Design method of tuned mass damper by LMI based robust control theory for seismic excitation
TL;DR: In this article , a robust control strategy based on a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control, is presented.
Abstract:
This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H¥ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models, and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.
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TL;DR: In this paper , a reduced-order state observer (ROSO) was proposed to reduce the complexity of base-isolation and ensure the reliability of the EID control system.
Abstract:
Active base isolation has been studied in the last few decades to improve the control performance of base isolation. As a two-degree-of-freedom active disturbance-rejection method, the equivalent-input-disturbance (EID) approach shows its validity for structural control. It uses a state observer to estimate the effect of disturbances on a control input channel. However, since the model of a base-isolated building has high degrees-of-freedom, a resulting control system has a high order. Thus, the use of a full-order state observer results in the complexity of a control-system implementation. To solve this problem, this paper presents an EID control system that uses a reduced-order state observer (ROSO) to reduce the expense of control-system implementation and ensure system reliability. First, the condition of using an ROSO in an EID control system is derived, and the configuration of an ROSO-based EID control system is presented. Next, the concept of perfect regulation is used to design the gain of the state observer. A stability condition of the system with prescribed control performance is derived in the form of a linear matrix inequality (LMI) that is used to design the gain of the state feedback. Finally, the seismic control of a base-isolated building demonstrates the validity of the method.
9 citations
TL;DR: In this paper , a mixed scheduling model is proposed to describe the transmission behaviors subject to stochastic communication protocol (SCP) and round-Robin protocol (RRP) for a class of networked time-delay systems where the measurements are transmitted through two individual communication channels.
Abstract: Dear Editor, This letter is concerned with the finite-horizon $l_{2}-l_{\infty}$ state estimation (SE) problem for a class of networked time-delay systems where the measurements are transmitted through two individual communication channels. With the aim of preventing the transmitted data from conflicts, the signal transmissions over such the communication channels are scheduled by different communication protocols, namely the stochastic communication protocol (SCP) and Round-Robin protocol (RRP). A mixed scheduling model is proposed to describe the transmission behaviors subject to such two protocols. The objective of this letter is to design an estimator such that the estimation error achieves the desired finite-horizon $l_{2}-l_{\infty}$ performance in the mean square. By using the Lyapunov stability theory, a sufficient condition is proposed to guarantee the existence of the desired estimator. An illustrative simulation example is given to verify the effectiveness and correctness of the proposed design scheme.
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TL;DR: In this paper, the analytical solutions for the H∞ and H 2 optimization problems of the Voigt type dynamic vibration absorber (DVA) attached to the damped primary systems are presented.
Abstract: H∞ and H 2 optimization problems of the Voigt type dynamic vibration absorber (DVA) are classical optimization problems, which have been already solved for a special case when the primary system has no damping. However, for the general case including a damped primary system, no one has solved these problems by algebraic approaches. Only the numerical solutions have been proposed until now. This paper presents the analytical solutions for the H∞and H 2 optimization of the DVA attached to the damped primary systems. In the H∞ optimization the DVA is designed such that the maximum amplitude magnification factor of the primary system is minimized; whereas in the H 2 optimization the DVA is designed such that the squared area under the response curve of the primary system is minimized. We found a series solution for the H∞ optimization and a closed-form algebraic solution for the H 2 optimization. The series solution is then compared with the numerical solution in order to check the accuracy in connection with the truncation error of the series. The exact solution presented in this paper is too complicated to handle by a hand-held calculator, so we proposed an approximate solution for the practical object.
311 citations
TL;DR: In this paper, a high-rise building was designed and modeled using linear elastic (and also nonlinear) degrading stiffness idealizations, and three different techniques were used to design an optimum tuned-mass damper (TMD) for the prototype.
Abstract: A realistic prototype high-rise building was designed and modeled using linear elastic (and also nonlinear) degrading stiffness idealizations. Using an effective damper mass ratio of 0.026, three different techniques were used to design an optimum tuned-mass damper (TMD) for the prototype. All were found to give essentially the same design. The response of the idealized prototype building to a strong ground motion was computed with and without a TMD. The TMD did not reduce the prototype's maximum response. Based on these results, vibration absorbers do not seem effective in reducing the maximum seismic response of tall buildings.
139 citations
TL;DR: In this article, the stiffness and damping coefficients of the tuned-mass dampers in a single-degree-of-freedom primary system have been optimized using a decentralized H2 control problem.
Abstract: The characteristics of multiple tuned-mass-dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers. Several papers have included some parameter optimization, all based on restrictive assumptions. In this paper, we propose an efficient numerical algorithm to directly optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system. We formulate the parameter optimization as a decentralized H2 control problem where the block-diagonal feedback gain matrix is composed of the stiffness and damping coefficients of the TMDs. The gradient of the root-mean-square response with respect to the design parameters is evaluated explicitly, and the optimization can be carried out efficiently. The effects of the mass distribution, number of dampers, total mass ratio, and uncertainties in system parameters are studied. Numerical results indicate that the optimal designs have neither uniformly spaced tuning frequencies nor identical damping coefficients, and that optimization of the individual parameters in the MTMD system yields a substantial improvement in performance. We also find that the distribution of mass among the TMDs has little impact on the performance of the system provided that the stiffness and damping can be individually optimized.
134 citations
TL;DR: In this paper, a two-DOF absorber with a negative damper in one of its two connections to the primary system was proposed to suppress single-mode vibration of a primary system.
Abstract: Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.
102 citations