Assumption Of Linear System Research Articles

Extended‐state‐observer‐based adaptive robust control of a single‐axis hydraulic shaking table

AbstractThe shaking table test has been widely recognized as one of the most reliable methods for assessing the dynamic response of structures and systems when exposed to a range of vibrations. Replicating these vibrations, recorded as acceleration signals, necessitates precise controller designs. However, traditional controller designs primarily rely on linear system assumptions, leading to complications in incorporating parametric uncertainty and uncertain non‐linearity. This paper presents a novel approach to the acceleration trajectory control problem of single‐axis hydraulic shaking table systems from a non‐linear perspective. This strategy employs a controller combined with an extended state observer (ESO) and adaptive control, offering a design that more closely reflects real‐world scenarios and requires less parameter adjustment. The ESO estimates the uncertain non‐linearity using the displacement signal, while the parametric uncertainty is tackled through adaptive control. The proposed controller's effectiveness is validated through theoretical proof using Lyapunov analysis. The analysis demonstrates that asymptotic tracking performance is guaranteed when the uncertain non‐linearity is time‐invariant. Moreover, with time‐variant uncertain non‐linearity, the controller can also ensure both prescribed transient tracking performance and final tracking accuracy. Comparative experiment results underscore the superior performance of the proposed controller.

Prediction of the driver’s head acceleration and vibration isolation performance of the seating suspension system using the time and frequency domain modeling

Long-time exposure to low-frequency vibration will negatively impact human health.A rapid biodynamic system modeling method has been proposed to study the human body’s response to the low-frequency vibration excitation in the whole vehicle environment. The sensitivity of design parameters of the seating suspension system to the vibration isolation performance will be studied. The dynamic model consists of a lumped parameter mass-spring-dashpot model of seven degrees of freedom (7DOF) and used for the prediction of the head acceleration in the time domain and peak transmissibility ratio in the frequency domain under a sinusoidal wave excitation and random road profile excitations of different road classes and vehicle speeds. A calculation formula has been established to predict the seat effective amplitude transmissibility (SEAT) from the transmissibility ratios and frequency weighting function of the ISO 8606, while the transmissibility ratios can be calculated from the frequency response analysis of the seven degrees of freedom system dynamic equations. The simulation results in the frequency domain have been verified by those in the time domain for the linear system assumption. The change trends of the driver’s head acceleration, SEAT value, and peak transmissibility ratio from the driver’s head to the seat base with respect to the stiffness and damping coefficients of the seat and cushion have been compared with and verified by one another.It is proved that in the vehicle system, individually, reducing the individual stiffness and damping coefficients of the seat structure, reducing the individual seat cushion stiffness, and increasing the individual seat cushion damping coefficient one by one will be able to reduce the driver’s head acceleration, peak transmissibility ratio, and SEAT value from the head to seat base, and improve the ride comfort. Simultaneously reducing the stiffness and damping coefficients of the seat and cushion will be able to reduce the driver’s head acceleration, peak transmissibility ratio, and SEAT value from the head to seat base and improve the ride comfort. The reduction effect of the driver’s head acceleration is more substantial under the Class E road profile of a large profile roughness than that under the other road classes.

Validating Linear Systems Analysis for Laminar fMRI: Temporal Additivity for Stimulus Duration Manipulations

Advancements in ultra-high field (7 T and higher) magnetic resonance imaging (MRI) scanners have made it possible to investigate both the structure and function of the human brain at a sub-millimeter scale. As neuronal feedforward and feedback information arrives in different layers, sub-millimeter functional MRI has the potential to uncover information processing between cortical micro-circuits across cortical depth, i.e. laminar fMRI. For nearly all conventional fMRI analyses, the main assumption is that the relationship between local neuronal activity and the blood oxygenation level dependent (BOLD) signal adheres to the principles of linear systems theory. For laminar fMRI, however, directional blood pooling across cortical depth stemming from the anatomy of the cortical vasculature, potentially violates these linear system assumptions, thereby complicating analysis and interpretation. Here we assess whether the temporal additivity requirement of linear systems theory holds for laminar fMRI. We measured responses elicited by viewing stimuli presented for different durations and evaluated how well the responses to shorter durations predicted those elicited by longer durations. We find that BOLD response predictions are consistently good predictors for observed responses, across all cortical depths, and in all measured visual field maps (V1, V2, and V3). Our results suggest that the temporal additivity assumption for linear systems theory holds for laminar fMRI. We thus show that the temporal additivity assumption holds across cortical depth for sub-millimeter gradient-echo BOLD fMRI in early visual cortex.

Pulsatile Aortic Pressure-Flow Analysis using Fractional Calculus for Minimally-invasive Applications

Time-dependent pulsatile pressure and flow waveforms in the aorta carry with them considerable information regarding the underlying dynamic behavior of the cardiovascular system. The aortic pressure-flow relationship has traditionally been described using integer calculus. As such, periodicity and linear system assumptions are necessarily imposed to extract hemodynamic information. We introduce the use of fractional calculus (FC) to relate minimally-invasive measurements, of the velocity of aortic blood flow with an esophageal Doppler monitor, to the derived aortic pressure. The basis for this research is a Taylor series model of the velocity of aortic blood flow with subsequent term-by-term fractional integration as well as fractional differentiation. These results demonstrate that this FC approach could potentially generate the aortic pressure waveform throughout systole. Further studies of its first derivative, or the time rate of pressure change,

Limits of linearity in squeeze film behavior of a single degree of freedom microsystem

This paper presents a theoretical investigation of squeeze film flow in systems employing microplates parallel to a substrate and undergoing large amplitude normal vibration. Most previous models of squeeze film damping assume small oscillation amplitude with linear system behavior, but it is often unclear how small the vibrations must be to actually elicit this response. In addition, fluid inertia effects are usually overlooked. This study provides a compact nonlinear solution for the incompressible hydrodynamic forces with specific terms describing fluid inertia and viscous damping. Numerical analysis (the explicit Runge-Kutta method) is applied to solve the nonlinear governing equation. The effects of frequency, oscillation amplitude, aspect ratio (of gap to length), and Reynolds number on the dynamic response of the system are investigated. The overall system response depends strongly on the actuation frequency and system properties. It is found that a simple criterion of validity for the linear system assumption is not possible. Near resonance, the vibration input amplitude (relative to the initial gap) must be very small indeed for linearity (∼0.001), while in other cases the relative amplitude can be greater than one.

