Discrete State-space Equation Research Articles

Numerical analysis of the dynamic characteristics of a fractional-order viscoelastic beam with fixed supports at both ends

In this paper, we present a generalized model of a viscoelastic beam, which takes into account the influence of axial forces and incorporates a fractional constitutive relationship. In addition, we propose a novel numerical calculation method for analyzing fractional-order viscoelastic beams. This method takes the transverse displacement and bending moment of the beam as state variables, transforms the beam model into a discrete state space equation through the application of the central difference method, and utilizes an improved precise integration algorithm to solve the equation. To evaluate the performance of the method, the responses of the beam under two types of excitations, namely uniformly distributed transverse load and the motion of the support at both ends, are calculated under fixed hinge conditions. The results demonstrate that the present method has excellent accuracy and convergence, and also reveal some nonlinear phenomena of the system.

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

Attitude motion parameters estimation of the space non-cooperative tumbling target is the premise of the on-orbit target capture task. However, existing methods cannot balance the estimation accuracy and efficiency. In this paper, an adaptive hybrid Kalman filter is presented to estimate the attitude, angular velocity and inertia motion parameters of the space non-cooperative tumbling target. First, the dynamic model of the non-cooperative tumbling target is derived, and the nonlinear discrete state-space equation is obtained. Then, a hybrid Kalman filter is designed by combining the extended Kalman filter and the unscented Kalman filter. The adaptive technique is introduced to track time-varying uncertain measurement noise caused by complex space disturbances. After that, based on the first-order linearization technique, the sufficient condition for the local convergence of the proposed method is proved. Finally, the numerical simulation experiment was conducted to compare the proposed method with the adaptive extended Kalman filter and the adaptive unscented Kalman filter. The experimental results show that the estimation accuracy of the proposed method is much higher than that of the adaptive extended Kalman filter and slightly lower than that of the adaptive unscented Kalman filter, and the iteration-average Central-Processing-Unit time is 64.2% smaller than that of the adaptive unscented Kalman filter and slightly longer than that of the adaptive extended Kalman filter. The proposed method achieves a much higher accuracy with a slight loss of iteration-average Central-Processing-Unit time.

Intelligent estimation for electric vehicle mass with unknown uncertainties based on particle filter

Vehicle mass is one of the most critical parameters in the vehicle control system, based on the discrete vehicle longitudinal dynamic equation after the forward Euler approximation, non-linear particle filter is introduced to estimate the vehicle mass intelligently, and it gains a competitive advantage that statistical characteristics of noise and uncertainties in the system are not necessary to be known or supposed in advance. As a sort of recursive, Bayesian state estimator, vehicle mass is regarded as a constant state variable to constitute the discrete state-space equation, motor torque is selected as input signal, and the measurable vehicle speed is selected to constitute the observation equation, parameters such as rolling resistance coefficient, air drag coefficient and road slop are considered as high-power noise and uncertainties. The performance of the proposed vehicle mass estimator is tested by several groups of load and the results demonstrate that the output of the particle filter based vehicle mass estimator can converge to the real value and keep steady.

Adopting combined strategies to make state of charge (SOC) estimation for practical use

The estimation of state of charge (SOC) requires the tradeoff between high accuracy and robustness in the design of the battery management system. There are varieties of studies being carried out around this issue, aiming to balance the model complication, algorithm complexity, estimation accuracy, as well as robustness. In this work, in order to solve the SOC estimation problem under real complex working conditions, we introduce a strategy that combines battery modeling tactics and algorithm developing techniques to make it. In detail, we employ a combined model and build discrete state-space equations based on it. For improving the estimation accuracy, we use the recursive least squares method with forgetting factor to identify the parameters of the model. The particle filter embedded genetic algorithm is employed for SOC estimation, which overcomes the particle degradation and diversity loss for further enhancing the accuracy and robustness of estimation. Finally, real road test data is applied to investigate the estimation performance of the developed SOC estimation strategy.

A Predictive Power Control Strategy for DFIGs Based on a Wind Energy Converter System

A feasible control strategy is proposed to control a doubly fed induction generator based on the wind energy converter system (DFIG-WECS). The main aim is to enhance the steady state and dynamic performance under the condition of the parameter perturbations and external disturbances and to satisfy the stator power response of the system. Within the proposed control method, the control scheme for the rotor side converter (RSC) is developed on the model predictive control. Firstly, the self-adaptive reference trajectory is established from the deduced discrete state-space equation of the generator. Then, the rotor voltage is calculated by minimizing the global performance index under the current prediction steps at the sampling instant. Through the control scheme for the grid side converter (GSC) and wind turbine, we have re-applied the conventional control. The effectiveness of the proposed control strategy is verified via time domain simulation of a 150 kW-575 V DFIG-WECS using Matlab/Simulink. The simulation result shows that the control of the DFIG with the proposed control method can enhance the steady and dynamic response capability better than the conventional ones when the system faces errors due to the parameter perturbations, external disturbances and the rotor speed.

