Forthcoming articles

International Journal of Modelling, Identification and Control

International Journal of Modelling, Identification and Control (IJMIC)

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International Journal of Modelling, Identification and Control (44 papers in press)

Regular Issues

  • Designing Route Guidance Strategy with Travellers Stochastic Compliance: A Bi-level Optimal Control Procedure
    by Wei-li Sun, Ling-long Hu, Ping Li, Hui Wang 
    Keywords: .

  • Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems   Order a copy of this article
    by Qinghai Li, Ye Lin, Rui-Chang Lin 
    Abstract: In this paper, the self-constructing recurrent fuzzy neural network (SCRFNN) is applied for nonlinear dynamical system identification (NDSI). The SCRFNN is a novel fuzzy neural network (FNN) by adding a recurrent path in each node of the hidden layer of self-constructing fuzzy neural network, which contains two learning phases. Specifically, the structure learning is based on partition of the input space and the parameter learning is based on the supervised gradient descent method using a delta adaptation law. This simple and efficient FNN can decrease the minimum firing strength in each learning cycle and the number of hidden neurons, and is able to generate a FNN with high accuracy and compact structure compared with several other neural networks. The performance of SCRFNN in NDSI is further verified in simulation.
    Keywords: self-constructing recurrent fuzzy neural network; nonlinear dynamic system identification; supervised gradient descent method.

  • Advanced control of three-phase battery electric vehicle charger with V2X technology   Order a copy of this article
    by Aziz Rachid, Hassan El Fadil, Abdellah Lassioui, Fouad Giri 
    Abstract: The bidirectional electric vehicle (EV) charging, so-called vehicle-to-everything (V2X), has a double interest: economic and ecological. It promotes low carbon and cheap electricity because its readily available. To ensure this functionality, electric vehicles use bidirectional chargers with single- or three-phase topologies. One of the main features of three-phase structures is the capability to avoid the problem of oscillating energy between the single-phase power grid and the dc bus. In this paper, the control of bidirectional three-phase battery electric vehicle charger with vehicle-to-grid functionality is addressed. The charger structure is composed of two power converters: a bidirectional three-phase ac-dc power converter and a bidirectional dc-dc power converter associated with an EV battery. The principal control objectives are the following: (i) estimation of the battery state of charge; (ii) unity power factor during the grid-to-vehicle operating mode; (iii) adjusting the reactive power injected into the power grid during vehicle-to-grid operating mode; (iv) dc-bus voltage regulation; and (v) ensuring and safeguarding the battery charging and discharging process. To this end and based on the system modelling into dq coordinates, a nonlinear backstepping controller is designed. The fact is that the battery state of charge is not accessible to measurement. Hence, a partial nonlinear observer is designed to estimate all state variables on the battery-side. The performances of the proposed output feedback controller are highlighted using theoretical analysis and numerical simulations, which clearly illustrate that all control objectives are achieved.
    Keywords: bidirectional three-phase ac-dc converter; bidirectional half-bridge dc-dc converter; BEV charger; reactive power compensation; nonlinear output feedback control; nonlinear observer; V2X charger.

  • Adaptive neuro-fuzzy system based maximum power point tracking for stand-alone photovoltaic system   Order a copy of this article
    by Ahmad Azar, Ali Malek, Toufik Bakir, Arezki Fekik, Ahmad Taher Azar, Khaled Mohamad Almustafa, Dallila Hocine, El-Bay Bourennane 
    Abstract: The Maximum Power Point Tracker (MPPT) plays a very important role to extract the maximum power of the photovoltaic (PV) system by ensuring its optimal production under sunshine and temperature variations. This study presents an algorithm-based MPPT named an Adaptive Neuro Fuzzy Inference System (ANFIS) which is built with the combination of the Artificial Neural Network (ANN) and the Fuzzy Logic Controller (FLC). The efficiency of the ANFIS algorithm is tested under Matlab/Simulink and compared with the fixed step conventional Perturb and Observe (P&O) and the gradient descent techniques under temperature and irradiance change. The obtained results showed a significant improvement in performances of the PV system using the ANFIS-MPPT technique, which provides also faster convergence and stability in the steady state, fewer oscillations around the MPP, and higher efficiency to track the maximum power from the PV system compared with other techniques under different operating conditions.
    Keywords: photovoltaic system; perturb and observe; maximum power point tracking; gradient descent; adaptive neuro fuzzy inference system; ANFIS.

  • A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation   Order a copy of this article
    by Sundarapandian Vaidyanathan, Irene M. Moroz, Aceng Sambas 
    Abstract: A new 4-D dynamical hyperjerk system with hyperchaos is reported in this work. The proposed nonlinear mechanical system with hyperchaos has two saddle-focus rest points exhibiting Hopf bifurcations. A detailed bifurcation analysis of the new hyperjerk plant with theory and simulations is discussed. As a control application, an integral sliding mode controller has been designed for the global hyperchaos synchronisation of the new hyperjerk system with itself. Finally, a circuit model using MultiSim of the new hyperjerk system with hyperchaos is designed for practical implementation.
    Keywords: hyperchaos; hyperjerk; sliding mode control; synchronisation; circuit design.

  • Prediction model based on XGBoost for mechanical properties of steel materials   Order a copy of this article
    by Jinxiang Chen, Feng Zhao, Yanguang Sun, Lin Zhang, Yilan Yin 
    Abstract: At present, the existing existing methods for designing, preparing and testing metal materials are mainly the 'local sample experimental test' method, which has insufficient accuracy, versatility and economy, long development cycle, insufficient knowledge acquisition, and no Lenovo's deduction and self-learning capabilities and other shortcomings. Aiming at these shortcomings, based on the existing steel mechanical performance prediction methods, this paper proposes a prediction model based on XGBoost algorithm based on big data analysis and machine learning methods. The model takes the prediction of mechanical properties of hot-rolled steel as the research background. The field production data of 17710 groups of a steel plant is taken as the sample data set, 90% of which is used as training sample and 10% of the data is used as test sample. Training and evaluation have yielded fairly good prediction accuracy. The results show that the prediction accuracy (R2 score) of the model against tensile strength, yield strength and elongation is 0.99895, 0.99576, 0.96260, respectively, which are superior to the prediction accuracy of BP neural network model. Basically, it can be concluded that this prediction model can predict the mechanical properties of steel more accurately.
    Keywords: intelligent prediction; XGBoost; machine learning; metal materials design; mechanical properties.

