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 (26 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
    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 decreases 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 network. 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.

  • A biotech measurement scheme and software application for the level determination of persons functional reserve based fuzzy logic rules   Order a copy of this article
    by Riad Taha Al-kasasbeh, Nikolay Korenevskiy, Adnan Mukattash, Altin Aikeeva, Dmitry Titov, Maksim Jurievich Ilyash 
    Abstract: The level of apersons functional reserve is determined by a number of different indicators, such as power imbalance of meridian structures, psycho-emotional tension, intellectual and physical exhaustion, parameters of pulse and arterial pressure at the impact of the dosed intellectual and physical activities on the basis of heterogeneous fuzzy model usage. The functional reserve helps to diagnose a lot of diseases. The theoretical results obtained in the form of fuzzy models are recommended in medical practice with cofficient of confidence at least 95%.
    Keywords: level of functional reserve; psycho-emotional pressure; intellectual exhaustion; physical exhaustion; heterogeneous fuzzy models.

  • Identification of nonlinear systems having discontinuous nonlinearity   Order a copy of this article
    by Adil Brouri 
    Abstract: This paper deals with the identification of nonlinear systems. Presently, the nonlinear system is described by Wiener model. The linear element is nonparametric and may be of unknown structure. The nonlinear part is allowed to be discontinuous or of hard type and, noninvertible. A two-stage identification method is developed to get a set of points of the nonlinear part and estimates of the linear dynamic element. This method is based on simple geometric analysis and involves easily generated excitation signals.
    Keywords: nonlinear systems; nonlinear systems identification; discontinuous nonlinearity; nonparametric linear block; hard nonlinearity; Wiener systems.

  • U-model enhanced MIMO decoupling control of thickness and plate type of cold rolling temper mill   Order a copy of this article
    by Pengwei Li, Weicun Zhang 
    Abstract: This paper presents a new design procedure for control of thickness and plate type of cold rolling temper mill. A novel concept for control system design, U-model-based design methodology with expanded Multi-Input and Multi-Output (MIMO) formulation for this application, makes separation of specifying closed loop performance-controller from process models. In contrast to classical and methodologies, this takes two parallel formations: 1) designs an invariant virtual controller with specified closed loop transfer function in a feedback control loop; 2) determines real controller output by resolving the inverse of the plant U-model. Further, this study analyses some of the associated properties for assurance and guidance for ongoing theoretical development and applications. To validate the design procedure, it takes several computational experiments to generate simulation results, the bench tests show the efficiency and effectiveness of the proposed MIMO U-model-based control system design.
    Keywords: cold rolling temper mill; plate type; plate thickness; U-model; U-control; model independent control system design.

  • A new chaotic dynamical system with a hyperbolic curve of rest points, its complete synchronisation via integral sliding mode control and circuit design   Order a copy of this article
    by Sundarapandian Vaidyanathan, Aceng Sambas, Chang-Hua Lien, Babatunde A. Idowu 
    Abstract: A new 3-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has a hyperbola of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. The new nonlinear plant shows multi-stability and coexisting attractors. The synchronisation of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit model using MultiSim of the new 3-D nonlinear plant with chaos is carried out for practical use.
    Keywords: chaos; chaotic systems; circuit design; synchronisation.

  • Towards improving constrained robust model predictive control with free control moves   Order a copy of this article
    by Xianghua Ma, Shuang Fang 
    Abstract: An existing robust model predictive control (RMPC) algorithm parameterises the infinite horizon control moves into a set of free control moves over a fixed horizon and a state feedback law in the terminal region. This paper is towards further improving the feasibility and optimality of this kind of RMPC. The improvement is by introducing an extended parameter-dependent Lyapunov function to substitute the original parameter-dependent Lyapunov function. Correspondingly, the terminal-weighting matrix is extended parameter-dependent, the local control law is a non-parallel distributed compensation, and the terminal constraint set is an intersection of more ellipsoids. The new technique is demonstrated by a simulation example.
    Keywords: model predictive control; polytopic description; parameter-dependent Lyapunov function; non-parallel distributed compensation law; linear matrix inequality.

