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It has been commonly assumed that an inerter–stiffness–damping isolator mounts on a rigid foundation, however, there exists a strong interaction among the vibration source, isolator, and the base structure for systems with flexible or nonrigid bases. This paper investigates a system consisting of an isolation object, mounted on flexible base plate through an inerter–spring–damping isolator. The steady-state response of the plate-exerted point force excitation can be obtained by using the eigenfunction expansion theorem and expressed by the eigenfunctions and natural frequencies of the system. The four-pole parameter of the inerter can be modeled from the formula calculation or its properties. The transmissibility relation of the proposed system is obtained by using the four-pole parameter theory, which is validated by creating the simulation model in Abaqus software. The power transmission ratio as an isolation performance index is proposed by the mobility relationship among the isolation object, the isolator, and the base. The novelty of this study is that the vibration transmissibility with the flexible base has a much better roll-off rate and anti-resonance peak than that of the rigid base in the high-frequency range, although the resonant peak is generated. A comprehensive parameter analysis shows that the isolation performance can be designed and adjusted by the thickness, material of the plate and the position of the isolator. The effects of feedback control on the resonant peak mitigation of the proposed system are discussed in detail based on Resonant Control, Positive Position Feedback, and Fractional Order Positive Position Feedback. The H2 optimization criterion is employed to obtain the optimal damping parameters of positive position feedback. [ABSTRACT FROM AUTHOR]

Flexible vibration has a great impact on flexible spacecraft attitude control, which will reduce the pointing accuracy of the spacecraft platform and bring severe challenges to the design of a high-precision attitude control system for flexible spacecraft. Aiming at the problem of attitude and vibration coupling control of flexible spacecraft, an anti-unwinding attitude coupling controller using the positive position feedback (PPF) control is proposed in this paper. The model compensation control term is constructed based on the prior information to improve the tracking performance. The proposed attitude coupling control method can effectively suppress the flexible vibration while achieving more accurate attitude control. The obtained closed-loop system under the proposed control scheme is asymptotically stable, which is proved by the Lyapunov stability theory. The numerical simulation illustrates that the proposed method can effectively improve the attitude control accuracy of the flexible spacecraft and is capable of large-angle attitude maneuver control because of its prominent performance in attitude tracking and its unwinding-free performance. • Coupling control for flexible spacecraft. • Active vibration control using positive position feedback. • Model compensation control term is constructed to improve the dynamic performance. • The obtained closed-loop system achieves the asymptotic stability and anti-unwinding performance. [ABSTRACT FROM AUTHOR]

This article presents the design of a nonlinear hybrid controller for an underactuated Duffing oscillator with 2 degrees of freedom. The main control purpose is to reduce the frequency‐response to specific resonant‐frequencies while maintaining its robustness to external disturbances. The resulting hybrid controller uses sliding mode control (SMC) with a positive position feedback (PPF) scheme. This is structured such that the SMC provides system robustness and tracking, while the PPF allows damping specific resonant frequencies. The system was evaluated using frequency sweeps in terms of acceleration in the second degree of freedom. In this case, the control input is applied through the first degree of freedom. Moreover, multi‐objective optimization is implemented to tune of the control parameters. Simulation results show that the system response to external vibrations can be reduced up to 83.88% by using the proposed PPF + SMC scheme. [ABSTRACT FROM AUTHOR]

Positive position feedback is an attractive control law for the control of plants having no high frequency roll-off. The tuning of the parameters of the positive position feedback to obtain the desired closed-loop performance is quite challenging. This paper presents a technique to design the positive position feedback controller with the optimal damping. The technique is demonstrated on a single degree-of-freedom system. The poles of the positive position feedback are tuned using the method of maximum damping, which states that the maximum damping is achieved when both closed-loop poles of the system are merged. The parameters of the positive position feedback are dependent on the desired target damping in the closed-loop system. However, arbitrary choice of target damping results in high response at the frequencies lower than the tuning frequency. The optimal value of the target damping is obtained by minimizing the H 2 norm of the closed-loop transfer function of the system. The influence of the various parameters of the positive position feedback on the closed-loop response of the system is also studied. Finally, the experiments are conducted to verify the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