  • Quasi-bilinear modelling and control of directional drilling   Order a copy of this article
    by Isonguyo Inyang, James Whidborne 
    Abstract: A Quasi-Bilinear Proportional-plus-Integral (QBPI) controller is proposed for the attitude control of directional drilling tools for the oil and gas industry; and it is designed based on the proposed quasi-bilinear model of the directional drilling tool. The quasi-bilinear model accurately depicts the nonlinear characteristics of the directional drilling tool to a greater extent than the existing linear model, thus extends the scope of appropriate performance. The proposed QBPI control system is an LTI system and it is shown to be exponentially stable. The proposed QBPI controller outstandingly diminishes the deleterious impact of disturbances and measurement delay regarding to performance and stability of the directional drilling tool, and it yields invariant azimuth responses. Drilling cycle scheme which captures the drilling cycle and toolface actuator dynamics of the directional drilling tool, is developed. The servo-velocity and servo-position loops of the toolface servo-control architecture are proven to be robustly stable using Kharitonov's theorem.
    Keywords: directional drilling; time delay; disturbances; attitude control; quasi-bilinear; drilling cycle.

  • A new switching table based neural network for direct power control of three-phase PWM-rectifier   Order a copy of this article
    by Arezki Fekik, Hakim Denoun, Mustapha Zaouia, Mohamed Lamine Hamida, Sundarapandian Vaidyanathan 
    Abstract: Direct power control (DPC) is one of the newest techniques to control the pulse width modulation converter without network voltage sensors. This control technique is built on the idea of direct torque control (DTC) for an induction motor, which is applied to eliminate the harmonic of the line current and to compensate the reactive power. The principle of this control is based on instant active and reactive power loops. This article proposes an intelligent control approach to improve this control technique, such as artificial neural network (ANN), applied to the switching table. The comparison with conventional DPC shows that the use of DPC-ANN ensures smooth control of active and reactive power in all sectors and reduces current ripple. Finally, the developed DPC was tested by simulation. The results proved the excellent performance of the proposed DPC scheme in comparison with the conventional DPC.
    Keywords: artificial neural network; direct power control; instantaneous active and reactive power; pulse width modulation; switching table; unity power factor.

  • Prediction model with optimal matching parameters for a dynamic track stabiliser during railway maintenance   Order a copy of this article
    by Bo Yan, Bin Hu, Yayu Huang 
    Abstract: Nowadays, high-speed and heavy duty trains make ballasted track extremely busy, and thus it is necessary to solve the conflict between the traffic density and the maintenance workload. However, since the mechanical properties of discrete ballast bed are complex, there is a lack of in-depth investigation into the working performance of large-scale railroad maintenance machinery. In this paper, we take the WD-320 dynamic track stabiliser as the research object, to study the effect of operation parameters on the quality state of the ballast bed. Based on the field test data, a prediction model for optimal matching of operation parameters has been constructed, which can be used to estimate, compare and determine the optimal operation parameter combination for the operation process. By operating according to the optimal operation parameter combination, the optimum quality state of the ballast bed can be quickly reached, to solve the conflict between the traffic density and the necessary maintenance window.
    Keywords: dynamic track stabiliser; sleeper lateral resistance; operation parameters; optimal matching; prediction model.

  • Actuator fault diagnosis for interconnected system via invertibility   Order a copy of this article
    by Mei Zhang, Ze-tao Li, Qin-mu Wu, Boutaieb Dahhou, Michel Cabassud 
    Abstract: This paper deals with the problem of actuator fault diagnosis for a class of interconnected invertible nonlinear systems. For that, the actuator is viewed as an independent dynamic subsystem in series with the plant dynamic subsystem, thus forming an interconnected system. The invertibility of the interconnected system in both normal and fault mode is investigated. An interconnected observer is proposed to monitor the performance of the interconnected system and provide fault information of the actuator subsystem. Then a local fault filtering algorithm is triggered to identify the root faulty parameter causing the detected actuator fault. According to the real situation of the industry, it is assumed that the output of the actuator is not available for measurement and should be reconstructed by the global output of the interconnected system. A method capable of supervising the actuator subsystem at both local and global levels is provided.
    Keywords: interconnected system; actuator fault diagnosis; fault distinguishability; invertibility; root faulty parameter.

  • System identification of proportional solenoid valve dynamics   Order a copy of this article
    by Bakir Hajdarevic, Jacob Herrmann, Andrea Da Cruz, David Kaczka 
    Abstract: As devices that convert electrical signals into mechanical forces and motions, proportional solenoid (PSOL) valves allow for modulation of flow or pressure in many industrial processes and medical applications. PSOL valves may also be incorporated into pneumatic or hydraulic systems using feedback loops, to allow for precise control of pressure or flow. Accordingly, the design process of any physical system using a PSOL mandates complete and accurate characterisation of its linearity and dynamic response. In this paper, we present a system identification technique for the characterisation of the linearity and dynamic response of a PSOL valve and its corresponding electronic control unit (ECU in the frequency-domain, using band-limited white noise as well as pseudo random non-sum non-difference (NSND) signals. The NSND waveforms consist of mutually prime frequencies over ranges from 0.195 to 37.4 Hz, to mitigate the effects of nonlinear distortions on the estimated linear system response. The parameters of several transfer function models, with varying numbers of poles and zeros, were simultaneously estimated from the voltage-flow frequency response of the system using a nonlinear gradient descent technique. The resulting candidate transfer function models were then assessed using the mean squared residual criterion (MSR) and the corrected Akaike Information Criterion (AICc). The MSR yielded a best fit transfer function consisting of ten poles and nine zeros, while the AICc yielded a simpler transfer function consisting of five poles and three zeros. Uncertainty analysis using a Monte Carlo simulation demonstrated fragile stability for the MSR-selected model with respect to varying parameter values within estimated uncertainties, yet a robust stability for the AICc-selected model. We conclude that our system identification technique for estimating linear transfer functions of ECU-PSOL systems will be useful for robust modelling, simulation, and design of pneumatic or hydraulic processes and applications.
    Keywords: proportional solenoid valve; mean squared residuals; Akaike information criterion; system identification; transfer functions; model optimisation; pneumatic systems.

