Vibration active control of structure with parameter perturbation using fractional order positive position feedback controller

Niu, Wenchao; Li, Bin; Tao, Xiaofeng; Wang, Wei

doi:10.1016/j.jsv.2018.05.038

Cited by 29 publications

(11 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The linear system is given by Equation ( 23) is topologically equivalent to the nonlinear system given by Equation ( 19) as long as the eigenvalues are hyperbolic. Thus, the stability of the nonlinear system given by Equation ( 19) depends on the eigenvalues of the obtained Jacobian matrix in Equation (23). Accordingly, the eigenvalues of the linear system given by Equation ( 23) can obtain as follows:…”

Section: Steady-state Vibration and Stability Investigationsmentioning

confidence: 99%

“…Recently, the fraction-order PPF controller was introduced as a new strategy to suppress the nonlinear vibrations of the nonlinear dynamical systems [22][23][24]. Marinangeli et al [22] applied both the conventional and the fractional-order PPF controllers to suppress the modal vibrations of a composite plate system with free-edges.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical and experimental results confirmed that the fractional-order PPF controller is the best control algorithm for suppressing the modal vibrations without spillover occurrence. Niu et al [23] studied the vibration control of a vertical tail system utilizing both the PPF controller and fractional-order PPF controller. The authors showed that the fractional-order controller is more efficient in suppressing both the periodic and random vibration responses.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

View full text Add to dashboard Cite

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

show abstract

Section: Steady-state Vibration and Stability Investigationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

View full text Add to dashboard Cite

show abstract

“…For different resonance cases the NIPPF control is applied to reduce the vibrations of duffing oscillator system near primary and super-harmonic resonances [19], through primary and internal resonance [20]. Omidi et al [21,22] presented three kinds of control to suppress the vibrations of vibrating systems such that, the Integral resonant controllers (IRC), PPF controllers and the non-linear Integral Positive Position feedback (NIPPF). The eminent type of decreasing the vibrations is NIPPF type .The NIPPF controller is used for deceasing the vibrations of the model of micro-electro-mechanical system near primary resonance and one-to-one internal resonance [23,24].…”

Section: Introductionmentioning

confidence: 99%

Eliminate the Nonlinear Oscillations of the Modified duffing Equation by using the Nonlinear Integrated Positive Position Feedback

Rahman

2022

ARJOM

View full text Add to dashboard Cite

In this article, the nonlinear integrated positive position feedback (NIPPF) control adds to a nonlinear dynamical system modeled as the well known Duffng oscillators. This control is proposed to mitigate system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow- ow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability of the steady-state solution is presented and studied applying frequency response equations near the simultaneous primary and internal resonance cases. Before and after (NIPPF) control the nonlinear systems' steady-state amplitude are examined, the comparison is made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves.

show abstract

“…Although this phenomenon will not destabilize the system if the feedback gain is chosen appropriately, reducing its effect will greatly enhance the performance of the system. One way to reduce such effect is to transform the classical PPF compensator into fractional format (Marinangeli et al, 2018; Niu et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

A novel design of positive position feedback controller based on maximum damping and H₂ optimization

Paknejad

Zhao

Osee

et al. 2020

Journal of Vibration and Control

View full text Add to dashboard Cite

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 [Formula: see text] 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.

show abstract

Vibration active control of structure with parameter perturbation using fractional order positive position feedback controller

Cited by 29 publications

References 27 publications

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Eliminate the Nonlinear Oscillations of the Modified duffing Equation by using the Nonlinear Integrated Positive Position Feedback

A novel design of positive position feedback controller based on maximum damping and H₂ optimization

Contact Info

Product

Resources

About

Vibration active control of structure with parameter perturbation using fractional order positive position feedback controller

Cited by 29 publications

References 27 publications

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Eliminate the Nonlinear Oscillations of the Modified duffing Equation by using the Nonlinear Integrated Positive Position Feedback

A novel design of positive position feedback controller based on maximum damping and H2 optimization

Contact Info

Product

Resources

About

A novel design of positive position feedback controller based on maximum damping and H₂ optimization