  • Modelling of multi-timescale demand response for power markets   Order a copy of this article
    by Dan Zhou, Huiwen Dai 
    Abstract: Demand response as an important part of smart grid makes the consumers participate in market operation that can lead to the benefit of both the utility and the consumers. In this paper, a multi-timescale demand response model that accounts for short-term and long-term demand characteristics is established. The short-term demand response and long-term demand response are combined by the electricity price elasticity matrix. The objective of optimisation is to minimise the peak-valley load difference in the total load,and particle swarm optimisation is adopt as the optimisation algorithm. The simulation results of IEEE-30 node distribution network show the feasibility and effectiveness of the proposed demand response model and pricing strategy. The research of this paper will provide technical support for the application of demand response mechanism after the new electric power reform.
    Keywords: demand response; power demand elasticity matrix; multi-timescale model; peak-valley difference optimisation; pricing strategy.

  • Application of multivariate adaptive regression in soft-sensing and control of UCG   Order a copy of this article
    by Jan Kacur, Marek Laciak, Milan Durdan, Patrik Flegner 
    Abstract: The technology of underground coal gasification (UCG) is still under development and provides an alternative to conventional coal mining. Process monitoring is the necessary part of a complex control system because it provides essential information for control level. Monitoring and control improve the behaviour and effectiveness of the technological process. This paper introduces a novel approach to soft-sensing in UCG based on multivariate adaptive regression splines (MARS). This technique can support monitoring the process variable that is inaccessible for standard measuring hardware. The MARS method was applied for modelling of underground temperature from the syngas composition. The paper also presents advanced approaches to control based on an adaptive regression model. Proposed control can increase or maintain the syngas calorific value during UCG operation. Proposed methods have shown interesting results and can be applied to industrial automation devices or implemented as support algorithms for the monitoring system. Methods were verified in experimental coal gasification on an ex-situ reactor.
    Keywords: UCG; monitoring; control; soft-sensing; regression; adaptation; gasification; coal.

  • A welding manipulator path planning method combining reinforcement learning and intelligent optimisation algorithm   Order a copy of this article
    by Junhua Zhang, Lianglun Cheng, Tao Wang, Wenya Xia, Dejun Yan 
    Abstract: We present DDPG-AACO, a hierarchical method for welding manipulator path planning of complex components welding tasks that combines reinforcement learning (RL) with the intelligent optimisation algorithm. The RL agent, trained with the deep deterministic policy gradient (DDPG), learns local path planning policies that control the welding manipulator to safely move between two welding seam endpoints. Next, on a distance matrix constructed by the lengths of local paths between every two welding seam endpoints,the adaptive ant colony optimisation (AACO) algorithm with artificially changed value of pheromones is adopted to realise the global path planning that the welding manipulator traverses all welding seams under a welding direction constraint and has the shortest path length. The simulation results show the effectiveness of the method. The DDPG is better than the deep Q-learning based methods when performing local path planning. Moreover, the length of the global path with direction constraint can converge to the minimum.
    Keywords: complex component; welding manipulator; path planning; direction constraint; DDPG; AACO.

  • Active disturbance rejection control of three-phase grid-connected photovoltaic systems   Order a copy of this article
    by Hezheng Li, Jing Bai, Shunshoku Kanae, Yanxi Li, Lin Yue 
    Abstract: In this paper, a three-phase grid-connected photovoltaic system based on active disturbance rejection controller (ARDC) is proposed to solve the problem of voltage instability that is caused by many internal uncertainties and external disturbances. A tracking differentiator is used to arrange the transient process to reduce the initial error, which solves the problem of large overshoot. The extended state observer is used to estimate the internal and external total disturbances in real-time, and adopts a linearisation technique via a dynamic compensation process, which can reject internal and external disturbances effectively. The simulation experiments show that ADRC has better performance than PI controller in reducing power loss and rejecting disturbances.
    Keywords: three-phase grid-connected photovoltaic system; tracking differentiator; extended state observer; internal and external disturbances.

  • Incentive Stackelberg game based path planning for payload transportation with two quadrotors   Order a copy of this article
    by Dongbing Gu 
    Abstract: This paper proposes a path planning approach to the task of transporting a cable-suspended payload with two quadrotors. The transporting system is provided with a desired payload path which is predefined by the user without the consideration of system dynamics. The path planning problem is to find the optimal paths for the quadrotors, which can make the payload to move along the closest path to the desired one under the constraint of system dynamics. This problem is formulated as an incentive dynamic Stackelberg game where one quadrotor plays a leader role while the other plays a follower role, and each of them is defined with an individual cost function. By using an incentive strategy, a game solution can be found based on the linearized dynamic system. The benefit of using two cost functions over one cost function is that the whole system operates more efficiently in terms of individual costs. In the paper, the nonlinear system dynamics is derived first, and then linearized into a linear system. Then an incentive strategy is applied to the linearized system to find the optimal paths for the quadrotors. Some simulation results are provided to show the performance of proposed path planning approach. The planned paths are also used in real experiments where the paths are tracked by two quadrotors using PID controllers.
    Keywords: UAV path planning; incentive dynamic Stackelberg game; aerial transportation; multiple quadrotor systems.