  • A real-time power-split strategy for a hybrid marine power plant using MPC   Order a copy of this article
    by Nikolaos Planakis, George Papalambrou, Nikolaos Kyrtatos 
    Abstract: In this work, the problem of energy management strategies in hybrid diesel-electric marine propulsion systems is investigated with the implementation of Model Predictive Control (MPC). The system behaviour is described by models based on system identification from experimental data. These models are used for the design of predictive controllers. The controllers are designed to tackle with physical and operating constraints of the hybrid system. Different MPC designs are considered, in order to evaluate the capabilities of the proposed control concept. The controllers were successfully tested at the test bed of the laboratory, by evaluating diverse strategies for disturbance rejection, system stability, and operation of the plant within the operators desirable limits.
    Keywords: predictive control; hybrid marine propulsion; diesel-electric; data-based modelling; real-time control; power-split control.

  • Oxygen therapy in chronic obstructive pulmonary disease: insight from convex optimisation   Order a copy of this article
    by Tanmay Pal, Pranab Kumar Dutta, Srinivasu Maka 
    Abstract: Application of additional oxygen for managing acute exacerbation of Chronic Obstructive Pulmonary Disease (COPD) has an associated risk of oxygen toxicity. The aim of this work is to determine the appropriate level of oxygen for managing this condition using a mathematical model. In this approach, a noted respiratory regulation model is modified by impaired diffusion, dead space and variable blood flow to simulate COPD condition. This condition is manifested as variation of the equilibrium point of the model. As variation of these quantities happens over a long time, the steady-state model obtained from the dynamic model is used for further analysis. Simulation of the model shows that alveolar oxygen partial pressure reduces to 67.37 mmHg in COPD condition from 96.6 mmHg in normal condition. Similarly, alveolar carbon dioxide partial pressure increases to 54.73 mmHg in COPD condition from 40.03 mmHg in normal condition. Consequently, minute ventilation become 10.85 L/min in COPD condition, which is 97.63% higher than normal condition. Using the model, it is established that higher inspired oxygen increases alveolar oxygen, as well as alveolar carbon dioxide. It is also shown that higher inspired oxygen increases oxygen saturation and lowers the mismatch of ventilation-perfusion ratio. Using a quadratic combination of alveolar oxygen and carbon dioxide pressure, an objective function is proposed to calculate the optimal level of inspired oxygen, which is 186.84 mmHg. Results obtained from this analysis methodology are in agreement with clinical data.
    Keywords: mathematical model; respiratory regulation; COPD; oxygen saturation; ventilation-Perfusion ratio; convex optimisation; oxygen therapy.

  • Neumann boundary geometric control of a fractional diffusion process   Order a copy of this article
    by Ahmed Maidi, Jean-Pierre Corriou 
    Abstract: In this paper, a boundary controller is developed for the fractional diffusion equation in the framework of geometric control. The case of Neumann actuation with a spatial weighted average output is addressed. This non-collocated configuration is characterised by an infinite characteristic index. To overcome this difficulty, the notion of the extended operator is exploited to derive an equivalent distributed control problem. The equivalent model, obtained by the Laplace transform in space domain, is used both for controller design and stability analysis of the resulting closed-loop. Thus, based on the notion of the characteristic index, a state feedback control that enforces an output tracking is designed. Then, the exponential stability of the closed-loop is demonstrated based on the semigroup theory. The effectiveness of the developed controller is shown, through numerical simulation, in the case of a heated aluminium rod that exhibits an anomalous diffusion phenomenon.
    Keywords: distributed parameter system; spatial fractional partial differential equation; fractional diffusion equation; Neumann actuation; geometric control; characteristic index.

  • A review on data-driven approaches for industrial process modelling   Order a copy of this article
    by Wei Guo, Tianhong Pan, Zhengming Li, Guoquan Li 
    Abstract: Data-driven techniques in industrial processes have been continually improved during the past decades. However, there are many challenging issues in this field when the collected data presents different characteristics. In order to sketch the principle of different modelling methods under various working conditions, data-driven modelling methods from the perspectives of data structures and model structures are reviewed in this paper. Firstly, the data collection and preprocessing procedure are inspected. Then, popular methods from linear (including the multivariate linear regression, latent variable projection, etc.) and nonlinear methods (including artificial intelligence, Gaussian process regression, local model, etc.) are discussed. Finally, the model calibration strategies (including offset-based method, recursive method, moving window method) are also reviewed. The major purpose is to support the industrial process modelling for technical users by providing a set of data-driven methods.
    Keywords: data-driven modelling; industrial process; machine learning.

  • Robust steering control for mobile-rack vehicles   Order a copy of this article
    by Boc Minh Hung, Sam-Sang You, Sang-Do Lee, Hwan-Seong Kim 
    Abstract: To achieve precise navigation of a mobile rack vehicle (MRV), the lateral control system should have good adaptability to the perturbations of vehicle parameters under measurement noises and exogenous disturbances. The MRV for smart warehouse considered in this paper is a four-wheeled vehicle with autonomous motion. Vehicle lateral dynamics are affected by the variations of vehicle mass with loading, speed, and the cornering stiffness. Therefore, the active control system must guarantee stability and performance against uncertainties, over a wide range of parameter changes. This paper aims to develop a robust controller that stabilises the perturbed dynamic model while guaranteeing a specified performance. Moreover, the reduced-order controller developed has the ability to attenuate noises and disturbances in a cold environment without rail track. Finally, the dynamic performance of the robust controller is evaluated over a wide range of parameter variations while achieving positioning precision against various uncertainties.
    Keywords: mobile-rack vehicle; smart warehouse; vehicle dynamics; uncertainty; robust control.

  • Observer-based output feedback integral terminal sliding mode control for nonlinear systems: multi-model approach   Order a copy of this article
    by Kaïs Hfaïedh, Karim Dahech, Tarak Damak 
    Abstract: In this paper we propose an observer-based output feedback integral terminal sliding mode control for nonlinear systems. The state estimation problem is treated by using the Utkin observer under a multi-model structure. The design of the control law is based on the sliding mode theory. In fact, we propose two types of integral terminal sliding mode, which are sign integral and fraction integral. The objective of such observer-based control algorithms is to estimate the states of the system and to stabilise the output tracking error to zero. The stability proof is demonstrated by the Lyapunov approach. A numerical example of denitrification process is presented in order to validate the performances of the proposed control laws.
    Keywords: nonlinear systems; multi-model approach; integral terminal sliding mode control; state observer; output feedback control.

