Errors In System Parameters Research Articles

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter.

The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

Performance bounds of adaptive MPC with bounded parameter uncertainties

Model predictive control is a control approach that minimizes a stage cost over a predicted system trajectory based on a model of the system and is capable of handling state and input constraints. For uncertain models, robust or adaptive methods can be used. Because the system model is used to calculate the control law, the closed-loop behavior of the system and thus its performance, measured by the sum of the stage costs, are related to the model used. If it is adapted online, a performance bound is difficult to obtain and thus the impact of model adaptation is mostly unknown. This work provides a (worst-case) performance bound for a linear adaptive predictive control scheme with a specific model parameter estimation. The proposed bound is expressed in terms of quantities such as the initial system parameter error and the constraint set, among others and can be calculated a priori. The results are discussed in a numerical example.

Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter

In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.

Event-Triggered Optimized Control for Nonlinear Delayed Stochastic Systems

This paper is concerned with the problem of event-triggered optimized control for uncertain nonlinear Itô-type stochastic systems with time-delay and unknown dynamic. By using fuzzy logic systems to approximate two unknown nonlinear functions with the delayed state and current state, respectively. The adaptive identifier is constructed to determine the stochastic system, and the optimized control is designed by using the identifier and adaptive dynamic programming (ADP) of actor-critic architecture. Almost all of the works are concentrated on ADP-based optimal control and it will inevitably cause the complexity of computation and requirements of persistence excitation (PE) assumption. In this paper, the ADP algorithm is obtained based on the negative gradient of a simple positive function (equivalent to the HJB equation), and so the proposed optimal control is simple and can release the PE assumption. Moreover, the event-triggered control approach is proposed to reduce computing burden and communication resources. Furthermore, we prove that the states of system and FLSs parameter errors are semi-globally uniformly ultimately bounded (SGUUB) in mean square via the adaptive identifier and the Lyapunov direct method as well as identifier-actor-critic architecture-based ADP algorithm. Finally, the effectiveness of the proposed method is illustrated through two numerical examples.

Dynamic modeling and self-tuning anti-sway control of a seven degree of freedom shipboard knuckle boom crane

This paper addresses the deficiency of research in anti-sway control for high degree of freedom (DOF) shipboard cranes by developing a dynamic model and anti-sway control system for a seven-DOF shipboard knuckle boom crane, mounted aboard a vessel that experiences six-DOF ship motion. The dynamic model provides fidelity beyond what is typically seen in literature, including the mass and inertia of the hydraulic actuators, sheaves and winch, along with internal actuator dynamics and a realistic cable fall angle. The crane’s kinematics are derived using both the standard transformation matrix approach and with dual quaternions, and the equations of motion obtained with the Lagrange approach. To provide anti-sway control, a self-tuning anti-sway trajectory modifier is combined with a nonlinear sliding mode controller and a nonlinear trajectory optimizer. Tested in simulation on a ship with six-DOF motion at sea state 6, the system with self-tuning disabled provided a 64% reduction in the average root-mean-square-error (RMSE) between the desired and actual payload positions across the x and y trajectories. Allowing the anti-sway trajectory modifier to self-tune provided a 74% reduction in RMSE under the same conditions. When a 5 kN disturbance force was applied to the payload, the system without self-tuning showed a 58% reduction in the average RMSE, while with self-tuning enabled showed a 77% reduction in RMSE. The self-tuning anti-sway control system was also shown to be robust to errors in system parameters, where errors up to ±20% in the simulated crane resulted in a maximum increase of average RMSE of only 6.3%. Within simulation, the anti-sway control system is shown to be highly effective at tracking a time-varying payload trajectory for a seven-DOF knuckle boom crane and reducing undesired payload motion, and is shown to be robust to both sudden disturbances and errors in system parameters.