  • Interval prediction of oscillating time series based on grey system modelling   Order a copy of this article
    by Gaofei Xu, Xiaohui Wang, Zhigang Li, Yang Zhao 
    Abstract: This paper presents an interval prediction algorithm based on grey system modelling, which is proposed for the forecasting of strong-oscillation time series with small samples. In the proposed algorithm, the upper and lower envelope of an oscillating sequence is obtained through cubic spline interpolation, and distance between the envelope and the fitted sequence derived from grey system model is dynamically expanded according to the oscillation intensity. After that, prediction value of the envelope distance sequence is calculated, and adjusted adaptively based on the new information priority principle. Finally, the interval prediction result is obtained. To verify the performance of the algorithm, five application cases from different fields were adopted. Compared with five representative algorithms in the recently related field, the proposed algorithm has distinct advantages in the prediction of small-sample strong-oscillation time series.
    Keywords: interval prediction; oscillating time series; small samples learning; spline interpolation; grey system modelling.

  • An improved genetic algorithm-based robot path planning method without collision in confined workspace   Order a copy of this article
    by Wenyu Tam, Lianglun Cheng, Tao Wang, Wenya Xia, Liangzhou Chen 
    Abstract: The manufacturing process of ships and marine engineering equipment involves a large number of welding processes of complex components. It is difficult for industrial robots to plan the welding path because of the complex distribution of the weld seams and environmental obstacles as well as the specific technological requirements of arc welding process. In this paper, the typical welding components are numerically modelled. Considering the joint collision-free constraint in the moving process of a robot and the welding technological constraints (e.g., welding direction) of some special welding seams, an improved Re-GA algorithm for planning robot welding operation path in complex workspace is proposed, and an optimal welding path can be obtained. The simulation results show that the Re-GA has reliable optimization ability in the case of a small population size.
    Keywords: Re-GA; complex components; pose match; directed path planning.

  • Fuzzy H_infinity filtering for nonlinear 2-D systems in the Roesser model   Order a copy of this article
    by Khalid Badie, Mohammed Alfidi, Zakaria Chalh 
    Abstract: This study focuses on the H_infinity filtering problem for two-dimensional (2-D) discrete Takagi-Sugeno (T-S) fuzzy systems in the Roesser model. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H_infinity performance of the filtering error system. By using a new structure of the fuzzy Lyapunov function, and some analysis techniques, the stability and a prescribed H_infinity performance index are guaranteed for the overall filtering-error system, such that the coupling between the Lyapunov matrix and the system matrices is removed. In addition, sufficient conditions for the existence of such a filter are established in term of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can be characterized. An illustrative example is presented to demonstrate the effectiveness of the developed results.
    Keywords: H_infinity filtering; two-dimensional fuzzy systems; Takagi-Sugeno model; linear matrix inequalities.

  • Robustness of current source inverter based on H? control   Order a copy of this article
    by Yu Xu, Yang Li, Hezheng Li, Shunshoku Kanae, Jing Bai 
    Abstract: Aiming at the problem that the control performance of three-phase current-source inverter(CSI) is affected by load parameters and external disturbances easily, a robust H? control strategy is proposed firstly in this paper. A mathematical model of three-phase CSI is established. According to the model of CSI with uncertain parameters, the state feedback H? controller is designed and the feedback control laws is obtained. A robust H? controller based on CSI control system is designed. Finally, the effectiveness and feasibility of the scheme are verified by simulation.
    Keywords: current source inverter; H? control;robustness.

  • A new robust adaptive fuzzy synergetic control for nonlinear systems with an application to an inverted pendulum   Order a copy of this article
    by Abderazak Saidi, Farid Naceri, Sundarapandian Vaidyanathan 
    Abstract: This paper deals with a nonlinear adaptive control design based on synergetic control, which also uses fuzzy systems to approximate the dynamics of non-linear systems. The stability of the closed-loop system is ensured by the Lyapunov synthesis in the sense that all the signals are bounded, and the controller parameters adjusted by adaptation laws. The proposed algorithm is applied to an inverted pendulum to track a sinusoidal reference trajectory. Simulations and discussion are presented to illustrate the new robust adaptive fuzzy synergetic control presented in this work.
    Keywords: adaptive control; fuzzy adaptive control; nonlinear systems; synergetic control.

