Finally, the proposed SCN-CGPC is implemented via a standalone external MST control system in a power plant. The effectiveness and practicability are validated with the real-world application.

Joint Channel Estimation and Equalization Using New AFB Output Signal Models for FBMC/OQAM Systems

Filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has been studied as an alternative waveform for post-orthogonal frequency division multiplexing (OFDM) wireless communications. However, due to the intrinsic imaginary inter-carrier/inter-symbol interference of FBMC/OQAM signals, accurate channel estimation and equalization remain open issues for FBMC/OQAM systems in dispersive channels. In this article, two new signal models of the analysis filter bank (AFB) output are first derived in the absence of any channel assumption and in the presence of a relaxed channel assumption, respectively. Based on the new-built models, initial channel estimation with least squares (LS) (IniCE-LS) is presented and its output is used as the initial condition of recursive weighted LS (RWLS) estimation; moreover, non-iterative and iterative channel equalization combined with RWLS channel estimation (i.e., N-ICE-RWLS and ICE-RWLS) are proposed by using the real-time reconstructed FBMC/OQAM data symbols as pilots. The proposed N-ICE-RWLS and ICE-RWLS schemes not only allow to improve channel estimation and equalization performance, but also achieve high transmission efficiency. Considering the requirements of practical application, we further develop the low-complexity implementation methods of N-ICE-RWLS and ICE-RWLS. All these schemes are validated by analyzing the channel estimation accuracy and bit error rate (BER) over various frequency selective channels.

Adaptive Predictive Control of a data center cooling unit

As server densities increase to support the rising demand for high density computing, traditional room cooling infrastructure is struggling to keep up. Rack-mounted cooling units are increasingly being deployed in data centers. These cooling units are located closer to the heat sources (the servers) which allow them to cool more efficiently than traditional cooling infrastructure. In this work, a Multi-Input Single-Output (MISO) Adaptive Predictive Controller (APC) for rack-mounted cooling units is investigated and implemented using a low-cost general-purpose microcontroller. The proposed APC is implemented using Weighted Recursive Least Squares (WRLS) and a sub-optimal but fast algorithm based on the General Predictive Controller (GPC) approach. These are combined with a variable forgetting factor and variable prediction horizon algorithms. In addition, methods are proposed to handle stability issues arising due to practical hardware limitations. The controller is implemented on a real single rack system and challenges for practical implementation are addressed and illustrated. The proposed APC is also compared (via simulation) to a standard APC with equivalent complexity and a split-range PI controller. The results show that the proposed controller outperforms both the standard APC and the split-range PI controllers with respect to Mean Squared Error (MSE).

A Nonlinear Model for Online Identifying a High-Speed Bidirectional DC Motor

The modeling system is a process to define the real physical system mathematically, and the input/output data are responsible for configuring the relation between them as a mathematical model. Most of the actual systems have nonlinear performance, and this nonlinear behavior is the inherent feature for those systems; Mechatronic systems are not an exception. Transforming the electrical energy to mechanical one or vice versa has not been done entirely. There are usually losses as heat, or due to reverse mechanical, electrical, or magnetic energy, takes irregular shapes, and they are concerned as the significant resource of that nonlinear behavior. The article introduces a nonlinear online Identification of a high-speed bidirectional DC motor with dead zone and Coulomb friction effect, which represent a primary nonlinear source, as well as viscosity forces. The Wiener block-oriented nonlinear system with neural networks are implemented to identify the nonlinear dynamic, mechatronic system. Online identification is adopted using the recursive weighted least squares(RWLS) method, which depends on the current and (to some extent) previous data. The identification fitness is found for various configurations with different polynomial orders, and the best model fitness is obtained about 98% according to normalized root mean square criterion for a third order polynomial.