  • Second-order terminal sliding mode control of five-phase IPMSM with super-twisting observer under demagnetisation fault   Order a copy of this article
    by Yaser Zafari, Sajjad Shoja Mahidabad 
    Abstract: This paper deals with demagnetisation fault detection and toleration for five-phase interior permanent magnet synchronous motors through second-order sliding mode observer/controller. At the beginning, a super-twisting flux-linkage observer is proposed to cope with the chattering problem. This observer estimates the flux-linkage through the stator estimated currents. Further, a novel second-order terminal sliding mode controller is developed for mechanical speed control in the presence of demagnetisation fault. Finally, comparative simulations validate the feasibility and effectiveness of the proposed observer/controller for a five-phase interior permanent magnet synchronous motor.
    Keywords: five-phase IPMSM; super-twisting observer; demagnetisation fault; second-order sliding mode controller.

  • Extended Kalman filter steady gain scheduling using k-means clustering   Order a copy of this article
    by Jun Chen 
    Abstract: This paper studies the gain scheduling problem for the extended Kalman Filter (EKF). To save throughput, the steady gain is usually used for the Kalman filter, which can be obtained by solving a algebraic Riccati equation. In the context of EKF, the underlying model is nonlinear, and hence there is no universal steady state gain. In this paper, we propose a methodology to schedule gain for EKF. The idea is to offline linearise the nonlinear model at various operating points, and, for each of the linearised systems, to compute the steady state gain corresponding to the conventional Kalman filter. The operating space of the nonlinear model is then divided into multiple zones, through the k-means clustering algorithm, so that within zone, the steady state gains are close to each other. For real time filtering, the centroid of each zone is used as gain for the correction step, instead of computing the time-varying gain online, hence saving throughput. We apply the proposed methodology in a two-state nonlinear system, and show the throughput saving without impacting filtering performance.
    Keywords: extended Kalman filter; steady gain; k-means; gain scheduling.

  • Active and reactive power control of a dual stator induction generator for wind energy conversion   Order a copy of this article
    by Fatma Lounas 
    Abstract: This paper deals with the active and reactive power control of a Dual Stator Induction Generator (DSIG) based Wind Energy Conversion System (WECS). The DSIG is used instead of a Doubly Fed Induction Generator (DFIG) to avoid the main drawback of the slip-ring system. The DSIG has two three-phase windings in the stator; one is used as a Power Winding (PW) and the other as a Control Winding (CW). The aim of this article is to establish the relationships between the powers delivered from the power winding and the voltages applied at the control winding terminals, to build a simplified diagram of the DSIG which permits to synthesise easily PI regulators. The DSIG-based WECS is modelled and implemented under the Matlab-Simulink environment and a set of simulation tests for both hypo-synchronous and hyper-synchronous operating modes are performed to prove the feasibility and the validity of the developed control laws.
    Keywords: wind energy; MPPT; dual stator induction machine; doubly fed induction machine active power; reactive power; direct control; field oriented control; PI controller.

  • Multi-source coordinated scheduling strategy of wind power-PV-CSP considering high energy load   Order a copy of this article
    by Xiaoying Zhang, Wei Xiong, Kun Wang, Xiaolan Wang, Wei Chen 
    Abstract: With the rapid development of new energy power generation, there are many new challenges occurred in power system scheduling. This paper assesses wind power, photovoltaic (PV), and concentrating solar power (CSP) as a new energy hybrid generation mode, and proposes to use high-energy load as a schedulable resource to participate in the optimal scheduling strategy of new energy hybrid power generation. The optimal scheduling mode considers the randomness of wind power and PV, the controllability of CSP plant and the adjustability of high energy load. The multi-objective optimisation scheduling models are constructed with the minimum power output fluctuation of hybrid system and the maximum economic benefits of grid-connected. The multi-objective differential evolution algorithm based on non-dominated sorting (NSMODE) is used to optimise the solution; the high energy load is introduced to solve the problem of abandoned wind and light caused by the integration of new energy hybrid systems. Finally, the simulation analysis of the scheduling mode, optimisation algorithm and abandoned wind and light is carried out. The simulation results show that the participation of CSP plant and the participation of high energy load make the power fluctuation of the hybrid power generation system decrease and the economic benefits of grid-connected increases, the amount of abandoned wind and light is significantly reduced, and the use rate of new energy is improved.
    Keywords: new energy hybrid power generation; multi-objective optimization; high energy load; NSMODE; optimal scheduling.

  • A hydraulic system based on the servo valve with dual input of machine and electricity   Order a copy of this article
    by Hao Yan, Bowen Jiang, Zheqing Zuo 
    Abstract: The hydraulic system based on the servo valve with dual input of machine and electricity consists of the valve control system and the mechanical feedback device, which has a higher reliability. When the power of the system is cut off, the system can continue working until the actuator returns to the original position. This system is widely used in some occasions with higher reliability requirements. In this paper, the mathematical model of the system is established, where a certain transmission ratio between the actuator and the mechanical feedback is considered. Meanwhile, the key system parameters are analysed in order to reflect their influences on the system performance. It is obtained that the uncertainties of key parameters of the hydraulic amplifier have a certain impact on the dynamic and static characteristics of the system.
    Keywords: servo valve; dual input; mechanical feedback; dynamic and static characteristics.

  • A divide-and-conquer based improved genetic algorithm for network selection in a heterogeneous wireless network   Order a copy of this article
    by Hui Sun, Chuang Yang, Rui Wang, Sabir Ghauri 
    Abstract: Developing and using wireless networks is a trend to serve passengers in aircraft cabins. Cognitive radio technology can be used in the aircraft cabin wireless environment to solve the spectrum resource scarcity problem. Heterogeneous network access issue should be noticeable in cognitive radio wireless networks. In this paper, a improved genetic algorithm (GA) based on the divide-and-conquer is proposed to handle this problem. The proposed approach is compared with original GA, Particle Swarm Optimisation (PSO) algorithm and Tabu Search (TS) algorithm. The simulation results prove that the proposed method is valid.
    Keywords: aircraft cabin; wireless network; heterogeneous; divide-and-conquer.