• Linear and nonlinear positive position feedback controllers are investigated. • Closed-form expressions of the optimal parameters of the controllers are obtained. • The nonlinear controller outperforms its linear counterpart for a Duffing oscillator. • The analytical study is validated experimentally. This paper investigates the potential of using a nonlinear positive position feedback controller for vibration mitigation of a Duffing oscillator. The proposed controller is designed based on the principle of similarity which states that anti-vibration devices should be governed by the same equations as those of the host structure. Closed-form expressions for the H ∞ optimal control parameters that minimise the maximal response of the structure are firstly derived for the linear positive position feedback controller and then extended to the nonlinear counterpart. The harmonic balance method is employed to approximate the analytical solutions. Both numerical simulations and experimental validations are performed to demonstrate the proposed control strategy. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a time-delayed positive position feedback (PPF) controller is applied to reduce the nonlinear oscillations of the dynamical system of a rotating blade. The main system is coupled to the controller whose natural frequency is approximately equal to the natural frequency of the main system. The main system has two oscillatory modes that are found to be powerfully linearly coupled. The approximate nonlinear dynamical behavior is studied and analyzed by applying the multiple time scales method. The effects of the time delay are investigated to indicate the safe region of operation. Time history and different curves are included to show the effectiveness of the controller. Eventually, validation curves are given to estimate the degree of closeness between the analytical and numerical solutions. Highlights • Actively controlling the vibrations of a compressor rotating blade. • Applying multiple time scales method to analyze its nonlinear dynamics. • Investigating the effects of different parameters and time delays on its behavior. • Extracting the optimum conditions for the best performance. • Validating the results with numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between three different controller methods added to a cracked beam under the action of a harmonic excitation. Those three controllers are Positive Position Feedback (PPF), Integral Resonant Control (IRC) and Nonlinear Integral Positive Position Feedback (NIPPF) which be added to the measured system. The multiple scales method (MSM) is applied for getting the approximate solution on behalf of measured design. This method is effective to solve the major equations of measured system. Stability and effect of different coefficients of the system are demonstrated. The approximate solution response is established via numerical simulation outcome. NIPPF controller is the best one gives better results compared to the other two controllers in decreasing the high amplitude of the system. Comparison between mathematical solution and numerical simulation are considered. Relationship of formerly available papers is considered. [ABSTRACT FROM AUTHOR]

A Fractional-Order Positive Position Feedback (FOPPF) controller is developed by transforming the integer-order exponent of the Positive Position Feedback (PPF) controller into a fractional format to increase the number of designable parameters. The sensitivity of these fractional-order exponents is investigated to assess their influence on the behavior of the FOPPF controller in frequency domain. An optimal design method of FOPPF controller is presented by taking account of the uncertainty of object structure, and constructing an objective function. This objective function is the weighted sum of the suppression ratio of the peak value of power spectral density and the suppression ratio of the root-mean-square value of the random response in the target frequency band. The performance of this controller is analyzed by numerical simulation and experiment using a vertical tail attaching macro fiber composite piezoelectric actuator. Results indicate that a wider band of effective phase compensation is obtained using the FOPPF controller than using the PPF one, and a higher robustness is achieved as well. The FOPPF controller is more effective on suppressing the both periodic and random vibration responses comparing with the PPF and modified PPF controller. [ABSTRACT FROM AUTHOR]

Within this article, an active Positive Position Feedback (PPF) controller is applied to suppress the horizontal vibration of a nonlinear magnetic levitation system. The purposed controller is designed to have a natural frequency equal to the excitation frequency of the magnetic levitation system. The multiple scales perturbation method is adopted to derive two nonlinear algebraic equations that describe the whole system vibration amplitudes in terms of the system and controller parameters. The solution's stability is studied utilizing the indirect method of Lyapunov. Then, numerical validations for the obtained analytical results are performed. The analyses illustrated a good agreement between the numerical and analytical solution, and showed the high efficiency of the PPF controller in suppressing the system vibrations in the presence of primary resonance and 1:1 internal resonance. Eventually, a comparison with previously published work is included. [ABSTRACT FROM AUTHOR]