선형시스템가정에 근거한 Muskingum 하도추적방법의 매개변수 결정

This study proposes the method for determining the Muskingum channel routing model parameters based on the assumption of linear system. The proposed method was applied to the Chungju dam basin for the evaluation. Additionally, the rainfall-runoff was repeated for the Yeongchun-Chungju dam reach using seven rainfall events observed. Summarizing the results is as follows. First, the concentration time and storage coefficient of a channel reach formed by the subdivision can be expressed as the difference between the concentration times and storage coefficients of upstream and downstream basins. The storage coefficients of the channel reach estimated is equal to the storage coefficient of the Muskingum channel routing model and the weight factor can be simply estimated using the ratio between the concentration time and storage coefficient. Second, the weight factor of the Muskingum model is in inverse proportion to the Russel coefficient, which is in between 0.4166 and 0.625 when considering the Russel coefficients generally applied. Finally the application to the Yeongchun-Chungju dam reach showed that the proposed method is still valid regardless of the limitations such as the uncertainty of the observed data.

Performance analysis of thermal energy system with linear system method

The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculation of system performance output is deduced on the system state equation. Two important vector of system are worked out under linear system assumption and transform. The transfer matrix is the characteristics of system itself and is constant for a similar condition, which greatly facilitates the analysis. The concept of thermal disturbance vector is proposed to construct the thermal disturbance input easily. The method can be helpful for analyzing any thermal disturbance input satisfying the assumption and also for supplementing the correction means of performance test. An example of 600MW power unit is presented to demonstrate its availability.

Incorporating subsurface-flow mechanism into geomorphology-based IUH modeling

Surface- and subsurface-runoff processes on hillslopes are quite different in nature; nevertheless, the geomorphological instantaneous unit hydrograph (GIUH) simulates runoff using only the surface-flow mechanism. In this study, the GIUH model was revised to consider both the surface- and subsurface-flow processes. Kinematic-wave approximation was used to estimate the mean value of the travel-time probability distributions for runoff in surface-flow regions and channels, and Darcy's law was adopted to estimate the runoff travel time in subsurface-flow regions. Based on the linear system assumption, the hydrologic response of a watershed is the superposition of the hydrologic responses resulting from the surface flow and subsurface flow of the watershed. The IUH can adequately reflect the variation of surface-flow roughness and hydraulic conductivity. An example watershed was selected to test the capability of the revised model. The simulated hydrographs obtained using the original and revised models were basically in good agreement with the observed hydrographs. However, significant improvement of the simulation was found in the recession limb of the simulated hydrograph because flood recession was dominated by the subsurface-flow process.

Automotive seat cushion nonlinear phenomenon: experimental and theoretical evaluation

The paper describes the nonlinear phenomenon of automotive seat cushion structure. The tested transfer function between seat butt and seat track reveals that both the magnitude and frequency of the transfer function shift smaller with excitation level increases. The transfer function's magnitude also becomes smaller with the sandbag mass increases, which contradicts with linear system assumption. The tested results reveal that automotive seat cushion structure is nonlinear. A nonlinear model is developed to validate the tested nonlinear phenomenon. The discovery is significant for understanding seat cushion structure, and further could provide analysis guidance to seat design in order to reach customer satisfaction.

Piezoceramic Hysteresis in the Adaptive Structural Vibration Control Problem

Structural vibration control via passive electrical shunting and active (hybrid) actuation of a piezoceramic wafer bonded onto the surface of a simply supported beam is investigated with emphasis on modeling and understanding the effect of piezoceramic nonlinearity on system performance. A nonlinear rate-independent hysteresis model, the Ishlinskii hysteresis (IM) model, is experimentally identified for the PZT wafer by itself and then integrated into the coupled dynamic equations of the overall system consisting of the beam and electrically shunted PZT wafer. Experimental studies of the system validate the theoretical model. This model is then used to investigate the impact of PZT hysteresis on its vibration control performance in passive and hybrid scenarios that have been optimized based on a linear system assumption. A multi-term describing function representation of the IM hysteresis model is formulated to aid in computational studies.

A disturbance observer for robot manipulators with application to electronic components assembly

The success of robotic assembly for odd form electronic components depends heavily on the ability to monitor and control the insertion force. For this purpose, a joint disturbance observer for robot manipulators is presented to estimate the reaction force due to component misinsertion. The derivation is presented in the time domain for a multi-degree-of-freedom manipulator without making the SISO linear system assumption. Based on the internal model control (IMC) concept, this observer is simple in structure. It is in the form of an integral controller and only requires measurements of joint position and velocity signals to be implemented. The observed perturbation signal includes the effects of model uncertainties as well as reaction force against the environment. Careful trajectory planning and detailed friction modeling are performed to enhance accuracy of the deduced reaction force. Experiments conducted on a SCARA robot for the insertion of PCB components demonstrated the performance of the proposed disturbance observer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>