  • Modelling and sliding mode control of a wireless power transfer system for a battery electric vehicle charger   Order a copy of this article
    by Abdellah Lasioui, Hassan El Fadil, Aziz Rachid, Fatima-Zahra Belhaj, Fouad Giri 
    Abstract: In this paper, a unidirectional wireless power transfer (WPT) system for a battery electric vehicle (BEV) charger is addressed. Firstly, a detailed analysis is given focusing on the following points: i) phase shift control technique, ii) reactive power compensation topologies, and iii) total harmonic distortion analysis. Secondly, a mathematical model is established for the studied system and its stability is discussed. It was found that the system presents an unstable behaviour when the voltage across the load is chosen as the system output. This nom minimum phase feature is dealt with using an indirect control strategy. Thirdly, based on the derived mathematical model, a nonlinear controller using the sliding mode control technique is developed. The control objectives are twofold: i) tight regulation of the output load voltage, and ii) asymptotic stability of the closed loop system. It is shown using theoretical analysis and simulation that the proposed controller meets all objectives.
    Keywords: electric vehicle; wireless power transfer; battery charger; phase shift control; sliding mode control.

  • Kalman filtering linear quadratic regulator for artificial pancreas in type-I diabetes patient   Order a copy of this article
    by Akshaya Kumar Patra, Anuja Nanda 
    Abstract: This manuscript presents a simulation model of the glucose metabolism process and design of a Kalman Filtering Linear Quadratic Regulator (KFLQR) to control the Blood Glucose (BG) concentration in Type-I Diabetes Mellitus (TIDM) patients. For designing of the KFLQR, a 9th order state-space model of the TIDM patient with Micro-Insulin Dispenser (MID) is considered. In this control strategy, the basic Linear Quadratic Regulator (LQR) is re-formulated with a state estimator based on the Kalman filtering approach for enhancement of control performance. The KFLQR is evaluated and compared with PID, LQR and pre-published control techniques suggested by different authors. The simulations are carried out through MATLAB/SIMULINK environment and the results indicate the better performance of the suggested algorithm to control the BG concentration within the normoglycaemic range in terms of accuracy, stability, quick damping and robustness.
    Keywords: type-I diabetes; MID; LQR; state estimator; KFLQR.

  • Modeling and multi loop Selective control of Industrial Coal Pulverizer
    by Vini Dadiala, Jignesh Patel, Jayesh Barve 
    Abstract: Coal based power generation continues to be the key player in power generation. However, the efficiency of a thermal plant lies in the range of 30-40%, a sizably less value. Pulverization of coal is an important, but an energy intensive process. Efficient control of the pulverizer can improve the efficiency of the overall plant. This paper discusses various computational results and their analysis for the case study of coal pulverizer carried out at a thermal power plant in Gujarat. It proposes a more accurate mathematical model for a pulverizer with static classifier and a 3PI (Proportional Integral) with selective control for improved performance. The proposed model is validated with real plant data from 150MW ESSAR thermal power plant, Gujarat, India. It is observed that the proposed model captures the system dynamics more effectively than the models existing in the literature. A 3PI with selective control strategy is proposed where the primary air flow is selected from the mill differential pressure loop and Air-fuel ratio loop depending on operating conditions. It is observed that the new model with proposed control has better load disturbance rejection properties and is found to be more robust to parametric variations as compared to the control strategy employed in the industry wherein the mill differential pressure is controlled manually.
    Keywords: Coal pulverizer, static classifier, coal mill modelling, parametric analysis, 3PI with selective control.

  • XGBoost-PCA-BPNN Prediction Model and Its Application on Predicting the Effectiveness of Non-surgical Periodontal Treatment
    by Jinxiang Chen, Dong Shi, Jinqi Fan, Huanxin Meng, Jian Jiao, Ruifang Lu 
    Abstract: An XGBoost-PCA-BPNN predication model is presented to classify and predict the objects based on the big data set with uncertain and coupling multi-dimensional characteristics, because the existing anyone single machine learning model cannot obtain the high prediction performances when it is applied to deal with the above problem. The XGBoost-PCA-BPNN model is applied to predict the effectiveness of non-surgical periodontal therapy (NSPT) for Chinese population with chronic periodontitis and the high prediction accuracy is obtained in this paper.\r\nFirstly, the advantages and the disadvantages of the existing machine learning approaches are analyzed. The XGBoost can handle\r\neffectively the coupling problems among multi-dimensional characteristics in big data sets. The PCA can reduce the dimension of inputs. BPNN can improve the accuracy of calculation, but the overfitting problems would be happened when it is used to handle the objects with multi-dimensional characteristics. The XGBoost-PCA-BPNN predication model is presented by combining XGBoost, PCA with BPNN in order to predict the objects with uncertain and coupling multi-dimensional characteristics.\r\nThe model is verified by applying it to predict the effectiveness of NSTP for the big data set with 45,000 clinical chronic periodontitis sites. 30,000 sites are used as training samples and 15,000 sites are regard as testing data. Prediction results show that the Xgboost-PCA-BPNN model has higher predication accuracy, faster convergence speed and better stability than Logistic regression, Xgboost, Xgboost-Logistic regression. The $R^2$-score of the Xgboost-PCA-BPNN model is 0.943. In addition, it can be seen that the effectiveness of NSTP are mainly influenced by PD, BI, sites,age.
    Keywords: Classification prediction, XGBoost, BPNN, non-surgical periodontal treatment, big data analysis, chronic periodontitis, effectiveness

  • Decoding fNIRS based imagined movements associated with speed and force for a brain-computer interface
    by Xinglong Geng, Zehan Li 
    Abstract: Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive technology applied in brain-computer interface (BCI) system. This study investigates fNIRS based imagined hand-clenching tasks, indicating that the combinations of speed and force have distinct patterns which can be decoded to develop a BCI system. Twelve healthy participants are instructed to perform imagined left or right hand-clenching tasks; oxy-hemoglobin (HbO2) and deoxy-hemoglobin (Hb) concentrations were acquired from motor cortex using a multi-channel fNIRS system. Feature selection method based on mutual information is employed to select the optimal features for classification, and support vector machine (SVM) is used as a classifier resulting in average accuracies of 84.9% and 86.1% for classifying left and right imagined movements, respectively. Compared with traditional fNIRS-BCI system, this study provides a possibility to generate a new control pattern for brain-controlled robots, e.g. speed or force control. There is also a potential application to combine fNIRS-BCI system with the exoskeleton to produce a complex rehabilitation strategy.
    Keywords: Brain-Computer Interface (BCI); Hand Clenching; Support Vector Machine (SVM)

