A Control Theoretic Framework for Optimally Locating Passive Vibration Isolators to Minimize Residual Vibration

2015 ◽  
Author(s):  
Amir H. Ghasemi ◽  
Jihyun Lee ◽  
Chinedum E. Okwudire
Keyword(s):  
Feedback Gain ◽  
Residual Vibration ◽  
Placement Problem ◽  
Vibration Isolators ◽  
Design Variables ◽  
Exogenous Disturbance ◽  
Ultra Precision ◽  
System States ◽  
Control Forces ◽  
Stiffness And Damping

This paper investigates the problem of optimally locating passive vibration isolators to minimize residual vibration caused by exogenous disturbance forces. The stiffness and damping properties of the isolators are assumed to be known and the task is to determine the isolator locations, which are nonlinearly related to system states. This paper proposes an approach for reformulating the nonlinear isolator placement problem as a LTI control problem by linking the control forces to measured outputs using a feedforward term. Accordingly, the isolator locations show up as a static output feedback gain matrix which is optimized for residual vibration reduction using standard H∞ optimal control methods. Simulations and experiments on SISO and MIMO case studies are used to demonstrate the merits of the proposed approach. Even though presented in the specific context of ultra-precision manufacturing machines, the proposed method is applicable to the optimal design of other passive systems with nonlinear relationships between design variables and system states.

A Linear Feedback Control Framework for Optimally Locating Passive Vibration Isolators With Known Stiffness and Damping Parameters

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jihyun Lee ◽  
Amir H. Ghasemi ◽  
Chinedum E. Okwudire ◽  
Jeffrey Scruggs
Keyword(s):  
Feedback Control ◽  
Transfer Functions ◽  
Linear Time ◽  
Optimal Placement ◽  
Linear Feedback ◽  
Feedback Gain ◽  
Placement Problem ◽  
Vibration Isolators ◽  
Linear Time Invariant ◽  
Stiffness And Damping

This paper investigates the problem of optimally locating passive vibration isolators to minimize unwanted vibration caused by exogenous disturbance forces. The stiffness and damping parameters of the isolators are assumed to be known, leaving the isolator locations, which are nonlinearly related to system states, as unknown optimization variables. An approach for reformulating the nonlinear isolator placement problem as a linear time-invariant (LTI) feedback control problem, by linking fictitious control forces to fictitious measured outputs using a nonzero feedforward term, is proposed. Accordingly, the isolator locations show up within a static output feedback gain matrix which can be optimized, using methods from optimal control theory, to minimize the H2 and/or H∞ norms of transfer functions representing unwanted vibration. The proposed framework also allows well-established LTI control theories to be applied to the analyses of the optimal isolator placement problem and its results. The merits of the proposed approach are demonstrated using single and multivariable case studies related to isolator placement in precision manufacturing machines. However, the framework is applicable to optimal placement of passive isolators, suspensions, or dampers in automotive, aerospace, civil, and other applications.

Optimal Motor Location for the Reduction of Residual Vibrations in Mode-Coupled Ultra-Precision Manufacturing Machines

2013 ◽  
Author(s):  
Chinedum E. Okwudire ◽  
Jihyun Lee
Keyword(s):  
Global Minimum ◽  
Low Frequency ◽  
Vibration Modes ◽  
Precision Manufacturing ◽  
Drastic Reduction ◽  
Residual Vibration ◽  
Vibration Isolators ◽  
Surface Finishes ◽  
Ultra Precision ◽  
Complex Parts

Ultra-precision manufacturing (UPM) machines are used to fabricate and measure complex parts having micrometer-level features and nanometer-level tolerances/surface finishes. Therefore, low-frequency residual vibrations that occur during the motion of the machines’ axes must be minimized. Recent research by the authors has revealed that coupling the vibration modes of passively-isolated machines by properly selecting the location of the vibration isolators could lead to a drastic reduction in residual vibrations. However, the effect of motor location on the residual vibrations of mode-coupled UPM machines has not been rigorously analyzed. In this paper, an objective function which minimizes residual vibration energy with respect to motor location is defined and analyzed. It is shown to have a guaranteed global minimum irrespective of the parameters of the UPM machine. Conditions that ensure that the global minimum is located in a practically feasible design space are explored. Finally, the merits of optimal motor placement on residual vibration reduction are demonstrated using simulations conducted on a 5-axis ultra-precision machine tool.

