Robust Design Method of Multi-Degree-of-Freedom Passive Tuned Mass Damper by Control Theory

2006 ◽  
Author(s):  
Daisuke Iba ◽  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Feedback Control ◽  
Control Theory ◽  
Output Feedback ◽  
Design Problem ◽  
Design Method ◽  
Tuned Mass Damper ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Feedback Gain ◽  
Mass Damper

This paper proposes a design method of a multi degree of freedom passive tuned mass damper with robust performance. In this study, the passive tuned mass damper is designed from the view of feedback control theory. Design parameters of the general passive tuned mass damper can be thought to be a feedback gain, and designed by replacing the design problem of the passive tuned mass damper with the output feedback control problem. Moreover, for giving the tuned mass damper robustness, an extended model is constructed by two main systems that have maximum and minimum natural frequencies in the given variable domain of parameters, and one static output feedback H∞ controller reduces the maximum value of frequency response of the extended plant. In this paper, it was confirmed to be able to design the single-degree-of-freedom tuned mass damper with robustness by this method. Moreover, this method was enhanced to the design problem of the multi-degree-of-freedom tuned mass damper that was placed on the multi-degree-of-freedom vibration system, and finally a numerical simulation confirmed the effectiveness.

Reduction of Quantization Error in Multirate Output Feedback Control

2016 ◽  
Vol 28 (5) ◽  
pp. 640-645
Author(s):  
Takao Sato ◽  
◽  
Hironobu Sakaguchi ◽  
Nozomu Araki ◽  
Yasuo Konishi
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Output Feedback ◽  
Design Method ◽  
Output Feedback Control ◽  
Quantization Error ◽  
Design Parameters ◽  
Control Input ◽  
State Variables ◽  
Feedback Control System

[abstFig src='/00280005/04.jpg' width='250' text='Multirate output feedback control' ] In the new design method we propose for a multirate output feedback control system, the hold interval of control input is longer than the sampling interval of plant output. In this system, unknown state variables are calculated using control input and plant output without observers. The multirate output feedback control system has been extended by introducing new design parameters that are designed independent of the calculation of the state variable. To our knowledge, however, no systematic design scheme has ever been proposed for design parameters in this case. In this study, quantization error is dealt with statistically and design parameters are decided to minimize quantization error.

Design method of tuned mass damper by LMI based robust control theory for seismic excitation

2022 ◽  
pp. 1-47
Author(s):  
Kou Miyamoto ◽  
Satoshi Nakano ◽  
Jinhua She ◽  
Daiki Sato ◽  
Yinli Chen ◽  
...  
Keyword(s):  
Robust Control ◽  
Control Theory ◽  
Passive Control ◽  
Structural Model ◽  
Design Method ◽  
Tuned Mass Damper ◽  
Structural Vibration ◽  
Linear Matrix ◽  
Mass Damper ◽  
Robust Control Theory

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.

A Computation-Efficient Framework for the Integrated Design of Structural and Control Systems

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Yilun Liu ◽  
Lei Zuo
Keyword(s):  
Control System ◽  
Decentralized Control ◽  
Output Feedback ◽  
Structural Design ◽  
Design Problem ◽  
Design Method ◽  
Integrated Design ◽  
Design Parameters ◽  
Feedback Controllers ◽  
Control Techniques

This paper proposes a new integrated design method to simultaneously optimize the coupled structural parameters and controllers of mechanical systems by combining decentralized control techniques and Riccati-based control theories. The proposed integrated design method aims at minimizing the closed-loop H2 norm from the disturbance to the system cost. In this paper, the integrated design problems have been formulated in the cases of full state-feedback controllers and full order output-feedback controllers. We extend the current linear time invariant (LTI) control system to a more general framework suitable for the needs of integrated design, where the structural design is treated as a passive control optimization tackled by decentralized control techniques with static output feedback, while the active controller is optimized by solving modified Riccati equations. By using this dual-loop control system framework, the original integrated design problem is transferred to a constrained structural design problem with some additional Riccati-equation based constraints simultaneously integrating the controller synthesis. This reduces the independent design variables from the structural design parameters and the parameters of the controller to the structural design parameters only. As a result, the optimization efficiency is significantly improved. Then the constrained structural design problem is reformed as an unconstrained optimization problem by introducing Lagrange multipliers and a Lagrange function. The corresponding optimal conditions for the integrated design are also derived, which can be efficiently solved by gradient-based optimization algorithms. Later, two design examples, an active–passive vehicle suspension system and an active–passive tuned mass damper (TMD) system, are presented. The improvement of the overall system performance is also presented in comparison with conventional design methods.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

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.

scholarly journals Parameter optimization of tuned mass damper for three-degree-of-freedom vibration systems

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Van Khang ◽  
Trieu Quoc Loc ◽  
Nguyen Anh Tuan
Keyword(s):  
Inequality Constraints ◽  
Tuned Mass Damper ◽  
Parameters Optimization ◽  
Degree Of Freedom ◽  
Aerospace Engineering ◽  
Lower And Upper Bounds ◽  
Mass Damper ◽  
Sequential Quadratic Programming Method ◽  
Quadratic Programming Method ◽  
Three Degree Of Freedom

There are problems in mechanical, structural and aerospace engineering that can be formulated as Nonlinear Programming. In this paper, the problem of parameters optimization of tuned mass damper for three-degree-of-freedom vibration systems is investigated using sequential quadratic programming method. The objective is to minimize the extreme vibration amplitude of vibration models. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model.

Constrained Optimization of Multi-Degree-of-Freedom Mechanisms for Near-Time Optimal Motions

1992 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Constrained Optimization ◽  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Pattern Search ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Maximum Acceleration ◽  
Time Optimal ◽  
Order Of Magnitude

Abstract This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal motions. The design objective is to select system parameters, such as link lengths and actuator sizes, so as to minimize the optimal motion time of the mechanism along a given path. The exact time optimization problem is approximated by a simpler procedure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, and the reachability constraints as explicit functions of the design parameters, we transform the constrained optimization to a simpler curve fitting problem that can be formulated analytically. This allows the use of efficient gradient type optimizations, instead of the pattern search optimization that is otherwise required. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation of the approximate with the exact solutions, and an order of magnitude better computational efficiency than the previously developed unconstrained optimization methods.

Direct Optimization of Multi-Degree-of-Freedom Mechanisms for Near Time Optimal Motions Along Specified Paths

1991 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Direct Optimization ◽  
Fitting Procedure ◽  
Time Optimal ◽  
Approximate Cost ◽  
The Given

Abstract A design method for selecting system parameters of multi-degree-of-freedom mechanisms for near minimum time motions along specified paths is presented. The time optimization problem is approximated by a simple curve fitting procedure that fits, what we call, the acceleration lines to the given path. The approximate cost function is explicit in the design parameters, facilitating the formulation of the design problem as a constrained optimization. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency than the previous unconstrained optimization methods.

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