  • Linear Discrete-time Modeling and Hybrid Fault-tolerant Controller Design for Complex Systems With The Components And Sensor Faults
    by Chunxiao He, Xisheng Li 
    Abstract: A linear discrete-time model with the additive fault is constructed for the systems with the components faults and sensor faults. A hybrid controller including the state feedback controller, the $H_\\infty$ filter and the fault-tolerant controller with $H_\\infty$ performance $\\gamma$ is designed in this paper. By using the Lyapunov function and linear matrix\r\ninequalities (LMIs) approach, the theorem solving the designed controller gains is derived. The effectiveness of the presented approaches is verified by using them to control the Vander Pol circuit system with the aging fault of components.\r\nSimulation results show that the designed controller can suppress the influence caused by components and sensor faults and stabilize the systems under meeting $H_\\infty$ index.
    Keywords: Fault-tolerant controller, modeling, hybrid controller, $H_\\infty$ filter, additive faults, sensor faults, components

  • A survey of control strategies for grid connected wind energy conversion system based permanent magnet synchronous generator and fed by multi-level converters
    by Youssef Errami, Abdellatif Obbadi, Smail Sahnoun 
    Abstract: In this study, two control strategies for speed and power control of three-level neutral-point (3L-NPC) clamped back to- back converters in Wind Energy Conversion System (WECS) with Permanent Magnet Synchronous Generator (PMSG) are proposed. The system consists of Generator Side Converters (GSCs) and Grid Side Converter (GSC) which share a common DC-link capacitor. The proposed control laws combine Sliding Mode Control (SMC) and Vector Oriented Control (VOC) to maximize the generated power from Wind Turbine Generators (WTGs). Considering the variation of wind speed, the GSC injects the generated power into the AC network, regulates DC-link voltage. Also, it is employed to achieve unity power factor. The GSCs are employed to achieve Maximum Power Point Tracking (MPPT). To validate the proposed approaches, simulations are carried out with MATLAB/Simulink software. The simulation results demonstrate a good performance in various scenarios.
    Keywords: Wind Electrical System; PMSG;3L-NPC; MPPT; SMC; VOC; grid

  • Input-to-state Stability of Systems with Non-instantaneous Impulses
    by Cheng Liu , Zheng Fang, Jing Chen 
    Abstract: In this paper, we investigate the input-to-state stability of systems with non-instantaneous impulses. By using the Lyapunov function with indefinite derivative and the average dwell time condition, we get a sufficient condition for the input-to-state stability of systems with non-instantaneous impulses, then we give an example in the end to show the efficiency of the theoretic result obtained in this paper.
    Keywords: Impulsive systems; non-instantaneous impulses; input-to-state stability; average dwell time condition.

  • Global stability and optimal control of melioidosis transmission model with hygiene care and treatment
    by RATCHADA VIRIYAPONG, Sunisa Tavaen 
    Abstract: A compartmental deterministic mathematical model for melioidosis transmission is proposed. It involves human and animal population and bacteria. We present two main equilibrium points (disease-free and endemic) with the analysis of their local stability. The basic reproduction number and its sensitivity index to the parameters in the model are calculated. Lyapunov’s direct method is used to analyze the global stability of endemic equilibrium point. Further, by using Pontryagins minimum principle, the optimal control problem is constructed with two controls i.e. hygiene care and treatment controls for human population. Finally, the numerical simulations are established and our results show that a combination of both controls give more impact in reducing the number of infected human and bacteria than in reducing the number of infected animals. Because melioidosis prevalence is still increasing, more e?ort in sharing knowledge and controlling the spreading of this disease is still much required.
    Keywords: Melioidosis; Hygiene Care; Numerical Study; Optimal Control; Treatment; Lyapunov’s direct method; Pontryagins minimum principle.

  • Nonlinear controller for MPPT based photovoltaic system under variable atmospheric conditions
    by Fatima Ez-Zahra Lamzouri, El-Mahjoub Boufounas, Aumeur El Amrani 
    Abstract: This present paper depicts a robust controller design combining backstepping approach and sliding mode controller (BSMC) based maximum power point tracking (MPPT) for a photovoltaic (PV) system. The investigated PV system is based on a PV module as power source, a DC–DC boost converter and a resistive load. A modified conventional perturb and observe (P&O) algorithm based MPPT control is designed, which presents good performances under constant atmospheric conditions. However, the solar radiation and cell temperature variations present a major effect on the PV output power. Thus, the proposed BSMC controller can allow to the PV system operate around the estimated MPPT under variable atmospheric conditions. Furthermore, the Lyapunov theory is used in order to demonstrate the stability of the PV system with BSMC controller. Moreover, the investigated control approach effectiveness is exhibited by comparing the developed BSMC controller, conventional sliding mode controller (SMC) and modified P&O algorithm. For the proposed BSMC approach, the obtained results with simulation illustrate good efficiency in terms of transition response, tracking error and fast response to atmospheric conditions variation.
    Keywords: Photovoltaic system; maximum power point tracking; sliding mode control; backstepping approach; perturb and observe algorithm.

  • A coevolutionary quantum krill herd algorithm for solving multi-objective optimization problems
    by Zhe Liu, Shurong Li 
    Abstract: Multi-objective optimization (MOO) has always been a challenging problem that received considerable attention in practical engineering applications due to the multicriteria objectives. This paper presents a coevolutionary quantum krill herd algorithm (CQKH) as a novel numerical method for solving MOO. The CQKH is a quantum-inspired evolutionary algorithm which improves the krill herd algorithm (KH) based on quantum representation and quantum rotation gate. As a result, CQKH has a stronger robustness and the capability of finding the optimal or near optimal solution faster by fewer individuals. In addition, the CQKH adopts a coevolutionary technique named multiple populations for multiple objectives (MPMO) to obtain the whole Pareto optimal front. The computation results of CQKH on numerical tests with various characteristics demonstrate its effectiveness and superiority compared to some state-of-the-art algorithms.
    Keywords: Multi-objective optimization; Coevolutionary quantum krill herd algorithm; Multiple populations for multiple objectives; Quantum representation; Quantum rotation gate.