A novel fractional order model based state-of-charge estimation method for lithium-ion battery

Accurate state of charge estimation of lithium-ion battery is directly related to the safe operation of electric vehicles and also an indispensable function of the battery management system. Four aspects of efforts are made to improve the estimation accuracy. First, for overcoming the drawbacks of equivalent circuit model and electrochemical model, the fractional order impedance model is built via electrochemical impedance spectroscopy data and the fractional element is used to describe the polarization effect in a simple and meaningful way. Second, the discrete state-space equations of the impedance model are inferred by Grünwald-Letnikov definition and parameters of the model including the order of the fractional element are identified together by genetic algorithm (GA) and the experiment data of the dynamic driving cycles. Third, the fractional order unscented Kalman filter technique is presented and the ‘short memory’ technique is employed to improve the computation efficiency of fractional operator. Lastly, experimental validation is implemented to verify the effectiveness of the proposed approach and results show that the SoC estimation accuracy can be improved by the proposed model and estimation method. The estimation error can be controlled within the range of 3%.

Model Predictive Control for Space Teleoperation Systems Based on a Mixed-H2/H∞ Approach

In this paper a novel model predictive control (MPC) approach is proposed based on mixed-H2/Hi control for space teleoperation systems with unknown, large time-varying delays and input constraints. This novel approach only measures the online delay; it does not presume the delay bounds. In addition, Hi control has been incorporated into the original MPC, which compensates for large time-varying delays, handles input constraints, and provides the desired tracking performance. First, the space teleoperation system is built based on a type of control architecture and then converted into a discrete state-space equation. Next, a state-feedback controller is designed based on linear matrix inequality (LMI). Meanwhile, the corresponding sufficient conditions are derived for the controller, enabling the closed-loop system to be asymptotically stable and guaranteeing the prescribed mixed-H2/Hi performance under input constraints. The parameters of the controller are calculated online by updating the mixed-H2/Hi optimizing problem during each interval. Finally, comparative simulations reveal that the proposed approach can achieve better performance in terms of tracking ability than that of traditional MPC. Moreover, it can ensure the input constraints in the unknown, large time-varying delay scenario whereas the original Hi control approach cannot guarantee performance.

FAULT DIAGNOSIS OF HYDRAULIC SERVO SYSTEM USING THE UNSCENTED KALMAN FILTER

AbstractFault occurrence can be embodied by the physical parameter variations of the hydraulic servo system. Faults can, therefore, be diagnosed according to the model coefficient variations of the hydraulic servo system. This paper proposes an approach for fault diagnosis based on the unscented Kalman filter (UKF) with a mathematical model of the hydraulic servo system. The mathematical model is established using the dynamic equations of the hydraulic servo system. Based on the fault mechanism analysis results, several important system model parameters that can separately represent different faults in different components of the hydraulic servo system are chosen. Discrete state space equations are derived from the dynamic equations. The UKF algorithm is used to estimate the important system model parameters of the hydraulic servo system by utilizing the discretized state space model. According to the variations of these model parameters, the fault modes and locations of the hydraulic servo system can be diagnosed and isolated. Two types of faults, namely, abrupt fault in servovalve gain and slow wear fault in hydraulic cylinder piston, which cannot be directly detected from the system output, are introduced individually to the hydraulic servo system in this work. By comparing with the extended Kalman Filter, three different experimental cases are used to validate the effectiveness of the UKF for hydraulic servo system fault diagnosis.

Modelling of HEV Lithium-Ion High Voltage Battery Pack using Dynamic Data

A new approach is proposed for developing a model for High Voltage (HV) Lithium-ion (Li-Ion) battery pack using Hybrid Electrical Vehicle (HEV) drive cycles data. A variety of drive cycle's data have been collected from the test vehicle at various operating conditions. The equivalent electrical circuit for the HV battery is formulated using mathematical equations and discrete state space equations. The Open Circuit Voltage (OCV), Offset Voltage at Zero Load conditions (VZL), battery pack internal resistance (Rbatt) are considered as various components of the mathematical equations and battery pack RC filter states are represented using discrete state space equations at various battery temperature (Batt Temp) conditions (-70C to 450C). The parameter estimation problem is then considered as the problem of simultaneously estimating the parameters of all the coefficients formulated in the battery pack mathematical and state space equations. This is mathematically posed as a constrained optimization problem and a variant of genetic algorithm (GA) is used to solve it. Modelling is done using MATLAB®/Simulink® tools. The developed model is validated on actual vehicle drive cycle data. The results obtained by the proposed approach are closely matching with the actual battery response under different drive cycles. The distinction of the approach is that it does not call for any lab tests, additional instrumentation and cell level measurements yet serves the purpose of fair fidelity model for the design, analysis and control of the HEV powernet.