High pointing accuracy and stabilization are significant for spacecrafts to carry out Earth observing, laser communication and space exploration missions. However, when a spacecraft undergoes large angle maneuver, the excited elastic oscillation of flexible appendages, for instance, solar wing and onboard antenna, would downgrade the performance of the spacecraft platform. This paper proposes a coupling control method, which synthesizes the adaptive sliding mode controller and the positive position feedback (PPF) controller, to control the attitude and suppress the elastic vibration simultaneously. Because of its prominent performance for attitude tracking and stabilization, the proposed method is capable of slewing the flexible spacecraft with a large angle. Also, the method is robust to parametric uncertainties of the spacecraft model. Numerical simulations are carried out with a hub-plate system which undergoes a single-axis attitude maneuver. An attitude control testbed for the flexible spacecraft is established and experiments are conducted to validate the coupling control method. Both numerical and experimental results demonstrate that the method discussed above can effectively decrease the stabilization time and improve the attitude accuracy of the flexible spacecraft. [ABSTRACT FROM AUTHOR]

This article presents a compensated positive position feedback strategy for active control of flexible structures with piezoelectric actuators. In the proposed compensated positive position feedback method, a negative feedback compensator is involved to remedy the deficiency of traditional positive position feedback and to introduce roll-off characteristic at low frequencies. Thus, compensated positive position feedback controllers can be developed with minimal influences on lower order modes and cause no steady-state error to the controlled system. For demonstration purpose, the design processes and the effectiveness of the compensated positive position feedback method are illustrated by active control of a cable net structure with integrated piezoelectric stacked actuators. The numerical simulations demonstrate that compared to the conventional positive position feedback method, the proposed compensated positive position feedback approach overcomes the fundamental defects of frequency shift and spillover into lower order modes and achieves the goal of step-tracking with zero steady-state error. These comparative results confirm the efficacy and superiority of the proposed compensated positive position feedback methodology in active control of flexible structures. [ABSTRACT FROM AUTHOR]

In this paper, Active Vibration Control (AVC) of a rectangular carbon fibre composite plate with free edges is presented. The plate is subjected to out-of-plane excitation by a modal vibration exciter and controlled by Macro Fibre Composite (MFC) transducers. Vibration measurements are performed by using a Laser Doppler Vibrometer (LDV) system. A fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF. MFC actuator and sensor are positioned on the plate based on maximal modal strain criterion, so as to control the second natural mode of the plate. Both integer and fractional-order PPF allowed for the effective control of the second mode of vibration. However, the newly proposed fractional-order controller is found to be more efficient in achieving the same performance with less actuation voltage. Moreover, it shows promising performance in reducing spillover effect due to uncontrolled modes. [ABSTRACT FROM AUTHOR]

The active car suspension system is presented here to suppress the vibration of the car by applying proportional derivative (PD) and positive position feedback (PPF) controllers with time delay. The control signal output of the controller is applied electrically to the magneto-rheological (MR) damper or Electrical-rheological (ER) damper which is attached parallel to the passive components to improve the suppression of the vibration. The electrical control signal is produced by electronic circuits or programmable logic controller and the two-position sensor feedback signal which are connected to the controller. The approximate solutions of PD and PPF suspension systems are obtained by applying multiple time scales perturbation method. The effects of parameters variation of both the system and the controllers are investigated to achieve the best performance. Simulation results show good performance of the designed controllers. [ABSTRACT FROM AUTHOR]

Positive position feedback is an important control vibration algorithm as it exhibits very high reduction ratios but at a specific bandwidth. Out of this bandwidth, there exist two peaks with high amplitudes, which is considered the major drawback of this controller. In this paper, we are going to improve its performance by suppressing the two peaks to acceptable levels. That can be done by coupling additional nonlinear saturation controllers (NSC) with the main system to impose a V-curve at each one of the peaks. The V-curves positions are controlled by adjusting the natural frequencies of the NSCs. The overall behaviors of the system with and without control are clarified by the extracted equations via the multiple time scales analysis. Time history and different response curves of the controlled system are included for showing the controller effect. Eventually, validation curves and comparison with previously work are included. [ABSTRACT FROM AUTHOR]

This paper presents the large angle attitude manoeuvre control design of a single-axis flexible spacecraft system that consists of a central rigid body and a cantilever beam with bonded piezoelectric sensor/actuator pairs as a flexible appendage. The proposed control strategy combines the attitude controller designed by the adaptive robust control technique with the active vibration controller designed by the positive position feedback control method. The desired angular position of the spacecraft is planned and an adaptive robust attitude control approach based on a projection type adaptation law is proposed to track the planned path and to achieve precise attitude manoeuvre control. Meanwhile, the positive position feedback control method is applied to actively increase the damping of the flexible appendage and to suppress the residual vibration induced by manoeuvre. Improved transient and steady state performance during and after large angle attitude manoeuvre can be both achieved by integration of the technical merits of all these control methods. Analytical and numerical results illustrate the effectiveness of this approach. [ABSTRACT FROM AUTHOR]