Special Issue on: ICMIC 2019 Mathematical Modelling and Advanced Control Approaches of Nonlinear Complex Dynamics

  • Estimation of inhalation exposure to metals among welders of a steel company using MEASE model: as a screening tool for estimates of occupational exposure   Order a copy of this article
    by Sara Karimi Zeverdegani, Younes Mehrifar, Masoud Rismanchian 
    Abstract: Estimation and assessment of substance exposure for metals is a tool to estimate inhalation exposures for metal substances. The aim of the present study was estimation of exposure to welding fumes using MEASE model, and also comparison of the estimated data with exposure levels by NIOSH 7300 in different welding processes. The metal fumes including Cu, Fe, Ca, Al, Mg, Mn, K and Na in the MIG, MAG and SMAW processes were measured according to NIOSH 7300. The occupational exposure estimation to the metal fumes was performed by MEASE model. There was fair agreement between measured and estimated values in terms of different metal fumes and welding processes(r = 0.131 to 0.933).A significant strong correlation was found between measured and estimated levels for Mg(r = 0.933;P = 0.001), Ca(r = 0.896; P = 0.001), K(r = 0.805; P = 0.001), Na(r = 0.716; P = 0.001), and Al (r = 0.756; P = 0.032). There was a significant strong correlation between measured and estimated values for SMAW(r = 0.708; P = 0.003) and MIG (r = 0.635; P = 0.036). The authors expect that the MEASE model cannot be wholly successfully applied for semiquantitative inhalation exposure assessment in occupational health surveys.
    Keywords: estimation; inhalation exposure; MEASE model ; metal fumes; welding processes.

  • Development of human lower extremity kinematic and dynamic models for exoskeleton robot-based physical therapy   Order a copy of this article
    by S.K. Hasan 
    Abstract: The World Health Organization reports that approximately one billion people are disabled in the world. Rehabilitation programs help promote functional recovery in disabled individuals. Exoskeleton robot-based physical therapy is an appealing solution for a large number of disabled people. Mechanical design, modelling, and control of exoskeleton robots require anthropometric data. A majority of anthropometrical data is not readily available from a single source. Furthermore, seven degrees of freedom human lower extremity kinematic and dynamic models are also not available. This paper presents dynamic modeling and simulation of the human lower extremity. The Lagrange energy method is used for developing a lower extremity dynamic model. The dynamic simulation utilizes a Computed torque controller. A Sliding mode controller is also developed for practical applications. The Sliding mode controller is a robust control scheme, which works efficiently in the presence of disturbances and parameter variations. Human lower extremity degrees of freedom, range of motion of various joints are integrated into the proposed model. Simulation results show the performance of the controller, joint torque, and power requirements for tracking a specified trajectory. The proposed model can be used as a reference to develop and verify a human lower extremity dynamic model. Since the human lower extremity exoskeleton robot should possess a similar dynamical behavior, the proposed model can easily produce the dynamic model of lower extremity exoskeleton robot by considering the masses, inertial properties and joint frictional forces of links in the exoskeleton robot. Because of its performance in the presence of simulated disturbances and parameter variations, it is seen that the sliding mode controller is an effective choice for controlling a real robot.
    Keywords: physiotherapy; exoskeleton robot; lower extremity anthropometric parameters; sliding mode controller; lower extremity kinematic and dynamic model.

  • Identification of a deterministic Wiener system based on input least squares algorithm and direct residual method   Order a copy of this article
    by Shaoxue Jing 
    Abstract: The Wiener system is a type of block-oriented system that consists of a linear model followed in series with a static nonlinear element. In this work, two novel identification methods are proposed to estimate the order and parameters of a class of Wiener system whose linear part is a finite impulse response function and whose nonlinear inverse function is a polynomial. First, a direct order identification method using the input-output data rather than an unknown intermediate variable is designed to estimate the order of the linear part. The method decreases the computational cost and improves the accuracy of order estimation, because it doesn't require calculating the intermediate variable. Second, an identification algorithm minimising the input prediction error is developed to obtain parameters of the Wiener system. Third, a numerical simulation and a case study verify the proposed algorithm. The proposed methods, with a little modification, can be applied to identify other block-oriented systems.
    Keywords: order estimation; parameter estimation; Wiener system; residual analysis.

  • Robust pole-placer power system stabilisers design via complex Kharitonovs theorem   Order a copy of this article
    by Mohamed Ayman, Mahmoud Soilman 
    Abstract: In this paper, synthesising robust three-parameters power system stabilisers (PSSs) having a common form of? (x?_1+x_2 s)/(1+x_3 s) is presented. Graphical characterisation of the set of stabilising PSSs is carried out using D-decomposition whereas the controller-parameter space is subdivided into root-invariant regions. The dynamic model of single-machine infinite-bus system (SMIB) is considered to accomplish the design. Rather than Hurwitz stability, D-decomposition is extended to consider D-stability, where D refers to a pre-specified damping cone in the open left half of the complex plane to enhance time-domain specifications. Pole clustering in the damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such a cone. Parametric uncertainties of the model imposed by continuous variation in load patterns is captured by an interval polynomial. As a result, computing the set of all robust D-stabilising PSSs calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by a complex version of Kharitonovs theorem. A less-conservative and computationally effective approach based on only two extreme plants is concluded from the geometry of the stability region in the controller parameter plane. Simulation results affirm the robust stability and performance of the proposed PSSs over wide range of operating points.
    Keywords: PSS design; robust control; D-decomposition; interval polynomial; Kharitonov’s theorem; complex polynomials.

  • Model-predictive-control complex-path tracking for self-driving cars   Order a copy of this article
    by Wael Farag 
    Abstract: In this paper, a comprehensive Model-Predictive-Control (MPC) controller that enables effective complex track manoeuvring for Self-Driving Cars (SDC) is proposed. The paper presents the full design details and the implementation stages of the proposed SDC-MPC. The controller receives several input signals, such as an accurate car position measurement from the localisation module of the SDC measured in global map coordinates, the instantaneous vehicle speed, and the reference trajectory from the path planner of the SDC. Then, the SDC-MPC generates a steering (angle) command to the SDC in addition to a throttle (speed/brake) command. The proposed cost function of the SDC-MPC (which is one of the main contributions of this paper) is very comprehensive and is composed of several terms. Each term has its own sub-objective that contributes to the overall optimization problem. The main goal is to find a solution that can satisfy the purposes of these terms according to their weights (contribution) in the combined objective (cost) function. Extensive simulation studies in complex tracks with many sharp turns have been carried out to evaluate the performance of the proposed controller at different speeds. The analysis shows that the proposed controller with its tuning technique outperforms the other classical ones like PID. The usefulness and the shortcomings of the proposed controller are also discussed in detail.
    Keywords: MPC control; self-driving car; autonomous driving; MPC tuning.