One approach to temperature distribution control in thermal power plant boilers

ABSTRACTOptimization of the combustion control process in a tangentially fired pulverized coal boiler, to achieve uniform temperature distribution, is discussed in the paper. This issue is even more critical in those thermal power plants which are not equipped with modern systems for combustion enhancement, such as low NOx burners. Research has shown that the temperature distribution inside the boiler of such power plant can be controlled by adjusting firing, through coal redistribution among the mills. Furthermore, disturbed flame symmetry (i.e. non-uniform temperature distribution in the boiler) is reflected in a large difference between the output temperatures measured on the left and right sides of the boiler. Given the non-stationary conditions typical of thermal power plant boilers, an adaptive control approach is proposed, based on PI controllers which are very popular in industry and widely accepted. Self-tuning of the PI controllers is based on dynamic model parameters derived applying the weighted recursive least squares (WRLS) method to real data recorded at Nikola Tesla B thermal power plant in Serbia, whose nominal power is 650 MW. The same model was later used to test the proposed control approach.

A fuzzy C‐regression model algorithm using a new PSO algorithm

SummaryIn this paper, a new methodology is introduced for the identification of the parameters of the multiple‐input–multiple‐output local linear Takagi‐Sugeno fuzzy models using the weighted recursive least squares (WRLS). The WRLS is sensitive to initialization, which leads to no convergence. In order to overcome this problem, adaptive chaos particle swarm optimization is proposed to optimize the initial states of WRLS. This new algorithm is improved versions of the original particle swarm optimization algorithm. Finally, comparative experiments are designed to verify the validity of the proposed clustering algorithm and the Takagi‐Sugeno fuzzy model identification method, and the results show that the new method is effective in describing a complicated nonlinear system with significantly high accuracies compared with approaches in the literature.

Self-Tuning Robust Fuzzy Controller Design Based on Multi-Objective Particle Swarm Optimization Adaptation Mechanism

In this paper, an adaptive fuzzy controller design methodology via multi-objective particle swarm optimization (MOPSO) based on robust stability criterion is proposed. The plant to be controlled is modeled from its input–output experimental data considering a Takagi–Sugeno (TS) fuzzy nonlinear autoregressive with exogenous input model, by using the fuzzy C-means clustering algorithm (antecedent parameters estimation) and the weighted recursive least squares (WRLS) algorithm (consequent parameters estimation). An adaptation mechanism as MOPSO problem for online tuning of a fuzzy model based digital proportional-integral-derivative (PID) controller parameters, based on the gain and phase margins specifications, is formulated. Experimental results for adaptive fuzzy digital PID control of a thermal plant with time-varying delay are presented to illustrate the efficiency and applicability of the proposed methodology.

Closed-Form Solution of TDOA-Based Geolocation and Tracking: A Recursive Weighted Least Square Approach

The location determination technique using time difference of arrival (TDOA) measurements has been widely used in the military and observation industry. The accuracy of geolocation estimation is a very significant problem because measurement data are affected by environmental noise. Environmental noise occurs due to measurement error and the non-line of sight (NLOS) problem. This paper presents a Kalman filter-based NLOS section identification method and an iterative estimation of emitter location using the recursive weighted least square (RWLS) algorithm. Using fixed receivers with known locations, we obtain TDOA data that contain environmental noise. We identify the NLOS section of each receiver using a Kalman filter. Using the identified line of sight (LOS) TDOA measurements, we accurately derive the estimated location of an emitter with a fast calculation speed using the proposed RWLS algorithm when we receive additional TDOA data. In order to confirm the performance of the RWLS algorithm, the presented simulation results show that the proposed technique achieves improved accuracy and speed for estimating the emitter location.

A Decentralized Positioning Scheme Based on Recursive Weighted Least Squares Optimization for Wireless Sensor Networks

This paper presents a new positioning scheme based on recursive weighted least squares (RWLS) optimization for wireless sensor networks. The proposed scheme is derived from minimizing a recursive-in-time cost function and then realized in an iterative decentralized manner. The target location is computed iteratively by taking a weighted average of the local estimates according to the reliability information, where a sensor computes a new estimate based on its own observation and the previous sensor's estimate. Computer simulation results demonstrate that the proposed scheme has better positioning accuracy than previous related methods.

