scholarly journals A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Michael J. Panza
Keyword(s):  
Transfer Function ◽  
Closed Form ◽  
State Space ◽  
Infinite Series ◽  
State Space Model ◽  
Closed Form Expression ◽  
Space Model ◽  
Finite State ◽  
Acoustic Reverberation ◽  
Finite State Space

The acoustic reverberation between two parallel reflecting planes can be represented by an infinite series of the images caused by the planes. To provide a more useful model for analysis and control, the infinite series version of the Green’s function is converted into a finite state space model that retains the high frequency character that enables broadband noise inputs to be examined. The infinite series is first summed into a very accurate, approximate closed form expression in the time domain in terms of a radical function. The radical is then transformed into an expression containing exponentials which have exact Laplace transforms that lead to an overall closed form transfer function for the system. The system transfer function is transformed into a third-order state space model that theoretically contains all of the frequency characteristics of the infinite series representation. The accuracy of the state space model is examined by comparing it to the infinite series solution for three typical types of acoustical inputs: exponential for impulse noise, single frequency sine for harmonic noise, and a multifrequency Schroeder phased harmonic sequence for random noise.

scholarly journals Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Michael J. Panza
Keyword(s):  
Closed Form ◽  
State Space ◽  
State Space Model ◽  
Closed Form Solution ◽  
String Model ◽  
Form Solution ◽  
Space Model ◽  
Function Solution ◽  
Plate Vibrations ◽  
Finite State

The Euler-Maclaurin sun formula is applied to the infinite series Green's function solution in the space-time Laplace transform domain for the one dimensional wave equation for a string fixed at each end. The resulting approximate closed form solution is used to derive a single third order input-output ordinary differential equation to model the string dynamics. The average modal density of a plate is shown to be comparable to a string. A finite three state-space model is developed for the string and applied to the vibrations of a plate subjected to broadband random and impulse inputs. The applications include the direct problem of determining the response to a disturbance input and the inverse problem of identifying the disturbance input with a finite state observer based on the finite string model. Numerical simulations using many plate modes are obtained in the time and frequency domains and are used to compare the multimodal plate model to the finite string based model and to demonstrate how the finite string based model can be used to represent the multimodal vibrations of the plate.

Modeling and Control of Biochemical Reactor

2013 ◽  
Vol 791-793 ◽  
pp. 818-821
Author(s):  
Shi Li ◽  
Xi Ju Zong ◽  
Yan Hu
Keyword(s):  
Transfer Function ◽  
State Space ◽  
State Space Model ◽  
Internal Model Control ◽  
Transfer Function Model ◽  
Function Model ◽  
Modeling And Control ◽  
Space Model ◽  
Biochemical Reactor ◽  
And Control

This paper is concerns with the study of modeling and control of biochemical reactor. Firstly, a mathematical model is established for a typical biochemical reactor, the mass balance equations are established individually for substrate concentration and biomass concentration. Then, the model is linearized at the steady-state point, two linear models are derived: state space model and transfer function model. The transfer function model is used in internal model control (IMC), where the filter parameter is selected and discussed. The state space model is applied in model predictive control (MPC), where controller parameters of control prediction horizon length and constraint of control variable variation are discussed.

Modeling and Control of Sludge Pyrolysis in a Fluidized Bed Reactor

2013 ◽  
Vol 846-847 ◽  
pp. 69-72
Author(s):  
Shi Li ◽  
Xi Ju Zong ◽  
Yan Hu
Keyword(s):  
Transfer Function ◽  
State Space ◽  
Fluidized Bed ◽  
State Space Model ◽  
Fluidized Bed Reactor ◽  
Transfer Function Model ◽  
Function Model ◽  
Modeling And Control ◽  
Space Model ◽  
And Control

This paper is concerns with the study of modeling and control of sludge pyrolysis in a fluidized bed reactor. Firstly, a mathematical model is established for sludge pyrolysis in a fluidized bed furnace, mass balance and energy equations are established. Then, the model is linearized at the steady-state point, two linear models are derived: state space model and transfer function model. The transfer function model is used in internal model control (IMC), where the filter parameter is selected and discussed. The state space model is applied in model predictive control (MPC), where controller parameters of prediction horizon length and control horizon length are discussed.

scholarly journals Track Irregularity Assessment in High-Speed Rail by Incorporating Carriage-Body Acceleration with Transfer Function

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Liubin Niu ◽  
Jinzhao Liu ◽  
Yunlai Zhou
Keyword(s):  
Transfer Function ◽  
State Space ◽  
High Speed ◽  
State Space Model ◽  
High Speed Rail ◽  
Arx Model ◽  
Body Acceleration ◽  
Space Model ◽  
Track Irregularity ◽  
Feasible Study

The determination of the precise track irregularity with unfavorable wavelength, which shall induce vehicle’s violent vibration in terms of the vehicle’s speeds, still challenges the researchers. This study proposes a feasible study of assessing the track irregularity by using the transfer function and the measured carriage-body acceleration by combining the ARX model with state space model. The ARX model and state space model are constructed using system identification to obtain the transfer relation between the track irregularity and the carriage-body acceleration, respectively. The model’s parameters are estimated by the measured data from the high-speed China Railway Comprehensive Inspection Train (CRCIT). The correlation value between the predicted and measured carriage-body acceleration shows that both models can effectively represent the transfer characteristics between the track irregularity and the carriage-body acceleration. Furthermore, the models can help assess the proportion of the vibration caused by track irregularity with the specific wavelengths and determine the track irregularity with unfavorable wavelength.

PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

2020 ◽  
Vol 8 (2) ◽  
pp. 159-169
Author(s):  
Xiangdong Liu ◽  
Xianglong Li ◽  
Shaozhi Zheng ◽  
Hangyong Qian
Keyword(s):  
Parameter Estimation ◽  
Interest Rates ◽  
Closed Form ◽  
State Space ◽  
Term Structure ◽  
Regime Switching ◽  
State Space Model ◽  
Gaussian State ◽  
Space Model ◽  
Non Gaussian

AbstractA parameter estimation method, called PMCMC in this paper, is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps. There is a closed form solution to term structure of interest rates under Markov regime. However, the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM) in the case of adding jumps. Although the difficulty of parameter estimation greatly prevents from researching models, we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility. The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR. Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.

Markov Data-Based LQG Control1

1998 ◽  
Vol 122 (3) ◽  
pp. 551-559 ◽  
Author(s):  
Guojun Shi ◽  
Robert E. Skelton
Keyword(s):  
Control Problem ◽  
State Space ◽  
Controller Design ◽  
Design Method ◽  
State Space Model ◽  
Closed Form Expression ◽  
Space Model ◽  
Weighting Matrix ◽  
Full State ◽  
Lqg Control

In this paper the Markov data-based LQG control problem is considered. The Markov data-based LQG control problem is to find the optimal control sequence which minimizes a quadratic cost function over some finite interval [0, N]. To solve this problem, we show that a complete input-output description of the system is not necessary. Obviously, a complete state space model is not necessary for this problem either. The main contributions of this paper include: (i) develop a new data-based LQG controller in a recursive form and a batch-form, (ii) derive a closed-form expression for the system’s optimal performance in terms of the Markov parameters, (iii) develop an algorithm for choosing the output weighting matrix, and (iv) demonstrate that the amount of information about the system required by the data-based controller design is less than the amount required to construct the full state space model. A numerical example is given to show the effectiveness of the data-based design method. [S0022-0434(00)02503-X]

Sign in / Sign up

Export Citation Format

Share Document