Special Issue on: Robotic Intelligent Control Systems

  • Backstepping controller design with a quadratic error for a double inverted pendulum   Order a copy of this article
    by Boutaina Elkinany, Mohammed Alfidi, Soukaina Krafes, Zakaria Chalh 
    Abstract: This study aims at presenting a conceptualisation of a double inverted pendulum system based on modelling, and controlling this model by applying only a single torque in the upper part instead of the lower part of the double inverted pendulum. Nonlinear dynamic equations were analysed using the Lagrangian dynamic formulation, and the graphical presentation of the system has been achieved through applying the bond graphs approach. The double inverted pendulum representation was incarnated using the 20-Sim software to build the system bond graphs in order to check on the motion. To achieve the system's stability, only one command was applied on the upper part. Most importantly, a control approach combining the backstepping method with the quadratic error was designed taking into consideration all nonlinearities that cannot be deleted. Indeed, the simulation results armed the effectiveness of the backstepping controller with the quadratic error and a good response of the system's flexibility was ensured in the sense that it can be adjusted from the initial position to the equilibrium position.
    Keywords: double inverted pendulum; backstepping controller; quadratic error; stability; Lyapunov.

  • A novel sliding mode composite control design for fast time performance of quadrotor UAV   Order a copy of this article
    by Sudhir Nadda 
    Abstract: The dynamical model of quadrotor unmanned aerial vehicle (UAV) is nonlinear, multivariable and unstable. Lots of control methods are available, but the existing controls are not sufficient to achieve stability and accuracy in shorter time. This study presents a composite control approach to perform the attitude and position tracking of a quadrotor UAV. The proposed control scheme has two steps. In the first step, the dynamical model is decomposed into two parts, i.e. a fully actuated subsystem and an underactuated subsystem. In the second step, the sliding mode control has been used to control the underactuated subsystem and terminal sliding mode control has been exploited to control the fully actuated subsystem. The terminal sliding mode control with nonlinear sliding surface for high accuracy tracking performance is applied to the fully actuated subsystem, and sliding mode control with linear sliding surface is applied to the underactuated subsystem. The application of terminal sliding mode provides the guarantee of finite time convergence. The stability of the system has been ensured by obtaining the condition on control parameter using Lyapunov criterion. The performance of the proposed control was evaluated and it has been found that there is substantive improvement over the performance of the conventional one.
    Keywords: quadrotor; terminal sliding mode control; sliding mode control; composite control.

  • Improving the performance of medical robotic system using H? loop shaping robust controller   Order a copy of this article
    by Shahad Sami Ali, Safanah Mudheher Raafat, Ayman AL-KHAZRAJI 
    Abstract: In order to solve the relevant and yet open problem of precise tracking, the current research synthesises a robust controller via H? loop shaping for a human swing lower limb system. The human walking is naturally difficult with particularly nonlinear dynamics. It is interpreted as pendulum links that stand for human thigh and shank. Actually, a reliable and efficient controller for a human swing leg robot system faces serious problems due to weight variations, modelling uncertainties and different disturbing effects. The current work takes into account these constraints through designing a robust controller based on loop-shaping framework. This provides an appropriate approach to compromise the robustness and precise tracking for a pre-specified variation of weight factors, and uncertainties in the dynamical models. In order to obtain the whole gesture of all muscles, two necessary control actions were developed and applied at the joints. Moreover, the paper demonstrates rigorously the robust stability and tracking. The obtained results from numerical examples confirm the effectiveness of the proposed controller as well as its remarkable simplicity.
    Keywords: robotic system; H? loop shaping; swing leg system; pendulum links; biped robot; robust control.

  • Fractal, chaos and neural networks in path generation of a mobile robot   Order a copy of this article
    by Salah Nasr, Kais Bouallegue, Hassen Mekki 
    Abstract: In this paper, we present different approaches using fractal, chaos and neural networks to generate the path of a mobile robot with obstacle avoidance. Firstly, the fractal process, which is inspired from Julia set, is applied to control the robot trajectory by designing fractal processes in cascade. This method increases the dynamic of robot trajectory with obstacle avoidance. Secondly, we believe that the edge of fractal approach is the chaotic system, so we use Lorenz chaotic attractor to control the same robot by combining the control parameter and the sine function in the second equation of the chaotic system. Thirdly, we use neural networks characterised by a variable structure model of neurons to control a robot. Numerical simulations are performed to verify the accuracy for each proposed approach.
    Keywords: mobile robot; chaos; fractal; neural networks; path planning; obstacle avoidance.

  • Hybrid ANFIS-ant colony based optimisation for UAV trajectory tracking control   Order a copy of this article
    by Boumediene Selma, Samira Chouraqui, Hassane Abouaïssa 
    Abstract: Development of Unmanned Aerial Vehicles (UAVs) has become one of the most important research areas in the field of autonomous aeronautical control. This paper proposes an optimal intelligent controller based on Adaptive-Network-based Fuzzy Inference System (ANFIS) and Ant Colony Optimisation (ACO) algorithm to govern the behaviour of a three degree of freedom quadrotor unmanned aerial vehicle. The quadrotor was chosen owing to its simple mechanical structure; nevertheless, these types of aircraft are highly nonlinear. Intelligent control such as fuzzy logic is a suitable choice for controlling nonlinear systems. The ANFIS controller is used to reproduce the desired trajectory of the quadrotor in a 2D vertical plane, and the ACO algorithm aims to facilitate convergence to the ANFIS optimal parameters in order to reduce learning errors and improve the quality of the controller. To evaluate the performance of the proposed ACO-tuned ANFIS controller, a comparison between the proposed ANFIS-ACO controller and other controllers, such as ANFIS only and Proportional-Integral-Derivative (PID) controllers, is illustrated using the same system. As expected, the hybrid ANFIS-ACO controller gives more satisfactory results than the other methods already developed in the same study.
    Keywords: unmanned aerial vehicle; optimal control; adaptive neuro-fuzzy inference system; ant colony algorithm.