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Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems

This paper presents a comprehensive overview of the application of Variable Structure Systems (VSSs) with Sliding Mode (SM) methods in motion control systems. Our aim is to give implementable sliding mode design solutions for complex motion systems, actuators and supply converters. This paper provides a frame for further study of sliding mode applications in motion control systems.

Variable Structure Systems With Sliding Modes in Motion Control—A Survey

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.

Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems

Research developments in vibration control of structures using passive tuned mass dampers

A typical design problem for which the fixed-points method was originally developed is that of minimizing the maximum amplitude magnification factor of a primary system by using a dynamic vibration absorber This is an example of usual cases for which their exact solutions are not obtained by the well-known heuristic approach. In this paper, more natural formulation of this problem is studied, and algebraic closed-form exact solutions to both the optimum tuning ratio and the optimum damping coefficient for this classic problem are derived under assumption of undamped primary system. It is also proven that the minimum amplitude magnification factor, resonance and anti-resonance frequencies are entirely algebraic.

Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)

H∞ optimization of the dynamic vibration absorbers is a classical optimization problem, and has been already solved more than 50 years ago. It is a well-known solution, but we know this solution is only an approximate one. Recently, one of the authors has proposed a new method for attaining the H∞ optimization of the absorber in linear systems. The new method enables us to obtain the exact algebraic solution of the H∞ optimization problem of the absorber. In this paper we first apply this method to the design optimization of a viscous damped (Voigt type) absorber and a hysteretic damped absorber attached to undamped primary systems. For each absorber, six different transfer functions are taken here as performance indices to vibration suppression or isolation. As a result, we found the closed-form exact solutions to all transfer functions. The solutions obtained here are then compared with those of the approximate ones. Finally, we present the closed-form exact solutions to the hysteretic damped absorber attached to damped primacy systems.

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

The present paper proposes an automatic path-tracking controller of a four-wheel steering (4WS) vehicle based on the sliding mode control theory. The controller has an advantage in that the front- and rear-wheel steering can be decoupled at the front and rear control points, which are defined as centres of percussion with respect to the rear and front wheels, respectively. Numerical simulations using a 27-degree-of-freedom vehicle model demonstrated the following characteristics: (1) the automatic 4WS controller has a more stable and more precise path-tracking capability than the 2WS controller, and (2) the automatic 4WS controller has robust stability against system uncertainties such as cornering power perturbation, path radius fluctuation, and cross-wind disturbance.

Automatic path-tracking controller of a four-wheel steering vehicle

In this paper, we propose a dynamic vibration absorber (DVA) with an air damper consisting of a piston and a cylinder. First, it will be shown that the air damper can conveniently be represented by the Maxwell model where a spring element and a dashpot are connected in series. The air damper has no ability to return the piston to its original position. For this reason, it is necessary for the piston to be supported by a spring which is placed in parallel with the damper. The air damped DVA can then be modeled by the three-element model. Many studies have been done on the Voigt type of DVA, and the accurate expressions of optimum tuning and damping parameters have already been derived by Hahnkamm and Brock et al. However, only a few papers have been published on the three-element type of DVA, and reliable expressions for it have not been derived until now. Therefore, we began our work by trying to derive expressions for optimum parameters of the three-element type of DVA. It was clear that the optimized three-element type of DVA is superior to the conventional Voigt type of DVA. The optimum parameters which we obtained from our expressions were tested on a vibratory model. The experiments showed that the our expression is very useful for designing the air damped DVA.

Osamu Nishihara

Papers

Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems

Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

Automatic path-tracking controller of a four-wheel steering vehicle

Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model