Joint State and Input Estimation for One-Dimensional Heat Conduction

This paper presents a joint state and input estimation algorithm for the one-dimensional heat-conduction problem. A computationally efficient method is proposed in this work to solve the inverse heat-conduction problem (IHCP) using orthogonal collocation method (OCM). A Kalman filter (KF) algorithm is used in conjunction with a recursive-weighted least-square (RWLS)-based method to simultaneously estimate the input boundary condition and the temperature field over the heat-conducting element. A comparison study of the algorithm is shown with explicit finite-difference method (FDM) of approximation and analytical solution of the forward problem, which clearly reveals the high accuracy with lower-dimensional modeling. The estimation results show that the performance of the estimator is robust to noise sensitivity up to a certain level, which is practically acceptable.

Tuning optimal PID controller

In this paper, a novel design method for determining the optimal proportional-integral-derivative (PID) controller parameters for nonlinear multiple-input multiple-output (MIMO) system using the particle swarm optimisation (PSO) algorithm is presented. Firstly, a nonlinear system was described based on Takagi-Sugeno (T-S) fuzzy models. Assuming that the antecedent parameters of T-S models were kept, the consequent parameters were identified online by using the weighted recursive least square (WRLS) method. Secondly, the identified parameters of fuzzy model were used to directly receive the model predicted output with direct iterative for the T-S model. The fast tuning of optimum PID controller parameters yields high-quality solution. In order to assist estimating the performance of the proposed PSO-PID controller, a new time-domain performance criterion function was also defined. Finally, the application results for continuous stirred tank reactor (CSTR) process show that the proposed algorithm is an effective control strategy with excellent tracing ability.

A novel weighted recursive least squares based on Euclidean particle swarm optimization

PurposeThe purpose of this paper is to present a new methodology for identification of the parameters of the local linear Takagi‐Sugeno fuzzy models using weighted recursive least squares. The weighted recursive least squares (WRLS) is sensitive to initialization which leads to no converge. In order to overcome this problem, Euclidean particle swarm optimization (EPSO) is employed to optimize the initial states of WRLS. Finally, validation results are given to demonstrate the effectiveness and accuracy of the proposed algorithm. A comparative study is presented. Validation results involving simulations of numerical examples and the liquid level process have demonstrated the practicality of the algorithm.Design/methodology/approachA new method for nonlinear system modelling. The proposed algorithm is employed to optimize the initial states of WRLS algorithm in two phases of learning algorithm.FindingsThe results obtained using this novel approach were comparable with other modeling approaches reported in the literature. The proposed algorithm is able to handle various types of modeling problems with high accuracy.Originality/valueIn this paper, a new method is employed to optimize the initial states of WRLS algorithm in two phases of the learning algorithm.

Direct Adaptive Fuzzy Predictive Control and its Application to CSTR Process

In order to obtain accurate prediction model and avoid solving nonlinear programming problem, a direct adaptive predictive control (DAPC) method is proposed. Firstly, a nonlinear system was described based on Takagi-Sugeno (T-S) fuzzy models. Assuming that that the antecedent parameters of T-S models were kept, the consequent parameters were identified on-line by using the weighted recursive least square (WRLS) method. Secondly, the identified parameters of fuzzy model were used to directly receive the model predicted output with direct iterative for the T-S model. Finally, the application results for continuous stirred tank reactor (CSTR) process show that the proposed algorithm is an effective control strategy with excellent tracing ability. The proposed algorithm is a good way to resolve the two major problems, modeling and optimization, and provides a guarantee for high-precision control of nonlinear systems.

Adaptive Neuro-Controller Based on Hybrid Multi Layered Perceptron Network for Dynamic Systems

In this paper, an intelligent controller namely Adaptive Neuro-controller (ANC) based on Hybrid Multi Layered Perceptron (HMLP) network has been developed for dynamic systems. The performance of ANC has been compared with the ANC based on Multi Layered Perceptron (MLP) network and Adaptive Parametric Black Box (APBB) Controller. The comparison are based on the time response and the capability of the controlled output to track the model reference output. All controllers are based on a black box approach that offers simpler design approach. The Model Reference Adaptive System (MRAS) has been used to generate the desired output path and to ensure the output of the controlled system follows the output of the reference model. Weighted Recursive Least Square (WRLS) algorithm has been used to adjust the controller parameters in order to minimize the error between the plant output and the model reference output. The controllers have been tested using a linear plant and a nonlinear plant with several varying operating conditions such as varying gain, noise and disturbance. Based on the simulation results and performance analysis for all controllers, it is observed that ANC based on HMLP network is controllable and more stable than ANC based on MLP network and APBB controller. It is also can be signify that the ANC based on HMLP network is sufficient to control the plants with unpredictable conditions.

