In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in ...In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.展开更多
In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved...In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved the existence, the uniqueness and the approximation of the optimal control element by utilizing space L2(0,l) 's the reflexivity, the smoothness and the strict convexity.展开更多
This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) probl...This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.展开更多
In this paper,a comparative study for kernel-PCA based linear parameter varying(LPV)model approximation of sufficiently nonlinear and reasonably practical systems is carried out.Linear matrix inequalities(LMIs)to be s...In this paper,a comparative study for kernel-PCA based linear parameter varying(LPV)model approximation of sufficiently nonlinear and reasonably practical systems is carried out.Linear matrix inequalities(LMIs)to be solved in LPV controller design process increase exponentially with the increase in a number of scheduling variables.Fifteen kernel functions are used to obtain the approximate LPV model of highly coupled nonlinear systems.An error to norm ratio of original and approximate LPV models is introduced as a measure of accuracy of the approximate LPV model.Simulation examples conclude the effectiveness of kernel-PCA for LPV model approximation as with the identification of accurate approximate LPV model,computation complexity involved in LPV controller design is decreased exponentially.展开更多
基金This research was funded by the Natural Science Research Project of Higher Education Institutions in Anhui Province(Grant No.2022AH040045)the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(Grant No.2021-YF22).
文摘In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.
文摘In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved the existence, the uniqueness and the approximation of the optimal control element by utilizing space L2(0,l) 's the reflexivity, the smoothness and the strict convexity.
基金supported by National Natural Science Foundation of China(Nos.61004017 and 60974103)
文摘This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.
文摘In this paper,a comparative study for kernel-PCA based linear parameter varying(LPV)model approximation of sufficiently nonlinear and reasonably practical systems is carried out.Linear matrix inequalities(LMIs)to be solved in LPV controller design process increase exponentially with the increase in a number of scheduling variables.Fifteen kernel functions are used to obtain the approximate LPV model of highly coupled nonlinear systems.An error to norm ratio of original and approximate LPV models is introduced as a measure of accuracy of the approximate LPV model.Simulation examples conclude the effectiveness of kernel-PCA for LPV model approximation as with the identification of accurate approximate LPV model,computation complexity involved in LPV controller design is decreased exponentially.