Design of a Damper for a Suspension System via Evolutive Optimization

2013 ◽  
Author(s):  
Carlos A. Duchanoy ◽  
Marco A. Moreno-Armendáriz ◽  
Carlos A. Cruz-Villar
Keyword(s):  
Dynamic Optimization ◽  
Optimization Algorithm ◽  
Physical Characteristics ◽  
Suspension System ◽  
Dynamic Interactions ◽  
Multi Objective ◽  
Damping Coefficients ◽  
Design Variables ◽  
Parameterized Model ◽  
Stiffness And Damping

In this paper a dynamic optimization methodology for designing a passive automotive damper is proposed. The methodology proposes to state the design problem as a dynamic optimization one by considering the nonlinear dynamic interactions between the damper and the other elements of the suspension system, emphasizing geometry, dimensional and movement constraints. In order to obtain realistic simulations of the suspension, a link between a Computer-Aided Engineering Model (CAEM) and a multi-objective dynamic optimization algorithm is developed. As design objectives we consider the vehicle safety and the passenger comfort which are represented by the contact area of the tire and the vibrations of the cockpit respectively. The damper is optimized by stating a set of physical variables that determine the stiffness and damping coefficients as independent variables for the dynamic optimization problem, they include the spring helix diameter, the spring wire diameter, the oil physical characteristics and the bleed orifice diameters among others. The optimization algorithm that we use to solve the problem at hand is a multi-objective evolutive optimization algorithm. For this purpose we developed a parameterized model of the damper which is used to link the CAE tools and the optimization software, thus enabling fitness evaluations during the dynamic optimization process. By selecting the physical characteristics of the damper as design variables instead of the typical stiffness and damping coefficients, it is possible to consider important design constrains as the damper size, movement limitations and anchor points. As result of the proposed methodology a set of blueprints of non dominated Pareto configurations of the damper are provided to the decision maker.

scholarly journals Investigation on the Mechanical Properties of MRE Compounds

Machines ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 36 ◽  
Author(s):  
Renato Brancati ◽  
Giandomenico Di Massa ◽  
Stefano Pagano
Keyword(s):  
Magnetic Field ◽  
Mechanical Properties ◽  
Smart Materials ◽  
Testing Machine ◽  
Static Test ◽  
Vibration Isolators ◽  
Elastomeric Matrix ◽  
Magneto Rheological ◽  
Stiffness And Damping ◽  
Rheological Effect

This paper describes an experimental investigation conducted on magneto-rheological elastomers (MREs) with the aim of adopting these materials to make mounts to be used as vibration isolators. These materials, consisting of an elastomeric matrix containing ferromagnetic particles, are considered to be smart materials, as it is possible to control their mechanical properties by means of an applied magnetic field. In the first part of the paper, the criteria adopted to define the characteristics of the material and the experimental procedures for making samples are described. The samples are subjected to a compressive static test and are then, adopting a testing machine specially configured, tested for shear periodic loads, each characterized by a different constant compressive preload. The testing machine is equipped with a coil, with which it is possible to vary the intensity of the magnetic field crossing the sample during testing to evaluate the magneto-rheological effect on the materials’ characteristics in terms of stiffness and damping.

A New Method for Simultaneous Optimization of a Structure With Active and Passive Control Variables

2015 ◽  
Author(s):  
Ui-Jin Jung ◽  
Gyung-Jin Park
Keyword(s):  
Control Systems ◽  
Large Scale ◽  
Optimization Problem ◽  
Integrated System ◽  
Static Loads ◽  
Design Variables ◽  
Response Optimization ◽  
The Time Domain ◽  
Control Forces ◽  
And Control

An optimization method is proposed for the simultaneous design of structural and control systems using the equivalent static loads. The two structural and control systems are not completely independent and need to be considered in a unified fashion. Furthermore, an integrated system design is unavoidable to exhibit a good performance in the time domain. The analysis for the integrated system is conducted for the transient-state in a dynamic manner. The constraints for the structural and control systems are defined in the time domain as well. Therefore, a physically small scale problem in structural analysis easily becomes quite a large scale in an optimization problem. A new equivalent static loads (ESLs) method, which deals with the structural design variables as well as the control design variables, is proposed to solve physically large scale problems. A finite element dynamic equation is defined with control forces and a dynamic response optimization problem is formulated. Linear static response optimization is carried out with the ESLs. The control forces for the linear static response optimization are considered as design variables. Shape variables are utilized to handle the design variables for the control forces. Several examples are solved to validate the proposed method.