  • Nonlinear interconnected high gain observer for series-parallel resonant DC/DC converter   Order a copy of this article
    by Ouadia El Maguiri 
    Abstract: We are considering the problem of state observation in series-parallel resonant converters (LCC). This is a crucial issue in (LCC) output voltage control as the control model is nonlinear and involves nonphysical state variables, namely real and imaginary parts of complex electrical variables. An interconnected high gain observer is designed to get online estimates of these states. The observer is shown to be globally asymptotically stable. The global stability of the observer is analytically treated using the lyapunov theory; finally we present numerical simulation to illustrate the performance of the suggested approach.
    Keywords: series-parallel resonant converter; averaging approximation; state variables observation; lyapunov theory; interconnected high gain observer.

  • Real-time sensor fault diagnosis method for closed-loop system based on dynamic trend   Order a copy of this article
    by WenBo Na, Yu Gao, TuoHong Zhu, XiuTong Zheng 
    Abstract: In order to solve the common problems of sensor fault detection, fault setting and fault location in the first-order closed-loop control system, a static fault diagnosis model based on the real-time trend of dynamic data flow is constructed. Aiming at the common fixed-value system and servo system in the first-order closed-loop control system, a data processing model based on sliding window is designed by collecting and analysing a large amount of real-time data, and the fault is isolated in the window based on the calibration parameters. Then, the adaptive threshold binarisation method is used to calculate the fault vector, and then the analytic model of fault location is obtained by the linear regression method. Finally, the feasibility and validity of closed-loop sensor fault diagnosis method based on dynamic data flow trend are verified by on-line simulation of Complex Process System Innovation Experimental Platform based on OPC communication technology.
    Keywords: dynamic trend; sliding window; sensor; fault diagnosis; closed-loop system.

  • A novel control structure for a pioneer mobile robot: simulation and practical implementation   Order a copy of this article
    by Lauhic Ndong Mezui, Donatien Nganga-Kouya, Maarouf Saad, Francis Okou, Brice Hernandez 
    Abstract: This paper presents a new control structure for a non-holonomic robot. It consists of two controllers in series: a nonlinear trajectory tracking controller based on robot kinematics and a multivariable quasi-linear controller based on robot dynamics. The Lyapunov theory is used to obtain the nonlinear control law and a frequency domain design approach is employed to find the transfer functions of the quasi-linear controller. The stability and sensitivity analysis criteria are considered to increase the performance of the robot. The stabilization time and overshoot are considerably reduced. The proposed controller is simple and insensitive to external disturbances. Simulation and real-time test results are used to evaluate the effectiveness of this new control structure.
    Keywords: mobile robot; non-holonomic; stability; sensitivity; robustness; transmission; trajectory tracking; quasi-linear controller.

  • Flexible flow shop scheduling with variable processing times based on differential shuffled frog leaping algorithm   Order a copy of this article
    by Zhijun Gao, Jiayu Peng, Meiqi Jia, Zhonghua Han 
    Abstract: In the problem of flexible flow shop scheduling with variable processing times, the change of processing speed often affects product quality and causes fluctuations in capacity, which makes it difficult to solve the scheduling problem. And these production lines widely exist in the actual production. Therefore, in the light of the Flexible Flow-shop Scheduling Problem with Variable Processing Times (FFSP-VPT), the FFSP-VPT mathematical model is established. The improved differential shuffled frog leaping algorithm is served as the global optimization algorithm, and the difference operator is introduced as a new location update strategy. Whats more, the crossover operation is taken to maintain the diversity of the population. It overcomes the shortcomings of the adaptive shuffled frog leaping algorithm which is easy to fall into local optimum and converges slowly. On the premise of ensuring the global optimisation goal, the two-stage coding method is used to determine the online sequence of the job and processing speed of the stage with variable processing times, so as to get much more effective solution to such problems. The simulation experiments confirm the improvement of the shuffled frog leaping algorithm in global search ability and its effectiveness in solving the flexible flow shop scheduling problem with variable processing times.
    Keywords: flexible flow shop; variable processing times; differential shuffled frog leaping algorithm; two-stage coding.

  • Advanced Control of Three-Phase Battery Electric Vehicle Charger with V2X technology
    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 it’s 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 its 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
    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 & 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, stability in steady state, less oscillations around the MPP and higher efficiency to track the maximum power from the PV system compared to other techniques under different operating conditions.
    Keywords: Photovoltaic system; Perturb & Observe (P&O); Maximum Power Point Tracking (MPPT); 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
    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
    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
    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