The present paper narrates the influence of nonideality of externally controlled components on multiple-steady-state transitions studied by using the regular solution model. Under certain conditions the splitting of t...The present paper narrates the influence of nonideality of externally controlled components on multiple-steady-state transitions studied by using the regular solution model. Under certain conditions the splitting of the original cusp causes 'twin' bifurcation points accompanied by isolas which could shrink to an elliptic singular point or a cusp, or even collapse to a hyperbolic singular point in the different cases.展开更多
The limiting performa nce analysis is used to study the optimal shock and impact isolation of mechanic al systems. The use of wavelets to approximate time-domain control functions is investigated. The formulation for...The limiting performa nce analysis is used to study the optimal shock and impact isolation of mechanic al systems. The use of wavelets to approximate time-domain control functions is investigated. The formulation for numerical computation is developed. Numerical examples include the optimal shock isolation of a SDOF system and the optimal i mpact isolation of a MDOF system. Computational results show that compactly supp orted wavelets can represent abrupt changes in control functions better than tri gonometric series and considerably increase computational efficiency.展开更多
This short communication uses numerical continuation to highlight the existence of an isola in a simple one-degree-of-freedom harmonically forced feedback system with actuator rate limiting as its only nonlinear eleme...This short communication uses numerical continuation to highlight the existence of an isola in a simple one-degree-of-freedom harmonically forced feedback system with actuator rate limiting as its only nonlinear element.It was found that the isola(1)contains only rate-limited responses,(2)merges with the main branch when the forcing amplitude is sufficiently large,and(3)includes stable solutions that create a second attractor in regions where rate limiting is not expected.Furthermore,the isola is composed of two solutions for a given forcing frequency.These solutions have the same amplitudes in the state(pitch rate)projection;however,they have distinct phases,and their amplitudes are also distinct when projected onto the integrator state in the controller.The rich dynamics observed in such a simple example underlines the impact of rate limiting on feedback systems.Specifically,the combination of feedback and rate limiting can create detrimental dynamics that is hard to predict and requires careful analysis.展开更多
文摘The present paper narrates the influence of nonideality of externally controlled components on multiple-steady-state transitions studied by using the regular solution model. Under certain conditions the splitting of the original cusp causes 'twin' bifurcation points accompanied by isolas which could shrink to an elliptic singular point or a cusp, or even collapse to a hyperbolic singular point in the different cases.
文摘The limiting performa nce analysis is used to study the optimal shock and impact isolation of mechanic al systems. The use of wavelets to approximate time-domain control functions is investigated. The formulation for numerical computation is developed. Numerical examples include the optimal shock isolation of a SDOF system and the optimal i mpact isolation of a MDOF system. Computational results show that compactly supp orted wavelets can represent abrupt changes in control functions better than tri gonometric series and considerably increase computational efficiency.
文摘This short communication uses numerical continuation to highlight the existence of an isola in a simple one-degree-of-freedom harmonically forced feedback system with actuator rate limiting as its only nonlinear element.It was found that the isola(1)contains only rate-limited responses,(2)merges with the main branch when the forcing amplitude is sufficiently large,and(3)includes stable solutions that create a second attractor in regions where rate limiting is not expected.Furthermore,the isola is composed of two solutions for a given forcing frequency.These solutions have the same amplitudes in the state(pitch rate)projection;however,they have distinct phases,and their amplitudes are also distinct when projected onto the integrator state in the controller.The rich dynamics observed in such a simple example underlines the impact of rate limiting on feedback systems.Specifically,the combination of feedback and rate limiting can create detrimental dynamics that is hard to predict and requires careful analysis.
