Jong-Bok Lee

A Stochastic Controller Design Using an Approximate Solution of FPK Equation

The Fokker-Planck-Kolmogorov (FPK) equation is a powerful tool with Markovian response for analyzing dynamic systems. In this study we consider the design of a stochastic controller using FPK for a system subjected to a wide band random disturbance with constant power spectral density. The time-domain dynamic system equation is transformed into a general dynamic statistical moment equation in the stochastic domain via the FPK equation. The system transformation cannot be realized in real time. In order to improve stochastic controller design in real time, a new method of designing a stochastic controller and its implementation are proposed. The practical efficiency of the proposed method using the approximate probability density function is verified via numerical simulation.

A Study of “Mode Selecting Stochastic Controller” for a Dynamic System Under Random Vibration

This paper presents a new stochastic controller applied on the vibration control system under irregular disturbances based on the mode selection scheme. Measured displacement and frequency characteristics are simultaneously used in designing a mode selecting controller. This technique is validated by applying to the suppression problem of a flexible beam with randomly vibrated circumstances. The presented method, called Mode Selecting Stochastic Controller, uses the frequency measurement of the flexible system based on a Fast-Fourier transformation algorithm. This controller is constructed by combining mode selection method with previous known Stochastic Controller in real time. Numerical simulations and several experiments are conducted to validate the proposed method. The performance of the proposed method is compared with a stochastic controller developed recently. This method was improved compared with previous one.

Experimental system identification in stochastic domain using cantilever beam

Unlikely to the conventional system identification method in deterministic domain, a stochastic approach has been attempted to figure out the system parameters of unknown system experiencing random disturbance whose stochastic information is not available. Interest is focused to identify an unknown stochastic dynamic system via stationary system output in stochastic sense. A concept to identify the system parameters in stochastic domain is proposed and implemented in terms of simulation and experiment as well. Previously developed stochastic transformation method via F-P-K (Fokker-Planck-Kolmogorov) equation is adopted to estimate the system output. Based on stationary system output only, it is attempted to identify the system parameters in inverse manner in stochastic domain successfully. Experimental study using cantilever beam is conducted to confirm quite noticeable performance of the proposed concept.

Model Tracking Dual Stochastic Controller Design Under Irregular Internal Noises

Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and 1/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation.

Model Reduction Using Stochastic Balance Technique

Recently, dynamic system has been enlarged and is normally exposed to various types of disturbance. Thus designing controller for these dynamic systems under random disturbance is not practically easy. As a result, the exact analysis for the system which is exposed to various irregular disturbance is quite important. In order to perform analysis, conventional BMR(balance model reduction) method is adopted and applied to moment equation in stochastic domain. Reliable reduced order system model has been obtained.

System Identification Using Stochastic Output Only

Most of the study on system identification has been carried out using input/output relation in physical domain. However identification concept of stochastic system has not been reported up to now. Interest is focused to identify an unknown dynamic system under random external disturbances which is not possible to measure. A concept to identify the system parameters in stochastic domain is proposed and implemented in terms of simulation. Attempt has been made to identify the system parameters in inverse manner in stochastic domain based on system output only. Simulation is conducted to reveal quite noticeable performance of the proposed concept.