The Butterworth filter is known to have maximally flat response. Incidentally, the same response is desired in precise positioning systems. This paper presents a method for obtaining a closed-loop Butterworth filter pattern using common control schemes for positioning applications, i.e. Integral Resonant Control (IRC), Integral Force Feedback (IFF), Positive Position Feedback (PPF), and Positive Velocity and Position Feedback (PVPF). Simulations show a significant increase in bandwidth over traditional design methods and verify the desired pole placement is achieved. The simulations also show a significant limitation of the achievable bandwidth in the case of IRC, IFF, and PPF. For this reason, only PVPF is considered in experimental analysis. Experiments are performed using a two-axis serial kinematic nanopositioning stage. The results show a significant improvement in bandwidth and increased positioning accuracy, specifically at the turn-around point. This allows a greater portion of the scan to be used and improved positioning accuracy at high scanning speeds.

The attitude regulation for a liquid-filled spacecraft in the presence of low frequency sinusoidal disturbance is considered in this paper. The liquid-filled spacecraft is modelled as a rigid body attached with a simple pendulum. A novel control scheme is proposed, which is composed of Active Disturbance Rejection Control (ADRC), Positive Position Feedback (PPF), Extended State Observer (ESO) and Singular Spectrum Analysis (SSA). The unknown sloshing mode could be estimated from the combined ESO and SSA, and accordingly ADRC and PPF controller is designed for the stabilization of the spacecraft. Particularly, the parameters of the disturbance are not required as long as its frequency is lower than the sloshing one. The proposed approach could provide stabilization for the spacecraft, rejection for the disturbance, and active damping for the sloshing. Its effectiveness is validated by numerical simulations. [ABSTRACT FROM AUTHOR]

Dynamic vibration and quasi-static deformation will occur simultaneously for flexible space structures subjected to sudden thermal loads. In this paper, the integrated controller based on modified positive position feedback (PPF) compensator is proposed as an innovative controller for active deformation reduction in flexible space trusses. The controller uses the concept of positive acceleration feedback combined with integral position feedback to provide effective vibration suppression of multiple modes and compensator of quasi-static deformation. To solve the problem of placement optimization for both sensors and actuators, the discrete glowworm swarm optimization (GSO) algorithm based on genic binary coding is suggested. A cantilevered truss is taken as an example for numerically evaluating the performance of the controller for thermally induced deformation control. Numerical results demonstrate that the discrete GSO algorithm is feasible in solving the combinatorial optimization problem. And the proposed controller is significantly effective in controlling both steady-state deformation and transient vibration. [ABSTRACT FROM AUTHOR]

In this paper, a time-delayed positive position feedback controller is proposed to reduce the horizontal vibration of a magnetically levitated body subjected to multi force excitations. This controller is coupled to the main system with 1:1 internal resonance. The method of multiple scales perturbation technique is employed to obtain an approximate solution which clarifies the nonlinear behavior for both amplitude and phase of the whole system. The effects of time delay magnitude are investigated to indicate the safe region of operation. Validation curves are involved to compare the approximate solution with the numerical simulation. [ABSTRACT FROM AUTHOR]

Multimode modified positive position feedback (MMPPF) is proposed to suppress vibrations at multi-resonance frequencies in flexible collocated structures. Typically, flexible structures have large numbers of active modes in low frequency bandwidths, which make them susceptible to multi-frequency resonant vibrations. Hence, it is essential for the controller to have effective suppression on all participating modes. The MMPPF controller consists of a first- and a second-order compensator for each mode, as they are all set parallel for all active modes. Because of suppression performance sensitivity to controller gain parameters, proper gain selection is essential. Here, the linear quadratic regulator (LQR) approach and a proposed method called M-norm are used for gain optimization of the MMPPF controller. The optimized controller is then evaluated experimentally using a cantilever beam, enhanced by a piezoelectric actuator. According to the obtained results, the MMPPF controller reduces vibration amplitudes to the expected lower level, under both LQR and M-norm optimization methods. In some cases, vibration amplitude at the place of piezo-actuator is reduced to even less than the vibration amplitude level of the disturbance input at clamped end. [ABSTRACT FROM AUTHOR]