INNOSAT ATTITUDE CONTROL SYSTEM BASED ON ADAPTIVE NEURO-CONTROLLER

The current research focuses on the designing of an intelligent controller for the Attitude Control System (ACS) of the Innovative Satellite (InnoSAT). The InnoSAT mission is to demonstrate local innovative space technology amongst the institutions of higher learning in the space sector. In this study, an Adaptive Neuro-controller (ANC) based on the Hybrid Multi Layered Perceptron (HMLP) network has been developed. The Model Reference Adaptive Control (MRAC) system is used as a control scheme to control a time varying systems where the performance specifications are given in terms of a reference model. The Weighted Recursive Least Square (WRLS) algorithm will adjust the controller parameters to minimize error between the plant output and the model reference output. The objective of this paper is to analyse the time response and the tracking performance of the ANC based on the HMLP network and the ANC based on the standard MLP network for controlling an InnoSAT attitude. These controllers have been tested using an InnoSAT model with some variations in operating conditions such as varying gain, measurement noise and disturbance torques. The simulation results indicated that the the ANC based on the HMLP network is adequate to control satellite attitude and give better results than the ANC based on the MLP network.

Efficient Recursive Estimators for a Linear, Time-Varying Gaussian Model with General Constraints

The adaptive estimation of a time-varying parameter vector in a linear Gaussian model is considered where we a priori know that the parameter vector belongs to a known arbitrary subset. We consider a family of efficient recursive estimators for this problem: the recursive constrained maximum likelihood (ML) estimator, the recursive affine minimax, and the recursive minimum mean square error (MMSE) estimator. We show that all three estimators can be substantially simplified by using the recursive weighted least squares (RWLS) algorithm in a first step as the RWLS computes the sufficient statistic for this estimation problem. The recursive constrained ML needs to solve an optimization problem in the second step for the case that the RWLS solution does not fulfill the constraint. In case of affine minimax, we have to solve an optimization problem and to perform an affine transform. The MMSE estimator needs to calculate the mean of a truncated Gaussian density in the second step which is done by Monte Carlo integration. A simple rejection scheme is used to take general constraints for the parameter vector into account. An example shows the superior performance of our proposed estimators in comparison to many other estimators.

Adaptive predictive functional control based on Takagi-Sugeno model and its application to pH process

In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem, an adaptive fuzzy predictive functional control (AFPFC) scheme for multivariable nonlinear systems was proposed. Firstly, multivariable nonlinear systems were described based on Takagi-Sugeno (T-S) fuzzy models; assuming that the antecedent parameters of T-S models were kept, the consequent parameters were identified on-line by using the weighted recursive least square (WRLS) method. Secondly, the identified T-S models were linearized to be time-varying state space model at each sampling instant. Finally, by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established. The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015; the tracking ability of the proposed AFPFC is superior to that of non-AFPFC (NAFPFC) for pH process without disturbances, the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC; when the process parameters of AFPFC vary with time the integrated absolute error (IAE) performance index still retains to be less than 200 compared with that of NAFPFC.

Modelling for the effective control of the electric flow heaters – Simulation validation

This paper suggests the possibility of improving the performance of the control system for electric flow heaters by applying the balance-based adaptive control (B-BAC) methodology, in which the synthesis of the control law is always preceded by the nonstationary balance-based modelling according to the general but also strictly defined rules. The resulting simplified model of a heater is derived assuming a large uncertainty on the process nonlinearities and it has the form of the first-order dynamic equation with the only one time-varying parameter that represents the unknown nonlinearities and modelling inaccuracies. The value of this parameter is unknown so we suggest its on-line estimation by the weighted recursive least-squares (WRLS) method. The modelling accuracy is investigated by the simulation in the application to the example nonlinear electric flow heater. It is also shown how to derive the B-BAController on the basis of the suggested model. The generality of the simplified model ensures that the B-BAC methodology can be applied to control a wide variety of electric flow heaters and its application results in more effective control system, which is also verified by simulation in the comparison to the conventional PI controller.