Non-Chaotic Cross-Well State Transfer of Duffing-Holmes Type Bistable Systems

2017 ◽  
Author(s):  
Mehmet R. Simsek ◽  
Onur Bilgen
Keyword(s):  
Stable Equilibrium ◽  
Harmonic Excitation ◽  
Open Loop ◽  
Feedback Controller ◽  
Bistable System ◽  
Hybrid Controller ◽  
Positive Position Feedback ◽  
Bistable Systems ◽  
State Transfer ◽  
Position Feedback

A control strategy called hybrid position feedback control is applied to a bistable system to prevent multiple crossovers during actuation from one stable equilibrium to the other. The hybrid controller is based on a conventional positive position feedback controller. The controller uses the inertial properties of the structure around the stable positions to achieve large displacements by destabilizing a positive position feedback controller. Once the unstable equilibrium is reached, the controller is stabilized to converge to the target stable equilibrium. The bistable system under harmonic excitation and hybrid controller are investigated for its behavior. In addition, energy analysis of the system controlled by the hybrid controller is investigated using numerical time domain methods. The energy variance by parameters and the comparison between the open-loop system with harmonic excitation and the controlled system is investigated.

The Duffing-Holmes Oscillator With Hybrid Position Feedback Controller: Stability and Response Analysis

2018 ◽  
Author(s):  
Mehmet R. Simsek ◽  
Onur Bilgen
Keyword(s):  
Stable Equilibrium ◽  
Turbine Blades ◽  
Response Analysis ◽  
Response Type ◽  
Wind Turbine Blades ◽  
Hybrid Controller ◽  
Position Feedback ◽  
Multiple Cross ◽  
Single Cross ◽  
Control Concept

The dynamic behavior of a Duffing-Holmes oscillator subjected to a Hybrid Position Feedback (HPF) controller is investigated. The so-called hybrid controller is a combination of two controllers, namely, the Negative Position Feedback (NPF), and Positive Position Feedback (PPF) controllers. The controller uses the inertial properties of the structure around its stable positions to achieve large displacements by effectively destabilizing the system using an NPF controller. Once the unstable equilibrium is reached, the system is stabilized to the target stable equilibrium using the PPF controller. This dynamic switch of controllers creates the HPF control concept, which specifically enables the monotonic and controlled transition between the states of bistable systems such as the Duffing-Holmes oscillator. This concept can be implemented to morphing structures such as bistable wings, wind turbine blades, and deployable structures. In this paper, a detailed response type and stability analyses of a Duffing-Holmes oscillator controlled by the HPF controller are presented. First, the response types for the components of the HPF, NPF and PPF controllers are analyzed individually. For the NPF controller, three response types are defined. These are intra-well, single cross-well, and multiple cross-well response types describing the possible responses. For the PPF controller, only two response types are defined. These are stabilized and not-stabilized, since the role of the PPF controller is to generate an attractor to the desired stable equilibrium. Finally, the complete HPF controller is analyzed in terms of response type. In this case, three response types are defined: intra-well, single cross-well and multiple cross-well. The paper summarizes all the response types with detailed analyses, and recommends controller parameters for best control performance.

The Duffing-Holmes Oscillator Under Hybrid Position Feedback Controller: Response Type and Basin of Attraction Analyses

2020 ◽  
Vol 20 (09) ◽  
pp. 2050101
Author(s):  
Mehmet R. Simsek ◽  
Onur Bilgen
Keyword(s):  
Linear Models ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Bistable System ◽  
Response Type ◽  
Hybrid Controller ◽  
Position Feedback ◽  
Control Concept ◽  
Convergence Type ◽  
Mass Spring

This paper presents a detailed response type and basin of attraction (BOA) analyses of a linear mass-spring-damper oscillator and a Duffing-Holmes (D-H) oscillator controlled by a class of position feedback controllers. First, the response-type comparison of both linear and D-H systems subjected to a, Negative Position Feedback (NPF), and Positive Position Feedback (PPF) controllers, and Hybrid Position Feedback (HPF) controller (which combines the previous two) is analyzed individually. Initially, the bistable system is expressed as two linear models around the stable equilibriums, and shows similar dynamic characteristics near the vicinity of stable equilibria. Three relevant response types are identified for the controlled D-H oscillator. These are the intra-well, single cross-well, and multiple cross-well response types describing all possible responses. With the BOA analyses, three response convergence types are defined. These are the convergence to state-1, convergence to state-2, and no convergence. The overall behavior of the bistable system under the hybrid controller is examined and described using these response- and convergence-type analyses. In this paper, it is shown that the HPF control concept provides desirable response for a wider range of systems and initial conditions when compared to the other simpler control schemes. The range of desirable controller parameters is identified.

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

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1155-1164 ◽  
Author(s):  
Ahmad Paknejad ◽  
Gouying Zhao ◽  
Michel Osée ◽  
Arnaud Deraemaeker ◽  
Frédéric Robert ◽  
...  
Keyword(s):  
Closed Loop ◽  
Feedback Controller ◽  
Single Degree Of Freedom ◽  
Positive Position Feedback ◽  
Loop Transfer Function ◽  
Optimal Damping ◽  
Optimal Value ◽  
Position Feedback ◽  
Tuning Frequency ◽  
Novel Design

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.

scholarly journals Positive Position Feedback Controller for Nonlinear Beam Subject to Harmonically Excitation

2019 ◽  
pp. 1-19
Author(s):  
Y. A. Amer ◽  
A. T. EL-Sayed ◽  
A. M. Abdel-Wahab ◽  
H. F. Salman
Keyword(s):  
Time History ◽  
Multiple Scale ◽  
Feedback Controller ◽  
Nonlinear Beam ◽  
Positive Position Feedback ◽  
Simultaneous Resonances ◽  
Position Feedback ◽  
Scale Perturbation ◽  
Response Equation ◽  
Steady State Solutions

In this paper, the vibration reduction of the harmonically excited nonlinear beam is introduced using positive position feedback controller (PPF). The multiple-scale perturbation techniques (MSPT) up is applied to second-order to obtain the analytic results. Numerical simulations are used to compare between time-history and the analytical solution. The frequency response equation (FRE) is studied to illustrate the steady state solutions near the simultaneous resonances. The influences of the different parameters and the system behavior at resonance case are studied to show the optimum conditions of decreasing the vibration. A comparison between the numerical and analytical solutions is presented to appear the validity of the results.

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