The superconducting heavy ion linear accelerator at Inter-University Accelerator Centre Delhi has been in operation since 2007. Initially, the superconducting niobium Quarter Wave Resonators (QWRs) in the linac were phase locked using a combination of electronic and mechanical controls which operated in fast (~10 μsec) and slow (~sec) time scales respectively. In this scheme, fast control was achieved through dynamic phase control whereas slow control of the frequency was done through the niobium tuner bellows installed at the drift tube end of the resonator and flexed using helium gas to change the resonance frequency. In order to improve the dynamics of this control system, an alternate scheme using piezoelectric actuator, instead of helium gas, to flex the same niobium bellows, has been implemented in the QWRs of the second and third accelerating modules of the linac. The piezoelectric actuator is used in closed loop along with the fast dynamic phase control scheme. The feedback loop of the piezoelectric control includes a dual control scheme - an integral control loop to arrest the slow drift, and the positive position feedback (PPF) based control loop to damp the microphonics. This control scheme has been found to arrest slow drifts in the resonator frequency more tightly along with damping of low frequency microphonics (~few tens of Hz) picked up by the resonator from its surrounding environment. This has substantially eased the load from the fast electronic control, resulting in the reduction of the radio frequency (RF) power requirement during operation. In addition, it has improved the stability of phase and amplitude of the QWRs. The details of the new scheme along with results obtained during the online run of the linac for beam acceleration are presented. [ABSTRACT FROM AUTHOR]

This paper introduces Nonlinear Modified Positive Position Feedback (NMPPF) control approach for nonlinear vibration suppression at primary resonance. Nonlinearity in the system is due to large deformations caused by high-amplitude disturbances, while this control approach is applicable to all types of nonlinearities in resonant structures. NMPPF controller consists of a resonant second-order nonlinear compensator, which is enhanced by a lossy integrating compensator. The two compensators create a combination of exponential and periodic control inputs, which needs innovative time scaling for using the Method of Multiple Scales to obtain the analytical solution of the closed-loop system. The results of the analytical solution for the closed-loop NMPPF controller are presented and compared with the result of the conventional PPF controller. Effects of the control parameters on the system response are comprehensively studied by parameter variations. The approximate solution is then verified using numerical simulations. According to the results, the NMPPF controller provides a higher level of suppression in the overall frequency domain, as the peak amplitude at the neighborhood frequencies of the primary mode is reduced by 44 %, compared to the PPF method. The tunable control parameters also give more flexibility to create the expected type of system response. [ABSTRACT FROM AUTHOR]

This work deals with the structural and dynamic analysis of a building-like structure consisting of a three-story building with one passive/active vibration absorber. The base of the structure is perturbed using a shaker, providing excitation forces and noisy excitations emulating ground transportation, underground railways and earthquakes, quite common in Mexico City. It is considered a realistic seismic record of 8.1Mw occurred at Mexico City, containing some resonant frequencies of the structure. The mechanical structure is modeled using Euler-Lagrange methodology and validated using experimental modal analysis techniques. The active control scheme is synthesized to actively attenuate the noise and vibration system response, caused by noisy excitation forces acting on the base, by employing Multiple Positive Position Feedback and Sliding Mode Control to improve the closed-loop system response and, simultaneously, attenuate three vibration modes. Simulation and experimental results describe the overall system performance. [ABSTRACT FROM AUTHOR]

In this paper, a study for positive position feedback controller is presented that is used to suppress the vibration amplitude of a nonlinear dynamic model at primary resonance and the presence of 1:1 internal resonance. We obtained an approximate solution by applying the multiple scales method. Then we conducted bifurcation analyses for open and closed loop systems. The stability of the system is investigated by applying the frequency-response equations. The effects of the different controller parameters on the behavior of the main system have been studied. Optimum working conditions of the system were extracted to be used in the design of such systems. Finally, numerical simulations are performed to demonstrate and validate the control law. We found that all predictions from analytical solutions are in good agreement with the numerical simulation. A comparison with the available published work is included at the end of the work. [ABSTRACT FROM AUTHOR]