H2 Optimization of Damped-Vibration Absorbers for Suppressing Vibrations in Beams With Constrained Minimization

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Murat Tursun ◽  
Eşref Eşkinat
Keyword(s):  
State Space ◽  
The State ◽  
Mode Shapes ◽  
Space Representation ◽  
Vibration Absorbers ◽  
State Space Representation ◽  
Lagrange’S Equation ◽  
System Output ◽  
External Forces ◽  
Mass Spring

Vibration absorbers are efficient and robust tools for reducing vibration and noise. Researchers use various alternative approaches and validate their methods with examples consisting of mass-spring-damper systems. Focusing on the minimization of the vibration amplitudes via passive absorber approach, a new and efficient method for calculating the optimum parameters of N absorbers attached to a uniform beam with M mode shapes (where N and M are any positive integers) has been developed. First, for the most general case, dissipation due to damping, kinetic, and potential energy and the effects of external forces are analyzed. The Lagrange's equation is used to provide the state space representation of the system. State space representation of a system with N absorbers and M mode shapes is composed. On the basis of the state space representation and the Lyapunov function, the H2 norm of the transfer function of the system is utilized in the newly developed optimization package. The system output is minimized by the optimization algorithm and displayed with a comparison between cases without an absorber and with randomly selected absorber parameters. As a conclusion, with the help of this method for calculation of optimal absorber parameters, one can easily design a mechanical system according to design criteria.

scholarly journals Shannon Entropy Analysis of the Genome Code

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Shannon Entropy ◽  
Large Volume ◽  
The State ◽  
Space Representation ◽  
Entropy Analysis ◽  
Genomic Information ◽  
State Space Representation

This paper studies the chromosome information of twenty five species, namely, mammals, fishes, birds, insects, nematodes, fungus, and one plant. A quantifying scheme inspired in the state space representation of dynamical systems is formulated. Based on this algorithm, the information of each chromosome is converted into a bidimensional distribution. The plots are then analyzed and characterized by means of Shannon entropy. The large volume of information is integrated by averaging the lengths and entropy quantities of each species. The results can be easily visualized revealing quantitative global genomic information.

Furnace Modelling Using State Space Representation

2006 ◽  
Vol 3 (1) ◽  
pp. 37
Author(s):  
Razidah Ismail
Keyword(s):  
State Space ◽  
Power Plants ◽  
Controller Design ◽  
Cost Savings ◽  
Combined Cycle ◽  
The State ◽  
Space Representation ◽  
State Variables ◽  
State Space Representation ◽  
Space Modeling

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.

Conversion Among Arma Models And State-Space Representation

2021 ◽  
Vol 9 (2) ◽  
pp. 53-59
Author(s):  
William W.S. Chen
Keyword(s):  
State Space ◽  
Arma Model ◽  
The State ◽  
Space Representation ◽  
Arma Models ◽  
State Space Representation ◽  
Markovian Representation

We present the ARMA models (or Non-Markovian) and state-space (or Markovian) representation relationship. Then we break the problem into three different cases to discuss how one form could be converted to another form. In case A, we assume that we know the state-space representation then we convert it into the ARMA model. In case B, we reverse the situation, given the ARMA model we convert into state-space representation. In Case C, we combine the first two cases, conversion the two forms in either directions. 

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