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Wind and solar power are known to be highly influenced by weather events and may ramp up or down abruptly. Such events in the power production influence not only the availability of energy, but also the stability of the entire power grid. By analysing significant amounts of data from several regions around the world with resolutions of seconds to minutes, we provide strong evidence that renewable wind and solar sources exhibit multiple types of variability and nonlinearity in the time scale of seconds and characterise their stochastic properties. In contrast to previous findings, we show that only the jumpy characteristic of renewable sources decreases when increasing the spatial size over which the renewable energies are harvested. Otherwise, the strong non-Gaussian, intermittent behaviour in the cumulative power of the total field survives even for a country-wide distribution of the systems. The strong fluctuating behaviour of renewable wind and solar sources can be well characterised by Kolmogorov-like power spectra and q-exponential probability density functions. Using the estimated potential shape of power time series, we quantify the jumpy or diffusive dynamic of the power. Finally we propose a time delayed feedback technique as a control algorithm to suppress the observed short term non-Gaussian statistics in spatially strong correlated and intermittent renewable sources.

This paper examines periodic and quasi-periodic (QP) vibration-based energy harvesting (EH) in a nonlinear energy sink (NES) absorber that is coupled to an electric circuit through a piezoelectric mechanism. For this investigation, we excite the primary system by harmonic force. To this system, we add linear delayed feedback controls implementations. The complexification-averaging (CX-A) method is employed to obtain approximate solutions. The analytically observed nonlinear behavior is numerically explained. In order to establish the feasibility of the control method, the energy balance of system is investigated. To systematically analyze the dynamic behaviors of the designed system, the stability of the system is studied using the reduced equations. We obtain the saddle-node (SN) and Hopf bifurcations by selecting specific parameters to establish the presence of periodic and QP solutions, after which we build and analyze the bifurcation diagrams. We exploit a time-delay mechanism implemented in a piezoelectric network and in a primary structure to enhance EH with good performance. Also, our findings demonstrate that the combination of time delay enables the system to harvest high periodic and QP powers. The QP power is obtained over a broad range of system parameters, yielding a reliable bandwidth of the harvester far from the hysteresis bandwidth.

In this study, time-delayed feedback control is investigated for an elastically mounted rectangular prism undergoing subcritical galloping in the transverse direction, when subjected to wind excitation. The mathematical model of the galloping system under consideration is established by using the quasi-steady aerodynamic theory. The control performance in terms of the galloping onset speed of the time-delayed displacement, velocity and acceleration feedback is investigated via linear stability analysis, respectively. Subsequently, the method of multiple scales is implemented for nonlinear analysis in order to derive the analytical expression of the vibration amplitude of the galloping system and determine the criticality curve that is the boundary of the subcritical and supercritical bifurcation regions. The results show that the hybrid objective of increasing the galloping onset speed, changing the Hopf bifurcation behavior from subcritical to supercritical and reducing the amplitude of limit-cycle oscillations can be achieved by means of delayed acceleration feedback. This study provides an analytical tool and procedure for time-delayed feedback control design of such a kind of flow–structure interaction system.

In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device. Two delay feedback control methods are provided to make the new model be stable. Linear stability analysis is carried out to obtain the stability of equilibrium and the stability boundary, corresponding to the critical value of Hopf bifurcation, dividing stable and unstable regimes of equilibrium. Next, we derive explicit formulae for determining the stability of Hopf bifurcating periodic solutions and the direction of Hopf bifurcation. Finally, detailed numerical simulations using MATLAB software are presented to demonstrate the application of the theoretical results, and we also compare the efficacy of the two control forces in new friction-induced models.

A time-delayed acceleration feedback control is proposed to improve the vibration performance of a nonlinear vehicle suspension system. First, the harmonic balance method is applied to obtain the vertical acceleration amplitude of the system excited by simple harmonic road excitation. Then, taking the amplitude of the sprung mass acceleration and control force into account, the single-objective and multiple-objective optimization problems of time-delayed feedback control parameters, respectively, are discussed. Finally, the mathematical simulation is provided to verify the correctness of the optimization results. It is concluded that the nonlinear suspension with optimal time-delayed feedback control has better vibration control performance compared to passive one. The acceleration amplitude of the sprung mass is significantly reduced by the single-objective optimization of the control parameters. Moreover, when the optimal time delay is introduced, the active control force input is fewer than that without time delay. The phenomenon of energy transfer between the sprung mass and the unsprung mass is observed in some road-excitation frequencies.

An approximation-based adaptive fault-tolerant (AFT) control problem is investigated for strict-feedback non-linear systems with unknown time-delayed non-linear faults. The error surfaces restricted by prescribed performance bounds are employed to guarantee the transient performance at the moment when faults with unknown occurrence time and magnitude occur. Based on the surfaces, we design a memoryless AFT control system where the function approximation technique using neural networks is applied to adaptively approximate unknown non-linear effects and changes in model dynamics because of the time-delayed faults. It is shown from Lyapunov stability theorem that the tracking error of the proposed control system is preserved within the prescribed performance bound and converges to an adjustable neighbourhood of the origin regardless of unknown time-delayed non-linear faults.

Industrial processes often involve a long time delay, which adversely affects the stability of closed-loop control systems. The traditional Smith Predictor (SP) is a model-based controller used in processes with large time delays. The variation of system parameters and load disturbance situations are disadvantages of the traditional SP, and researchers have, therefore, proposed modified SP structures. In this paper, a design method based on the direct synthesis approach on a modified SP structure is discussed. In the design, an I-PD controller structure is used on the set-point tracking side of the SP, and a cascading PD lead–lag controller is used on the disturbance rejection side. In contrast with other studies in the literature, the use of simpler controllers enables the mathematical expressions that arise in the direct synthesis method to be significantly reduced. The proposed method is examined under the disturbance input effects for normal and parameter-changing conditions on system models with unstable second-order plus time-delay processes. The first plant model has two unstable poles, the second has one stable and one unstable pole, and the third has one unstable and one zero pole. When the results obtained using the proposed method were compared with other methods, significant improvements were achieved in terms of set-point tracking, disturbance rejection, and robustness conditions.

An odd number of real Floquet multipliers greater than unity prevents the classical time delayed feedback control from stabilizing torsion-free orbits of nonautonomous systems. This paper investigates this limitation in the context of the method of harmonic oscillators. This method aims to stabilize periodic orbits of dynamical systems through a proper coupling to a system of harmonic oscillators. The results show that the method of harmonics oscillators does not suffer from this limitation for a proper coupling condition. A practical approach of designing the coupling condition that allows stabilizing torsion-free orbits of nonautonomous systems is presented. The success of the proposed approach is demonstrated using numerical examples.

In the present paper, we consider an approximate approach for predicting the responses of the quasi-integrable Hamiltonian system with multi-time-delayed feedback control under combined Gaussian and Poisson white noise excitations. Two-step approximation is taken here to obtain the responses of such system. First, based on the property of the system solution, the time-delayed system state variables are approximated by using the system state variables without time delay. After this approximation, the system is converted to the one without time delay but with delay time as parameters. Then, stochastic averaging method for quasi-integrable Hamiltonian system under combined Gaussian and Poisson white noises is applied to simplify the converted system to obtain the averaged stochastic integro-differential equations and generalized Fokker–Planck–Kolmogorov equations for both non-resonant and resonant cases. Finally, two examples are worked out to show the detailed procedure of proposed method for the illustrative purpose. And the influences of the time delay on the responses of the systems are also discussed. In addition, the validity of the results obtained by present method is verified by Monte Carlo simulation.

Background The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients. Methods We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients. Results The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group. Conclusions The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.