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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.

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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.