Dynamic analysis and identification of unbalance and misalignment in a rigid rotor with two offset discs levitated by active magnetic bearings: a novel trial misalignment approach

Rotating machinery is an essential and crucial component of numerous mechanical systems in modern industries, transport vehicles, and in several other applications. Excessive vibrations on rotating equipment due to multiple faults may cause catastrophic failure in machines and lead to hazardous accidents. So, there is a need for perceiving the dynamic nature and identifying the faults for the safe, smooth and effective operation of machines. This paper proposes a novel trial misalignment approach to estimate the misalignment with a similar concept as the trial unbalance in the rotor balancing. Active magnetic bearing (AMB) misalignment with the rotor has been investigated with residual misalignment and additional trial misalignment cases. Additional trial misalignments are provided in addition to the unknown misalignments of the residual misalignment case. For the execution of this methodology, the dynamic model of a four-degree-of-freedom unbalanced and misaligned rigid rotor with two offset discs supported by two active magnetic bearings has been mathematically developed. The offset discs result in the gyroscopic effect at high rotor speeds. Equations of motion of the rotor-AMB system have been derived and solved to generate the time domain rotor displacement and controlling current responses at AMB positions. A fast Fourier transform technique has been utilized to convert the time domain responses into the frequency domain for estimation of unbalance eccentricities and phases together with force-displacement and force-current stiffnesses of misaligned AMBs as well as AMB's constant forces using the developed identification algorithm. Identified values of AMB's parameters for both residual and additional trial misalignment cases are evaluated to estimate the four unknown misalignments. Testing of the algorithm has also been carried out at multiple spin speeds against measurement signal noise in rotor responses and bias errors in rotor system parameters to check its effectiveness and robustness. The algorithm is found to be exhibiting excellent.

Output Control of Three-Axis PMSG Wind Turbine Considering Torsional Vibration Using H Infinity Control

Due to changes in wind, the torque obtained from the wind turbine always fluctuates. Here, the wind turbine and the rotor of the generator are connected by a shaft that is one elastic body, and each rotating body has different inertia. The difference in inertia between the wind turbine and the generator causes a torsion between the wind generator and the generator; metal fatigue and torsion can damage the shaft. Therefore, it is necessary to consider the axial torsional vibration suppression of a geared wind power generator using a permanent magnet synchronous generator (PMSG). In addition, errors in axis system parameters occur due to long-term operation of the generator, and it is important to estimate for accurate control. In this paper, we propose torque estimation using H ∞ observer and axial torsional vibration suppression control in a three inertia system. The H ∞ controller is introduced into the armature current control system (q-axis current control system) of the wind power generator. Even if parameter errors and high-frequency disturbances are included, the shaft torsional torque is estimated by the H ∞ observer that can perform robust estimation. Moreover, by eliminating the resonance point of the shaft system, vibration suppression of the shaft torsional torque is achieved. The results by the proposed method can suppress axial torsional vibration and show the effect better than the results using Proportional-Integral (PI) control.

Individual Load Model Parameter Estimation in Distribution Systems Using Load Switching Events

There currently exists a mature literature on modeling the aggregate load of a distribution feeder by making use of measurements at its feeder-head at substation. The primary application of such feeder-aggregated load models is in sub-transmission or transmission system analysis. However, there is a growing need in practice also to model each individual load across the feeder. If available, such individual load models have applications in power distribution system analysis, e.g., to better integrate distributed energy resources or to improve power quality and reliability. Motivated by this observation, in this paper, we propose a new method for individual load modeling in power distribution systems. It works by using the measurements only at the feeder-head. It takes an innovative approach to analyzing the load switching events across the distribution feeder itself, instead of or in addition to relying on upstream voltage events that are commonly used in feeder-aggregated load modeling. By tracking the downstream load switching events, the proposed method can make a robust estimation of the ZIP load model parameters for all individual loads. The proposed method is examined on small illustrative test-feeders as well as the IEEE 33-bus test system under various operating scenarios. The adverse impact of errors in measurements and system parameters are also investigated on the performance of the developed load modeling method.

