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In the implementation of active or semi-active control systems, it is necessary to process the measured signals because they are not perfect in reality. At present, the current energy-dissipating method for controlling semi-active dampers is flawed because of some restrictions on processing and measuring the signals. Thus, a detection methodology of signal control is proposed in this research based on the direction of structural motion; a velocity estimating calculator is developed by using the least-square polynomial regression. Comparison of the analytical results and experimental data confirms that the proposed calculator is effective in predicting when to switch the moving direction of a semi-active damper. It can detect when the direction of the structure motion reverses as well as when to compensate the poor influence on the performance of a semi-active damper caused by the delayed response. Additionally, the noise of displacement signal will not affect the phase difference of predictive signals.

Bifurcation morphing created by means of nonlinear feedback excitation is a vibration-based method for sensing. In this work, several new studies are presented to connect previously demonstrated theory to increasingly more practical applications. In particular, in the process of designing nonlinear feedback auxiliary signals, time delays in the circuitry are unavoidable. Advantages as well as possible side effects and disadvantages of time delays are discussed. Furthermore, additional time delay is considered as a new design parameter. Increasing the time delay has advantages such as enhanced robustness and sensitivity, which are demonstrated computationally. Moreover, calibration using multiple sensor locations is discussed. A clamped-free cantilever beam structure is modeled and used for computational validation. The beam model resembles cantilever-based resonant sensor systems. Thus, potential applications of the new algorithm are discussed and the results stress the importance of nonlinear features for enhancing sensing performance in mechanical sensors without structural modifications.

In this paper, an active controller for buildings with bilinear hysteresis and time delay is studied. The bilinear hysteretic model is treated as a stiffness restoring force. By using specific transformation and augmentation of state parameters, the equation of motion of the system with an explicit time delay is transformed into a standard state space where there is no explicit time delay. A linear quadratic Gaussian control method is proposed for the controller design with time delay. The method is verified with numerical simulations of three-story and 20-story buildings. Comparison study of simulation results indicates that the control performance will deteriorate if the time delay is not taken into account in the control design. The proposed time-delay controller not only effectively compensate the time delay for better control effectiveness, but it also works well with both small and large time-delay problems.

Nonlinear resonance response of an electrostatic-actuated nanobeam is controlled by using a delayed axial electrostatic force with near-half the natural frequency. A graphene sensor pasted on the surface of the nanobeam is used to extract the vibration voltage signal. An axial-delayed capacitive controller is designed to produce delayed axial force to control the nonlinear vibration of the nanobeam. The vibration voltage signal from the graphene sensor is input to the axial-delayed capacitive controller to attenuate the nonlinear vibration of the nanobeam. The dynamic response of the resonator is investigated by using the method of multiple scales directly. The sufficient conditions of guaranteeing the system stability and the saddle-node bifurcation are studied. The attenuation ratio is defined as the ratio of the peak amplitude of the nonlinear vibration system with control to that without control. A critical feedback gain is given, which can shift the frequency–amplitude curves from the nonlinear vibration to a linear vibration. An optimal method in which the attenuation ratio is taken as objective function and the aforementioned sufficient conditions as the constraint conditions is given to calculate the optimal feedback gains. Numerical simulations are conducted for uniform nanobeams.

In this research, the periodic response and stability of a nonlinear maglev system under the combined effects of steady and unsteady aerodynamic lifts is investigated, considering time delay in the feedback control loop. First, a nonlinear maglev system with a single levitation point that accounts for the nonlinearity of the electromagnetic force, time delay in the feedback control loop, and effect of aerodynamic lift is established. Then the periodic solutions of the maglev system with aerodynamic lift and time delays are obtained by an incremental harmonic balance analysis, in which the explicit time-delay action matrices used indicate that the effect of time delay on the response of the maglev system is periodic. The stability of the periodic solutions based on a finite difference continuous time approximation method and Floquet theory is studied, from which the critical time delay is obtained. Also, the relationship between the periodic vibration amplitude and the time delay is examined, along with the steady aerodynamic lift coefficient, and frequency of the unsteady aerodynamic lift, as well as the variation of critical delay with respect to the position feedback and velocity feedback with the control gain parameters. In addition, the stability boundary for the simultaneous time-delayed position and velocity feedback is obtained.

A vibration control signal sensing method is proposed utilizing the grid electrode displacement sensitive effect of field-effect transistors. The signal sensing method is applied to nonlinear resonance delay control of a nanobeam that is used as the core component of nano–microdevices. The nonlinear vibration dynamical model of the nanobeam based on the field-effect tube sensing is established and the differential equation of motion with time delay control is presented. The amplitude frequency response equation and phase frequency response equation of the nanobeam are obtained by analyzing the first-order approximate solution of the primary and superharmonic vibration of the nonlinear equation with multi-scale method. The vibration feedback gain and time delay can affect the vibration amplitude and nonlinear behavior of the nanobeam. The nonlinear vibration of the nanobeam can be adjusted and effectively controlled by selecting appropriate feedback gains and time delays.

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method.

Hopf bifurcation, as the most representative dynamic bifurcation, is closely related to the stability of many engineering structures. In this work, the stochastic Hopf bifurcation (SHB) of a controlled quasi-integrable Hamiltonian system (H.S.) of multi-degree-of-freedom (MDOF) is investigated, where the system is subjected to wide-band noise and controlled by a Fractional-order Proportional-Derivative (FOPD) controller with time delay. By decoupling FOPD control force and simplifying it without time delay, the averaged Itô differential equations of the approximated system are derived with the technique of stochastic averaging. Then, the average bifurcation parameter expression of system is obtained, which can determine the criterion of the SHB deduced by the FOPD control force. Last, an illustration of coupled Rayleigh oscillators is given to demonstrate the validity of the procedure. The influences of time delay, noise intensities and fractional order on the system SHB are discussed.

Real-time hybrid simulation (RTHS) is recently applied to study the vibration of the vehicle–bridge coupling system, where bridges and the vehicle are the numerical and experimental substructures respectively. Inevitable time delay of the boundary loading imposed to the experimental substructure will greatly affect the accuracy and stability of RTHS. To minimize the time delay effects, this paper proposes a recursive prediction optimal (RPO) compensator based on optimal control and recursive least squares. The numerical simulation of the RTHS of the vehicle–bridge coupling system is conducted using MATLAB/Simulink. The performance of the RPO method is compared with three traditional time delay compensation methods (i.e. the polynomial extrapolation (NI), the inverse compensation (IC) and the derivative feedforward (DF)) through both open-loop and RTHS simulations. The RPO method shows the best compensation performance in the frequency range up to 20Hz.

The stability of the parametric resonance of a controlled stay cable with time delay is investigated. The in-plane nonlinear equations of motion are initially determined via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics are obtained. These equations are then utilized to investigate the effect of time delays on the amplitude and frequency-response behavior and, subsequently, on the stability of the parametric resonance of the controlled cable, that it is shown to depend on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency. The stability region of the parametric resonance is shifted, and the effects of control on the cable become worse by increasing time delay. The work plays a guiding role in the parametric design of the control system for stay cables.