Second-order State-space Model Research Articles

The Nonlinear Dynamic Response of Intrapartum Fetal Heart Rate to Uterine Pressure.

The research objective of our group is to improve the intrapartum detection of cardiotocography tracings associated with an increased risk of developing fetal acidosis and subsequent hypoxic-ischemic encephalopathy (HIE). The detection methods that we aim to develop must be sensitive to abnormal tracings without causing excessive unnecessary interventions. Past studies showed that the dynamic response of fetal heart rate (FHR) to uterine pressure (UP) during the intrapartum could be modelled using linear systems. In this study, we examined the assumption of linearity by comparing the performance of linear dynamic and nonlinear dynamic models of the UP-FHR system. The linear systems were defined by second-order state-space models. The nonlinear systems were defined by Hammerstein models: a cascade of a static nonlinearity and a linear second-order state-space model. Our results showed that nonlinear dynamic models were better than linear systems in 81.8% of UP-FHR segments.

Investigating the flexibility of a novel multi-zone air heating and ventilation system using model predictive control

In forced air heating systems, there are basically two approaches to set the temperature of each zone within a multi-zone building: regulating the supply airflow rate and regulating the supply air temperature (or a combination of these two parameters). Conventional variable air volume (VAV) systems usually maintain the supply air temperature constant within all rooms and regulate only the supply airflow rate to the room. Recently, a novel multi-zone air heating and ventilation (MZHV) system has been developed, which is capable of regulating both the supply airflow rate and the supply air temperature to the rooms independently of each other. This paper investigates the flexibility of the novel MZHV system and compares it with the conventional VAV systems. The MZHV system as well as a multi-zone case study building are modeled in a high-fidelity simulation environment (IDA ICE). Instead of traditional rule-based control schemes, a model predictive control (MPC) scheme is developed to control real-time power consumption of the multi-zone building. For this purpose, a second-order state space model is identified for each zone and calibrated against the results from the high fidelity simulations. MPC is implemented in MATLAB environment by using the second-order state space models. Two co-simulations are performed to compare the flexibility of the novel MZHV system with a conventional VAV system. The results show that the MZHV system provides a significant flexibility in terms of the energy usage, without affecting the comfort levels. This flexibility can for example be exploited to reduce the overall energy usage or provide ancillary services for a smart electricity grid.

Adaptive Model Predictive Vibration Control of a Cantilever Beam with Real-Time Parameter Estimation

This paper presents an adaptive-predictive vibration control system using extended Kalman filtering for the joint estimation of system states and model parameters. A fixed-free cantilever beam equipped with piezoceramic actuators serves as a test platform to validate the proposed control strategy. Deflection readings taken at the end of the beam have been used to reconstruct the position and velocity information for a second-order state-space model. In addition to the states, the dynamic system has been augmented by the unknown model parameters: stiffness, damping constant, and a voltage/force conversion constant, characterizing the actuating effect of the piezoceramic transducers. The states and parameters of this augmented system have been estimated in real time, using the hybrid extended Kalman filter. The estimated model parameters have been applied to define the continuous state-space model of the vibrating system, which in turn is discretized for the predictive controller. The model predictive control algorithm generates state predictions and dual-mode quadratic cost prediction matrices based on the updated discrete state-space models. The resulting cost function is then minimized using quadratic programming to find the sequence of optimal but constrained control inputs. The proposed active vibration control system is implemented and evaluated experimentally to investigate the viability of the control method.

Estimation of free flow speed and critical density in a segmented freeway using missing data and Monte Carlo-based expectation maximisation algorithm

This study is concerned with the estimation of two key parameters in a stochastic non-linear second-order state-space model of traffic flow using the maximum likelihood approach while employing a recursive Monte Carl-based filtering and smoothing to solve related expectation maximisation (EM) algorithm. A maximum likelihood (ML) framework is employed in the interests of statistical efficiency. EM algorithm may be used to compute these ML estimates and Monte Carlo approach is used to compute required conditional expectations. Considered parameters, free flow speed and critical density are traffic flow characteristics which are key parameters used for traffic control, ramp metering, incident management etc. A set of field traffic data from the Interstate-494 highway located in Metro Freeway Network Area at Minnesota is used to demonstrate the effectiveness of the proposed approach.

A third-order state-space model for fatigue crack growth

A second-order state-space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1-4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075-T6 and 2024-T3 at constant-amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third-order state-space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second-order state-space model is treated as the third state variable in this model. Through simulations, it is shown that the third-order state-space model gives better predictions than the second-order state-space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.