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IEEE Transactions on Industrial Electronics (02780046)71(12)pp. 15372-15382
This article presents a comprehensive approach to addressing the challenges of unbalanced rotors in permanent magnet (PM) synchronous machines by proposing a load torque (LT) observer for unbalance detection and a current injection technique for minimizing torque oscillations resulting from the unbalanced rotor. The primary objective is to enhance the operational efficiency and performance of electric motors by identifying the effects of the unbalanced rotor on the motor torque. The proposed LT observer utilizes real-time speed measurement to estimate the total LT. To significantly reduce the torque oscillations from the unbalanced rotor, optimum current components are injected with meticulously calculated amplitude and phase. The proposed method operates in synchronization with the rotor position, and the injected currents are extracted via an optimization problem from an adaptive model that is continuously updated through a parameter's identification method. The effectiveness of the proposed approach is demonstrated through experimental evaluations on a representative experimental setup. The results reveal that the LT observer accurately detects rotor unbalance and the current injection technique successfully minimizes motor torque oscillations, resulting in smoother motor operation, reduced noise, and improved overall efficiency. © 1982-2012 IEEE.
International Journal of Systems Science (00207721)55(13)pp. 2741-2758
Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Journal of the Franklin Institute (00160032)360(14)pp. 10728-10744
This paper deals with state estimation for a class of Lipschitz nonlinear systems under a time-varying disconnected communication network. A distributed observer consists of some local observers that are connected to each other through a communication network. We consider a situation where a communication network does not remain connected all the time, and the network may be caused by intermittent communication link failure. Moreover, each local observer has access to a local measurement, which may be insufficient to ensure the system's observability, but the collection of all measurements in the network ensures observability. In this condition, the purpose is to design a distributed observer where the estimated state vectors of all local observers converge to the state vector of the system asymptotically, while local observers exchange estimated state vectors through a communication network and use their local measurements. According to theoretical analysis, a nonlinear and a robust nonlinear distributed observer exist when in addition to the union of all communication topologies being strongly connected during a time interval, the component of each communication graph is also strongly connected during each subinterval. The existence conditions of the distributed observers are derived in terms of a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the presented method is numerically verified using some simulation examples. © 2023 The Franklin Institute
Journal of Navigation (03734633)76(6)pp. 709-730
This paper proposes a switched model to improve the estimation of Euler angles and decrease the inertial navigation system (INS) error, when the centrifugal acceleration occurs. Depending on the situation, one of the subsystems of the proposed switched model is activated for the estimation procedure. During global positioning system (GPS) outages, an extended Kalman filter (EKF) operates in the prediction mode and corrects the INS information, based on the system error model. Compared with previous works, the main advantages of the proposed switched-based adaptive EKF (SAEKF) method are (i) elimination of INS error, during the centrifugal acceleration, and (ii) high accuracy in estimating the attitude and positioning, particularly during GPS outages. To validate the efficiency of the proposed method in various trajectories, an experimental flight test is performed and discussed, involving a microelectromechanical (MEMS)-based INS. The comparative study shows that the proposed method considerably improves the accuracy in various scenarios. © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Institute of Navigation.
European Journal of Control (09473580)63pp. 206-213
In this paper, a low order asymptotic predictor is introduced for nonlinear systems based on measurable outputs. Predictors play basic role in the control of dead-time systems having no delay-free input. Generalized Lipschitz Condition is employed here to develop Sequential Sub-Predictors (SSP) for complex nonlinear systems. Compared with existing synthesis methods which involve Lipschitz Condition, Generalized Lipschitz condition relaxes the conservative of the stability results using some modified matrix inequalities. The proposed idea can be more attractive for unstable systems due to reduce significantly the order of the predictors. Also using the proposed method, the effect of the external disturbance can be minimized based on H∞ index. Afterward, a SSP-based controller is presented to illustrate the effectiveness of proposed method to stabilize nonlinear systems with input-delay. Finally, the predictor capability is investigated by simulation examples. © 2021 European Control Association
Control Engineering Practice (09670661)107
In this paper, a novel observer-based force control scheme is proposed to guarantee the position and force tracking in nonlinear teleoperation systems, subject to constant communication time delay. Stability of the teleoperation system is analytically proved using the Lyapunov stability theorem. Enough condition for asymptotic convergence of the force and position are derived. The transparency is also improved by force tracking capability of the system. The teleoperation controller is then applied to a pair of planar 2-DOF robots, connected via a communication channel with constant time delay. The experimental and simulation results demonstrate the effectiveness of the proposed control algorithm, in force estimation and dealing with time delay. © 2020 Elsevier Ltd
IEEE Transactions on Control Systems Technology (10636536)28(5)pp. 1997-2004
This brief considers sliding mode control of hysteresis in piezoelectric actuators. For modeling of hysteresis, the Bouc-Wen model that is based on differential equations is utilized. One of the states of this model is unmeasurable. Therefore, a state observer is proposed, and the proper selection of observer parameters is discussed. Based on the observed state, a control rule is proposed, and asymptotic stability of the observer-based closed-loop system is proven using the Lyapunov theory. This brief also presents a design method, i.e., sufficient conditions on design parameters for closed-loop stability are derived explicitly. Furthermore, the mass, stiffness, and damping coefficients in the model are assumed unknown. The values of these parameters are estimated using an online adaptation rule, and the control rule is modified based on the estimated parameters. The adaptation rule is extracted so that the asymptotic stability of the whole system is guaranteed. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed scenarios. © 1993-2012 IEEE.