An improved optimal control strategy for hybrid AC/DC power system

The additional modulation function of high voltage direct current (HVDC) links can improve the system stability while the unavoidable random external disturbance and sudden changes seriously affect the controller performance and the system stability. In this paper, an improved control scheme based on inverse optimal adaptive control is proposed for the hybrid AC/DC system which considers the system parameter error, external disturbance and other random perturbation. The proposed control scheme combines the inverse optimal control approach and the adaptive control method to account for the modelling errors and uncertainty, which aims at the disturbance attenuation and the optimal operating of the hybrid AC/DC power system. Besides, the improved PI (Proportional-Integral) controller based on the lead-lag link for the current control of HVDC system is proposed to further improve system dynamic performance. Simulations conducted on a typical hybrid AC/DC system show the correctness and validity of the proposed control method.

A Robust Load Frequency Control Scheme for Power Systems Based on Second-Order Sliding Mode and Extended Disturbance Observer

This paper proposes a new robust load frequency control (LFC) scheme for multiarea power systems based on the second-order sliding mode control and an extended disturbance observer. First, a reduced-order model of the power system LFC is derived. In this model, the load variations and net exchange tie-line power deviations are combined as a lumped disturbance which can be estimated by the extended disturbance observer. Second, a novel sliding surface is designed with the new transformed state variables obtained from the estimated disturbance. The system dynamics can be indicated by sliding surface design using the eigenvalue assignment or the optimal sliding manifold technique. The sliding variable is driven to the sliding surface with a second-order sliding mode algorithm named supertwisting algorithm. The stability of the proposed LFC scheme and the extended disturbance observer is proved using Lyapunov method. The merits of the scheme include faster response speed, stronger robustness against disturbances arising from power system parameter errors, and unmodeled dynamics, and the full consideration of tie-line power flow scheduling variations. Finally, numerical simulations verify the effectiveness of the LFC scheme and reveal its advantages over the state of the arts.

Model based identification of crack and bearing dynamic parameters in flexible rotor systems supported with an auxiliary active magnetic bearing

In this paper, possibility of identification of a crack appearing in flexible rotor systems supported with active magnetic bearing has been investigated. A cracked rotor with active magnetic bearing (AMB) support in auxiliary bearing configuration has been analysed for identification of crack and end support bearing stiffness. Presence of AMB in an auxiliary bearing configuration provides additional damping to the rotor system, thus attenuates the vibrations induced by rotor flaws. Identification strategies based on vibration responses of such a rotor may not produce correct results. However, loss of diagnostic information due to attenuation of the vibration signal could be compensated for, by supplementing the vibration signal with the AMB control current history. With inclusion of the control current history, the crack force and other parameters could be identified. A cracked rotor with multiple discs has been modelled by standard finite elements method, with consideration of gyroscopic effect due to rigid discs. Breathing behaviour of the crack has been modelled with a switching crack excitation function, containing multiple harmonics of both forward and backward nature. Full spectrum of the frequency domain of the response is utilised to develop the identification algorithms. This algorithm identifies the crack force in form of additive crack stiffness and simultaneously estimates the disc unbalances, end support bearing stiffness and active magnetic bearing dynamic parameters as well. The algorithm has been tested in a simple rotor system for the measurement noise and bias errors in system parameters, and found robust.

Identificación de Parámetros Erróneos en Sistemas Eléctricos de Potencia y Corrección en base a Mediciones Sincrofasoriales

Los algoritmos convencionales de estimación de estado de sistemas de potencia se basan en la suposición de que los parámetros tales como la resistencia y reactancia de las líneas de transmisión, los taps de transformadores y el estado de los interruptores no tienen errores. En la realidad, estos parámetros no se conocen con certeza. Los errores en las impedancias de las ramas son menos visibles que los errores en los estados de los interruptores y pueden producir errores en los resultados del estimador que pueden pasar inadvertidos por largo tiempo. Los errores en los parámetros pueden producir un impacto sobre la estimación de estado similar o superior al de los errores no detectados en las mediciones.
 En este documento se desarrolla un programa de identificación de errores en los parámetros basado en un algoritmo que utiliza Multiplicadores de Lagrange. Este algoritmo se aplica a casos de estudio en diferentes condiciones de demanda obtenidos de los sistemas de tiempo real EMS y fuera de línea. Una vez identificado el equipo de red que presenta errores de parámetros, se plantean alternativas de cálculo para la corrección de parámetros, utilizando mediciones de equipos de medición fasorial PMUs.

