Nonlinear positive position feedback control for mitigation of nonlinear vibrations

Abstract

a b s t r a c tThis 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 1 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.vibration absorbers can be designed as a mirror of the primary structures i.e. nonlinear vibration absorbers should possess the same nonlinearities as those in the primary systems. This design principle is also referred to as the principle of similarity. It was reported that nonlinear primary systems attached with nonlinear vibration absorbers designed based on the principle of similarity behave in a similar fashion as their linear counterpart. Although this concept is promising, it may become cumbersome and expensive to realise them in practice using passive means for complex nonlinear primary systems.On the other hand, in an active approach it is attempted to introduce the desired nonlinear control forces using sensors and actuators. This may yield a nonlinear anti-vibration system that is less complex. Various types of active controllers have been investigated for vibration attenuation of nonlinear systems [16][17][18][19][20][21][22][23][24][25]. Among them, linear positive position feedback (LPPF) and nonlinear positive position feedback (NPPF) controllers are found to be particularly effective if they are aimed to damp one particular structural vibration mode. This type of controller is implemented by feeding the structural position directly to a linear or nonlinear compensator, whose output is then fed through a fixed gain positively back to drive the actuator. In this context, they would be well suited for the applications where piezoelectric sensors and actuators are employed for vibration damping. This is because the voltage from the sensor is proportional to the strain of the attached structure, which can be directly measured to drive the strain-based piezoelectric actuators. Warminski et al. [21] compared the control performance of a LPPF controller with three other controllers, namely proportional position feedback, cubic position feedback and nonlinear saturation feedback, for suppression of nonlinear composite beam vibrations. It was found that the LPPF controller is only effective for weakly nonlinear systems and the nonlinear saturation controller was concluded to be superior for the nonlinear primary structure under consideration. The performance of the LPPF controller was also investigated in [22], but on a four-degree-of-freedo...

Active nonlinear inerter damper for vibration mitigation of Duffing oscillators

“…Instead, a pair of one-term harmonic balance approximation is assumed as the solutions as in Ref. [7]:…”

“…On the other hand, active approaches might be appealing which might lead to a less complex solution. Zhao et al [7] applied the same tuning strategy as proposed in Ref. [5] on a nonlinear positive position feedback (NPPF) controller aiming to optimally damp a Duffing oscillator based on the H ∞ criterion.…”

“…This work is built upon the previous developments [7,8] to investigate the potential of using an active nonlinear inerter damper (ANLID) for vibration mitigation of a Duffing oscillator (primary structure). More specifically, a cubic nonlinear term is added in the original linear controller [8] in order to counteract the nonlinear dynamics of the primary structure.…”

Hybrid Electromagnetic Shunt Damper for Vibration Control

“…The following equations are obtained by equating the polynomial coefficients of the denominator of the fraction on the right-hand side of Eqs. (18) and (19):…”

“…Indeed, a good vibration control can be realized by using the active control systems when the electromagnetic device is used as an actuator. For example, designs of positive position feedback (PPF) control based on maximum damping criterion [18] and H ∞ optimization [19] have been proposed and then validated experimentally using an electromagnetic transducer. Furthermore, because the transducer can be used as both actuator and sensor, an active impedance control system has been introduced by implementing a feedback loop between the coil terminal current and voltage of the device [20,21].…”