Active Vibration Control of the Axially Moving String by Wave Cancellation

1995 ◽  
Vol 117 (1) ◽  
pp. 49-55 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan

Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the controlled system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.

Author(s):  
C. H. Chung ◽  
C. A. Tan

Abstract Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the closed-loop system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.


1991 ◽  
Vol 58 (1) ◽  
pp. 189-196 ◽  
Author(s):  
B. Yang ◽  
C. D. Mote

A new method is presented for active vibration control of the axially moving string, one of the most common models of axially moving continua. The control is formulated in the Laplace transform domain. The transfer function of a closed-loop system, consisting of the plant, a feedback control law and the dynamics of the sensing and actuation devices, is derived. Analysis of the root loci of the closedloop system gives two stability criteria. Stabilizing controller design is carried out of both collocation and noncollocation of the sensor and actuator. It is found that all the modes of vibration can be stabilized and that in principle the spillover instability can be avoided. Also, the steady-state response of the stabilized string to periodic, external excitation is presented in closed form.


1996 ◽  
Vol 118 (3) ◽  
pp. 306-312 ◽  
Author(s):  
S. Ying ◽  
C. A. Tan

Active vibration control of an axially moving string using space feedforward and feedback controllers is presented. Closed-form results for the transverse response of both the uncontrolled and controlled string are given in the s domain. The space feedforward controller is established by employing the idea of wave cancellation. The proposed control law indicates that vibration in the region downstream of the control force can be cancelled. With the space feedforward control, the mode shapes of the axially moving string are changed such that the free response tends to zero in the downstream region. An interesting physical interpretation is that the control force acts effectively as a holder (active support) which limits the vibration of the string to the upstream region and eliminates any vibration in the downstream region. Simulation results show that the response of the string to both sinusoidal and random excitations is suppressed by applying the space feedforward control. The feedback controller is introduced to attenuate the response of the string due to undesired disturbances in the downstream.


1999 ◽  
Vol 121 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Rong-Fong Fung ◽  
Chun-Chang Tseng

This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) boundary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.


Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4694
Author(s):  
Mengde Zhou ◽  
Wei Liu ◽  
Qinqin Wang ◽  
Bing Liang ◽  
Linlin Tang ◽  
...  

Active vibration control is the most effective method for stochastic multidimensional vibration in wind tunnel tests, in which vibration monitoring is the core foundation. Vibrations are induced by the disturbances of several complex air flow instabilities under extreme test conditions with high attack angles. Here, a decoupled unified observation method is proposed in order to fully monitor stochastic multidimensional vibration. First, stochastic multidimensional vibration is explained using the Cartesian coordinate system. Then, the multidimensional vibration decoupling of the pitch plane and the yaw plane is realized according to the proposed decoupling design principle of the long cantilever sting. A unified observation method is presented, based on inertial force theory, to observe multidimensional vibration due to acceleration in each decoupling plane. Verification experiments were conducted in lab and a transonic wind tunnel, using an established real-time monitoring system. The results of lab experiments indicate that, in the frequency region of 0–120 Hz, three vibration modes of a selected stochastic vibration can be decoupled and observed through the vibration components in pitch plane and yaw plane. In addition, wind tunnel tests were carried out according to the working conditions (α = −4~10° with γ = 45°) at Ma = 0.6 and Ma = 0.7, respectively. The results show that six vibration modes of two selected stochastic vibrations can be decoupled and observed through the vibration components in pitch plane and yaw plane. The experimental results prove that stochastic vibration can be fully monitored in multiple dimensions through the vibration components in pitch plane and yaw plane using the proposed decoupled unified observation method. Therefore, these results lay the foundation for active vibration control.


Author(s):  
Junyoung Park ◽  
Alan Palazzolo ◽  
Raymond Beach

Theory and simulation results have demonstrated that four, variable speed flywheels could potentially provide the energy storage and attitude control functions of existing batteries and control moment gyros on a satellite. Past modeling and control algorithms were based on the assumption of rigidity in the flywheel’s bearings and the satellite structure. This paper provides simulation results and theory, which eliminates this assumption utilizing control algorithms for active vibration control (AVC), flywheel shaft levitation, and integrated power transfer and attitude control (IPAC), that are effective even with low stiffness active magnetic bearings (AMBs) and flexible satellite appendages. The flywheel AVC and levitation tasks are provided by a multiple input–multiple output control law that enhances stability by reducing the dependence of the forward and backward gyroscopic poles with changes in flywheel speed. The control law is shown to be effective even for (1) large polar to transverse inertia ratios, which increases the stored energy density while causing the poles to become more speed dependent, and for (2) low bandwidth controllers shaped to suppress high frequency noise. Passive vibration dampers are designed to reduce the vibrations of flexible appendages of the satellite. Notch, low-pass, and bandpass filters are implemented in the AMB system to reduce and cancel high frequency, dynamic bearing forces and motor torques due to flywheel mass imbalance. Successful IPAC simulation results are presented with a 12% initial attitude error, large polar to transverse inertia ratio (IP∕IT), structural flexibility, and unbalance mass disturbance.


Author(s):  
Chin An Tan ◽  
Shenger Ying

Abstract The active wave control of the linear, axially moving string with general boundary conditions is presented in this paper. Considerations of general boundary conditions are important from both practical and experimental viewpoints. The active control law is established by employing the idea of wave cancellation. An exact, closed-form expression for the transverse response of the controlled system, consisting of the flexible structure, the wave controller, and the sensing and actuation devices, is derived in the frequency domain. Two actuation forces, one upstream and one downstream of an excitation force, are applied. The proposed control law shows that all modes of the string are controlled and the vibration in the regions upstream and downstream of the control forces can be cancelled. However, these results are based on ideal conditions and the assumption of zero initial conditions at the non-fixed boundaries. Effects of non-zero boundary motions at the instant of application of the control forces are examined and the control is shown to be effective under these conditions. The stability and robustness of the control forces are improved by the introduction of a stabilization coefficient in the control law. The effectiveness, robustness and stability of the control forces are demonstrated by simulations and verified by experiments on axially moving belt drive and chain drive systems.


2001 ◽  
Vol 17 (4) ◽  
pp. 173-177
Author(s):  
Der-An Wang ◽  
Yii-Mai Huang

ABSTRACTActive vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The concept of independent modal space control is adopted. Both the feedforward and feedback control is implemented here to reduce the beam vibration. Because of the existence of the disturbance forces, the feedforward control is applied by employing the idea of force cancellation. A modal space disturbance force observer is then established in this paper to observe the disturbance modal forces for the feedforward control. For obtaining the feedforward and feedback control gains with the optimal sense, the nearly optimal control law is derived, where the modal disturbance forces are regarded as additional states. The vibration control performances and the asymptotic properties of the control law are discussed.


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