State-Of-Charge Estimation of Li-Ion Battery Using Extended Kalman Filter

The Li-ion battery is studied base on its equivalent circuit PNGV model. The model parameters are identified by HPPC test. The discrete state space equation is established according to the model. The basic theory of extended Kalman filter algorithm is studied and then the filtering algorithm is set up under the noisy environments. Finally, a kind of electric car is used for testing under the UDDS driving condition. The difference between the simulation value using extended Kalman filter under the noisy environment and the theoretical value is compared. The result indicated that the extended Kalman filter keeps an excellent precision in state of charge estimation of Li-ion battery and performs well when disturbance happens. DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.3894

Ultra-short-term multi-node load forecasting – a composite approach

In the electric power system, grasping active and reactive load variation regularity of each node is a key problem for optimal dispatch, preventive control, security assessment and transmission capacity evaluation. This study presents a novel composite approach of ultra-short-term forecasting for multi-node active and reactive load. It proposes a hierarchy and sub-area idea to construct a framework of self-adapting dynamic load models. With load forecasting at the top layer implemented by the recursive least square support vector machines (RLS-SVM) algorithm, discrete state-space equations are established to describe the dynamic characteristics of the multi-node active load distribution factors and power factors, and then the Takagi–Sugeno (TS) fuzzy control technique is introduced to realise feedback compensation. The application of the proposed technique in the actual power system control centre of Shandong Province is verified and satisfactory results are found.

FEM Formulation for Dynamic Instability of Fluid-Conveying Pipe on Nonuniform Elastic Foundation

In this study, we investigate the effect of a nonuniform Winkler-type elastic foundation on the stability of pipes conveying fluid fixed at the upstream end only. A stability analysis of transverse motion aims at determining the flutter velocity as a function of the governing control parameters such as fluid mass over the pipe mass ratio, or foundation stiffness. The global stability of the system is analyzed applying an ad-hoc developed finite-element formulation that leads to a discrete state-space equation of motion. It is shown that for a uniform foundation, an increased stiffness of the Winkler coefficient leads to an increased critical flow speed for any value fluid/pipe mass ratio, while in the case of a nonuniform elastic foundation, the system may present higher or lower critical flow speed depending on the fluid/pipe mass ratio. Special attention is paid to the “𝓈” type behavior of the instability curves, as reported in numerous papers.

A Physically based Load Model of Residential Electric Thermal Storage: Application to LM Programs

This paper describes and assesses a physically based load model of residential Electric Thermal Storage (ETS) devices, for both static and dynamic loads. This load model is based on an energy balance between the indoor environment, the dwelling constructive parameters, the ETS device, and the internal mass through a discrete state-space equation system. Therefore, detailed information about several physical magnitudes of the whole system are given along the time: ceramic brick temperature, electrical demand, heat fluxes, and indoor temperature. The main application of this load model has been oriented towards the simulation of the ETS device performances, in order to assess load management (LM) programs. The proposed model has been implemented and validated using data collected for the last two years in residential areas, in order to evaluate its accuracy and flexibility. Finally, a simulation case study is presented to show the possibilities of limiting and reducing the actual winter-peak by means of an LM program, proposed by the authors, that takes into account customer minimum comfort levels and the experimental data of residential load curve profiles.

Implementation and assessment of physically based electrical load models: application to direct load control residential programmes

The purpose of the paper is to describe physically based electrical models of heating, ventillation and air conditioning residential loads. These models are based on energy balances between the internal air, the dwelling constructive elements, the conditioner appliances and the external environment through a discrete state-space equation system. The main objective of these dynamic models is to evaluate load management programmes, above all direct load control actions. The models have been implemented and tested to assess their accuracy and suitability in this specific kind of applications. In this way, simulated results have been compared with data collected over a period of one year in different cities and for different load performances—steady state as well as response to remote control actions. The advantages of the models proposed here are also compared with models previously developed and described in the literature.

Solution and identification of discrete state-space equations via Walsh functions

A pair of discrete Walsh operational matrices is proposed which corresponds to the known operational matrix of continuous systems. Using these matrices, a procedure is presented for the solution and identification of discrete, linear, time-invariant, multivariable systems described by the state-space model. The above problems being considered are only two of the possible applications using the discrete Walsh functions with operational matrices.