Journal of the Franklin Institute (00160032)357(3)pp. 1457-1472
The output feedback stabilization of Lipschitz nonlinear systems is addressed. The synthesis of reduced-order controller is formulated as static output feedback problem. Based on coupled algebraic Riccati inequalities, the stability analysis of closed loop dynamic is presented. By utilizing some structural knowledge of Lipschitz nonlinearity, the sufficient conditions to obtain static as well as dynamic output feedback gains are given. For the class of Lipschitz nonlinearity, it is shown that the proposed condition is a necessary and sufficient condition to achieve static gain. The cone complementary linearization method is then applied to satisfy the proposed stability condition and to obtain an output feedback regulator. The effectiveness of proposed method is finally demonstrated through simulation results on some practical systems. © 2019 The Franklin Institute
ISA Transactions (00190578)91pp. 125-134
Asymptotic stabilization of a class of nonlinear systems with known constant long input delay is addressed in the presence of external disturbance by applying sliding mode control method. Modified prediction variable scheme is employed to compensate long delays in the input, where conventional prediction variable approaches cannot be employed. This is mainly due to the fact that the external disturbance appears in the prediction variable, which renders the controller dependent on the external disturbance. In order to tackle this problem, the nonlinear disturbance observer based predictor is used. A suitable disturbance observer is designed to estimate the external disturbance that appears in the prediction variable. Respected to some existing results, the prediction-based control for more general class of the nonlinear systems in the presence of external disturbance is the main contribution of this paper. Actuator and sensor delays exist in the most common dynamic systems. So, the proposed control scheme can be employed in many conventional systems. The simulation results indicate the robustness and efficiency of the proposed controller. © 2019 ISA
In this paper, a finite time control method for an uncertain nonlinear system is proposed. An adaptive sliding mode disturbance observer is designed to estimate the disturbance in finite time. The assumptions on the disturbance are relaxed in the sense that, its first derivative upper bound is considered to be unknown and only the order of its second derivative upper bound is known. Based on the output of proposed disturbance observer, a terminal sliding mode control scheme for the uncertain nonlinear system is presented. The designed control law is continuous and nonsingular. Furthermore, compared with some existing sliding mode controllers, the conditions on the controller parameters bounds are relaxed. It is proved that the disturbance observer error as well as the system states converges to the origin in finite time. Finally, the effectiveness of the proposed method is shown by numerical simulations. © 2019 Elsevier Ltd
IET Control Theory and Applications (17518644)13(13)pp. 2047-2055
In this study, stabilisation of input-delay non-linear systems in the presence of disturbance based on prediction variable is studied. For both disturbance estimation and delay compensation, an extended prediction variable as well as adaptive sliding mode controller are proposed in which the open-loop system is not required to be stable. In the proposed prediction variable one needs to estimate disturbance in the future. In order to solve this problem a new non-linear disturbance observer (NDOB) is proposed. Considering the NDOB in the closed-loop system, the stability analysis of error dynamic is performed. And the asymptotic stability of non-linear system with input delay is guaranteed for some class of disturbance. Simulation results finally validate the good performance and robustness of the proposed controller based on disturbance observer. © The Institution of Engineering and Technology 2019.