On Selection of Control Parameters for H∞ Output Feedback

2005 ◽  
Author(s):  
Chang-Ching Chang ◽  
Chi-Chang Lin
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Output Feedback ◽  
Delay Time ◽  
Output Feedback Control ◽  
Feedback Gain ◽  
Control Force ◽  
Control Parameters ◽  
Structural Responses ◽  
Control Forces

In this paper, an H∞ direct output feedback control algorithm through minimizing the entropy, a performance index measuring the tradeoff between H∞ optimality and H2 optimality, is employed to design the control system in reducing structural responses due to dynamic loads such as earthquakes. The control forces are obtained from the multiplication of direct output measurements by a pre-calculated time-invariant feedback gain matrix. To achieve optimal control performance, the strategy to select both control parameters γ and α is extensively investigated. The decrease of γ or increase of α results in better control effectiveness, but larger control force requirement. For a single degree-of-freedom (SDOF) damped structure, exact solutions of output feedback gains and control parameters are derived. It can be proved analytically that the LQR control is a special case of the proposed H∞ control. Direct velocity feedback control is effective in reducing structural responses with very small number of sensors and controllers compared with the DOFs of the structure. In active control of a real structure, control force execution time delay cannot be avoided. Relatively small delay time not only can render the control ineffective, but also may cause system instability. In this study, explicit formulas to calculate maximum allowable delay time and critical control parameters are derived for the design of a stable control system. Some solutions are also proposed to increase the maximum allowable delay time.

An Efficient Technique for Design of Hydraulic Engine Mount via Design Variable-Embedded Damping Modeling

2005 ◽  
Vol 127 (1) ◽  
pp. 93-99 ◽  
Author(s):  
Jun-Hwa Lee ◽  
Kwang-Joon Kim
Keyword(s):  
Dynamic Characteristics ◽  
Low Frequency ◽  
High Amplitude ◽  
Nonlinear Damping ◽  
Efficient Design ◽  
Equivalent Viscous Damping ◽  
Damping Characteristics ◽  
Design Variables ◽  
Engine Mount ◽  
Stiffness And Damping

For an efficient design of hydraulic mounts, it is most important to have a good mathematical model available, which must be simple yet capable of representing dynamic characteristics of the hydraulic mounts accurately. Under high amplitude excitations in the low-frequency range, the hydraulic mounts show strongly frequency-dependent stiffness and damping characteristics, which are related with so-called inertia track dynamics. Since nonlinear damping models based on fluid mechanics are typically used to predict the dynamic characteristics of the hydraulic mounts, relations between various design variables, such as geometry of the inertia track, and resultant stiffness and damping characteristics are understood only by tedious numerical computations. In this paper, the use of an equivalent viscous damping model—derived from a nonlinear model and represented in terms of design variables in an explicit manner—is proposed and, based on the equivalent linear model, are presented simple as well as very useful formulas for an efficient design of the hydraulic mounts.

Identification of Dynamic Rates of Elastomeric Vibration Isolators in Automotive Vehicles

2004 ◽  
Author(s):  
Donald J. Nefske ◽  
Shung H. (Sue) Sung ◽  
Douglas A. Feldmaier
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Stiffness ◽  
Element Model ◽  
Interior Noise ◽  
Rear Suspension ◽  
Model Comparisons ◽  
Vibration Isolators ◽  
Vehicle System ◽  
Stiffness And Damping

Dynamic stiffness and damping rates of elastomeric vibration isolators used in automotive vehicles are identified from static isolator tests and the use of an isolator finite element model. Comparisons are made of the predicted versus measured dynamic stiffness and damping rates from 0 to 300 Hz of a rear suspension isolator to validate the technique. The identified dynamic rates of the elastomeric isolators of a representative vehicle are then input to the vehicle system finite-element model to compare the predicted versus measured vehicle vibration and interior noise response for laboratory shaker excitation.

A Design Technique for a Magnetic Bearing-Rotor in a Turbo Blower Considering Critical Speeds

2012 ◽  
Vol 569 ◽  
pp. 564-567
Author(s):  
Hoon Hyung Jung ◽  
Seung Hee Kang ◽  
Bang Hyun Cho ◽  
Chae Sil Kim
Keyword(s):  
Element Model ◽  
Magnetic Bearing ◽  
Design Technique ◽  
Loop Control ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Turbo Blower ◽  
Bearing Stiffness ◽  
Control Forces ◽  
Stiffness And Damping

This paper introduces a rotor design technique for a turbo blower supported by magnetic bearings that considers the critical speeds of the rotor. An important factor for rotor critical speeds is the stiffness of its bearings. The magnetic bearing acts as a negative spring, called the position stiffness prior to operation, and rotor systems are initially unstable until the stiffness (current stiffness) and damping in the active control rotating system are determined using closed loop control forces. This paper describes a finite element model for the rotor, derives the stiffness equations for the magnetic bearing, and defines the total magnetic bearing stiffness including the position stiffness and current stiffness. Finally, the magnetic bearing stiffness that avoids the rotor critical speeds is chosen.

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Pole Placement ◽  
Feedback Gain ◽  
Time Varying ◽  
Placement Problem ◽  
Single Input ◽  
Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

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