Model-based fatigue crack identification in rotors integrated with active magnetic bearings

This paper investigates the behavior of a rotor-bearing system with a breathing crack, under the action of active magnetic bearings, implemented to suppress the vibration induced by the presence of the crack and the unbalance. In such a case, identification of the crack with help of vibration signals may be difficult; other observables such as the controller current may be utilized for the purpose. Linear system equations of motion together with the switching crack excitation function are used to develop the identification algorithm. The use of full spectrum analysis is made to determine the crack force coefficients of the harmonics exciting the rotor in the same and the reverse direction of the rotor spin. Usage of these coefficients in the identification algorithm estimates the viscous damping, disc unbalance and additive crack stiffness. The algorithm has been tested for measurement noise and bias errors in system parameters, for robustness. In practical terms, the situation analyzed in this paper relates to identification of crack and other parameters in a rotor integrated with an active magnetic bearing.

Robust space time processing based on bi-iterative scheme of secondary data selection and PSWF method

Prolate spheroidal wave function (PSWF) method could improve the target detection performance for space-time adaptive processing (STAP) in nonhomogeneous environment. However, it may be ineffective with system parameter error. In this paper, we correct the system parameter with clutter spectrum analysis. Since contaminated samples contained in the secondary data set have detrimental impact on this spectrum analysis, the traditional sample selection method of generalized inner production (GIP) is combined with PSWF method, and then a bi-iterative scheme is proposed. Firstly, the system parameter for PSWF is estimated via the analysis of spectrum image, which is constructed with the secondary data set. Then, the covariance matrix is derived by PSWF method with the estimated parameter. Thirdly, the GIP sample selection technique is implemented with the PSWF covariance matrix, and the secondary data set would be updated. Repeat these steps until a stable parameter is obtained. Several vital issues such as how to estimate the parameter with real data and why the precision of covariance matrix could be improved during the iteration are analyzed. In the end, the validity of the proposed algorithm is substantiated by practical and simulation results.

Model-Based Switching-Crack Identification in a Jeffcott Rotor With an Offset Disk Integrated With an Active Magnetic Bearing

Vibration characteristics of a cracked Jeffcott rotor with an offset disk under the action of an active magnetic bearing (AMB), implemented to improve the radial positioning of the rotor, has been studied. Presence of the AMB suppresses the vibration induced due to the crack and unbalance; identification of the crack could be made by utilizing the vibration signal in conjunction with the controller current of the AMB. A four degrees-of-freedom (DOF) cracked rotor is modeled considering the gyroscopic effect due to the offset disk and a switching crack excitation function (SCEF) to introduce the breathing of crack. The dynamic condensation is applied to eliminate rotational displacements, which would pose practical difficulty in accurate measurement, from the system equations of motion (EOM) to develop an identification algorithm. Frequency domain transformation of the EOM is made with the help of the full spectrum analysis. An algorithm developed with the purpose of crack identification in the form of additive crack stiffness estimates the viscous damping, disk unbalance, and AMB constants as well. The algorithm has been tested for the measurement noise (in the displacement and the current) and bias errors in system parameters, and found to be robust.

Analysis of the MPC Using in the Control of a Mechatronic System with Flexible Elements

The analysis of negative impact of flexible mechatronic system parameter error and its reduction is presented in this contribution. The MPC method is proposed to use for reduction of double notch filter insufficient effect, which was initially integrated into system for flexible joint parasitic frequencies elimination. Simulation experiments results – response of system angular velocity and control process quality analysis confirmed the correctness of proposition of MPC controller using.