Journal of Optimization Theory and Applications (00223239)180(3)pp. 1036-1064
Many real-world dynamics can be modeled as nonlinear time-delay systems. In order to capture a more realistic model for system dynamics, the exact values of time-delay should be taken into account. For nonlinear time-delay systems, the estimation of delays in both state and output equations is discussed. A cost function is defined based on least-square error between actual and estimated values of the output measurement. The value of time-delays in the nonlinear system are then derived using a gradient-based optimization method. Because of the implicit description of the cost function with respect to the delay value, its gradients cannot be obtained by standard analytical differentiation rules. In this case, the optimal computational methods are utilized to derive two formulas for computing the gradient. An optimization scheme is then formulated to estimate both state and output delays. The effectiveness of the proposed estimation method is finally demonstrated using the simulation results on a benchmark chemical process. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Koofigar, H.R.,
Ekramian, M.,
Mahzounieh, A.,
Mahzounieh, A.,
Koofigar, H.R.,
Ekramian, M. 2025 29th International Computer Conference, Computer Society of Iran, CSICC 2025pp. 1216-1220
The aim of this paper is to propose an identification scheme for linear switched systems with state space description. The method consists of two stages: First, output matrix elements are identified by Kaczmarz Algorithm and then by k-means clustering algorithm, switching time is estimated; Second, by passing the estimated switching time to an adaptive observer in serial-parallel form, input and state matrices are estimated. Identification method is tested on numerical simulation. © 2019 IEEE.
International Journal of Systems Science (00207721)49(13)pp. 2784-2796
The mechanical impedance of the human arm can be measured to quantitatively assess the motor function. In this paper, an adaptive least square estimation method is proposed for online measurement of the mechanical impedance of the arm, without force or acceleration sensors, which extremely reduces the expenses and complexity of rehabilitation robots. The proposed strategy may also be used for monitoring the dynamic changes of the mechanical impedance. Estimation of time-varying force is also the other capability of the algorithm. The closed-loop stability of the system is analytically shown using the Lyapunov stability theorem. To show the applications of the proposed scheme, two main scenarios are described which can be used for the rehabilitation robots to assess the motor recovery of the patients undergoing the rehabilitation sessions. To validate the scheme, a 2-DOF manipulator is adopted to illustrate the accuracy of the impedance and force estimations in noiseless and noisy conditions. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
International Journal of Systems Science (00207721)49(12)pp. 2558-2570
This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
In this paper, a sliding mode observer for the class of Lipschitz nonlinear systems with uncertainty is proposed. The uncertainty is assumed to be bounded and the matching condition is first taken into account. The generalized Lipschitz condition is employed to consider some structural knowledge of Lipschitz nonlinearity. This yields less conservative results in stability analysis of proposed observer dynamics. The results are then extended to the unmatched uncertainty. Moreover, a synthesis method in terms of some linear matrix inequalities is established to achieve the proposed sliding mode observer. The simulation results on manipulator with revolute joints actuator are finally given to exhibit the effectiveness of the proposed observer and related synthesis method. © 2018 IEEE.
Transactions of the Institute of Measurement and Control (14770369)40(3)pp. 712-718
The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities. © 2018, © The Author(s) 2018.
This paper proposes an observer for the class of triangular nonlinear systems including the model uncertainty, with constant delays in the state and input equations. It is assumed that the nonlinear perturbations satisfy the Lipschitz condition and the uncertain part is bounded. The main idea is based on the designing a high-gain observer in combination with the sliding mode observer which leads to a robust high-gain observer that has not been sufficiently studied previously. A compensation term is included in the observer dynamics that is designed based on the solution of a Lyapunov inequality. For stability analysis, if the matching condition is satisfied, by using a suitable Lyapunov-Krasovski functional, simple sufficient conditions are provided that guarantees the observation error converges to the origin asymptotically. The simulation results for a nonlinear system in triangular form illustrate the effectiveness of the proposed approach. © 2017 IEEE.
International Journal of Systems Science (00207721)48(16)pp. 3411-3418
An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Nonlinear Dynamics (0924090X)89(4)pp. 2879-2887
A robust nonlinear observer for a class of nonlinear time-delay systems is introduced. The generalized sector constraint is employed to deal with many commonly encountered nonlinearity in dynamic equation. It is assumed that time-varying delay exists in both state and output equations, and further it directly appears in nonlinear function. By utilizing two correction terms in nonlinear observer related to the dynamic equation as well as system’s nonlinearity, the stability analysis of observer error dynamic is presented. For uncertain systems, a synthesis method to obtain robust nonlinear observer is then given in terms of some LMI’s. The effectiveness of proposed observer and related synthesis method are finally demonstrated through simulation examples. © 2017, Springer Science+Business Media B.V.
In this paper, the stability analysis of networked control systems, as important class of time delay systems is presented. The analysis method utilizes a new Lyapunov-Krasovskii functional to provide less conservative results with respect to the existing methods in literature. The delay dependent stability criteria based on improved version of Wirtinger inequality and reciprocally convex combination inequality are derived in terms of linear matrix inequalities. A numerical example is finally given to show the effectiveness and benefits of the proposed analysis methods compared with some recent results. © 2017 IEEE.
Transactions of the Institute of Measurement and Control (14770369)38(3)pp. 364-369
A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input. © SAGE Publications.
Koofigar, H.R.,
Ekramian, M.,
Dehghan, S.A.M.,
Dehghan, S.A.M.,
Koofigar, H.R.,
Ekramian, M. 2025 29th International Computer Conference, Computer Society of Iran, CSICC 2025pp. 102-106
This paper presents a nonlinear 4-channel bilateral teleoperation system, without using force sensor. In the design procedure, the adaptive control laws estimate and compensate the exerted forces on both master and slave robots. The estimated forces are then used in a control loop for modifying the trajectory of both robots to meet the full transparency condition. The stability and the transparency of the teleoperation system are analyzed, based on the Lyapunov theorem. Some simulations are also presented for a two planar two-degree of freedom manipulator to show the efficiency of the proposed control algorithm. © 2016 IEEE.
Aim of this paper is to estimate time delays in nonlinear dynamic systems with unknown time-delays, such that time-delays appear in both state and output equations. The problem of estimating unknown delays is formulated as a dynamic optimization problem in which the cost function is defined based on the least-squares error between predicted and actual system output. Using proposed estimation method derives unknown time-delays by evaluating the gradient of cost function. Since, the gradient cannot be obtained analytically by standard differentiation rules, a practical computational method is presented to compute gradient and related cost function. The effectiveness of proposed algorithm is finally demonstrated by applying it to a practical example. © 2016 IEEE.
Journal of Engineering (United Kingdom) (23144912)2014
Tandem cold rolling process is a nonlinear complex system with external and internal uncertainties and significant disturbances. The improvement in the quality of the final output depends on the control strategy of centerline thickness and interstand tension. This paper focuses on interstand tension control problem in 5-stand tandem cold rolling mills. Tension dynamics can be described by a nominal model perturbed by parametric uncertainties. In order to overcome the model uncertainties and external disturbances, suboptimal H∞ and μ controllers are proposed and the Hankel-norm approximation is used to reduce the order of μ controller. The performance of the proposed controllers is demonstrated by some simulations. © 2014 Behrooz Shafiei et al.
Ekramian, M.,
Sheikholeslam, F.,
Hosseinnia, S.,
Yazdanpanah m.j., Systems and Control Letters (01676911)62(4)pp. 319-323
The problem of adaptive observer synthesis for Lipschitz nonlinear systems is addressed. In the case of known parameters, the convergence property of state observer is first discussed. Based on a generalized Lipschitz condition, the sufficient conditions to ensure the stability of observer error dynamics are presented in terms of some LMIs. In the case of system dynamics with some unknown parameters, the proposed conditions along with an equality constraint are then employed to guarantee the convergence property of an adaptive state observer. Moreover, an adaptive observer form is derived which can be utilized in designing the reduced order state observer. The simulation results are finally given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems. © 2013 Elsevier B.V. All rights reserved.
International Journal of Systems Science (00207721)44(11)pp. 2094-2103
The problem of designing an observer for nonlinear Lipschitz systems affected by system and sensor noises is addressed. Related to the system nonlinearity, the stability of observer dynamic with static and dynamic gain is considered. The advantage of using dynamic gain to deal with large Lipschitz nonlinearity is discussed and it is proved that no dynamic gain can stabilise the observer for a larger Lipschitz constant as compared with the static gain. However, a nonlinear observer with dynamic gain has some additional degrees of freedom which can be utilised to attenuate noise effect on the observer behaviour. Using mixed and criteria, this article introduces a method to obtain a dynamic gain which can deal with system nonlinearity and noise simultaneously. The effectiveness of the proposed method is finally demonstrated by some simulation results. © 2013 Copyright Taylor and Francis Group, LLC.
IET Control Theory and Applications (17518644)7(2)pp. 253-260
The problem of designing Luenberger-like observer for non-linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger-like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach. © The Institution of Engineering and Technology 2013.
IET Control Theory and Applications (17518644)5(16)pp. 1813-1818
The stability-sufficient condition in designing an observer for non-linear Lipschitz systems is extended such that it does not neglect the structure of given non-linearity and can be less conservative in applying to many non-linear systems. A design procedure based on full control problem is then presented to satisfy the extended condition by means of a constant observer gain. Finally, simulation examples are given to exhibit the effectiveness of the proposed condition and design procedure in dealing with some large Lipschitz non-linearities. © 2011 The Institution of Engineering and Technology.