Distributed Model Predictive Control of a Wind Farm for Optimal Active Power ControlPart II: Implementation With Clustering-Based Piece-Wise Affine Wind Turbine Model

This paper presents distributed model predictive control (D-MPC) of a wind farm for optimal active power control using the fast gradient method via dual decomposition. The objectives of the D-MPC control of the wind farm are power reference tracking from the system operator and wind turbine mechanical load minimization. The optimization of the active power control of the wind farm is distributed to the local wind turbine controllers. The D-MPC developed was implemented using the clustering-based piece-wise affine wind turbine model. With the fast gradient method, the convergence rate of the D-MPC has been significantly improved, which reduces the iteration numbers. Accordingly, the communication burden is reduced. A wind farm with ten wind turbines was used as the test system. Case studies were conducted and analyzed, which include the operation of the wind farm with the D-MPC under low and high wind conditions, and the dynamic performance with a wind turbine out of service. The robustness of the D-MPC to errors and uncertainties was tested by case studies with consideration of the errors of system parameters.

Blind Received Signal Strength Difference Based Source Localization With System Parameter Errors

The problem of passive source localization has been extensively studied due to its many applications in signal processing and wireless communications. Signal strength-based localization methods have the advantages of low cost and simple implementation. In this paper, blind source localization with unknown transmit power and unknown path loss exponent is considered based on the received signal strength difference (RSSD). A nonlinear RSSD-based model is formulated for systems perturbed by noise. Solutions obtained using conventional least squares methods suffer from significant performance degradation as they only consider errors in the data vector. Thus, an extended total least squares (ETLS) method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relationship between the observation matrix and data vector. The nonlinear and nonconvex RSSD-based localization problem is then transformed to an ETLS problem with fewer constraints. This is transformed to a convex semidefinite programming (SDP) problem using relaxation. The corresponding ETLS-SDP method is extended to the case with an unknown path loss exponent to jointly estimate the unknown source location and path loss exponent without resorting to transmit power estimation which is sensitive to errors. The mean squared error of the proposed ETLS method is obtained and the corresponding Cramér-Rao lower bound (CRLB) is derived as a performance benchmark. Performance results are presented that show that the RSSD-based ETLS-SDP method attains the CRLB for a sufficiently large signal-to-noise ratio (SNR).

Distributed Detection in Coexisting Large-Scale Sensor Networks

This paper considers signal detection in coexisting wireless sensor networks. We characterize the aggregate signal and interference from a Poisson random field of nodes and define a binary hypothesis testing problem to detect a signal in the presence of interference. For the testing problem, we introduce the maximum likelihood (ML) detector and simpler alternatives. The proposed mixed-fractional lower order moment detector is computationally simple and close to the ML performance, and robust to estimation errors in system parameters. We also derived asymptotic theoretical performances for the proposed simple detectors. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the receivers.

Optical System Error Analysis and Calibration Method of High-Accuracy Star Trackers

The star tracker is a high-accuracy attitude measurement device widely used in spacecraft. Its performance depends largely on the precision of the optical system parameters. Therefore, the analysis of the optical system parameter errors and a precise calibration model are crucial to the accuracy of the star tracker. Research in this field is relatively lacking a systematic and universal analysis up to now. This paper proposes in detail an approach for the synthetic error analysis of the star tracker, without the complicated theoretical derivation. This approach can determine the error propagation relationship of the star tracker, and can build intuitively and systematically an error model. The analysis results can be used as a foundation and a guide for the optical design, calibration, and compensation of the star tracker. A calibration experiment is designed and conducted. Excellent calibration results are achieved based on the calibration model. To summarize, the error analysis approach and the calibration method are proved to be adequate and precise, and could provide an important guarantee for the design, manufacture, and measurement of high-accuracy star trackers.