State-space Model Representation Research Articles

Development and Validation of the IAG Dynamic Stall Model in State-Space Representation for Wind Turbine Airfoils

Considering the dynamic stall effects in engineering calculations is essential for correcting the aerodynamic loads acting on wind turbines, both during power production and stand-still cases, and impacts significantly the turbine aeroelastic stability. The employed dynamic stall model needs to be accurate and robust for a wide range of airfoils and range of angle of attack. The present studies are intended to demonstrate the performance of a recently implemented “IAG dynamic stall” model in a wind turbine design tool Bladed. The model is transformed from the indicial type of formulation into a state-space representation. The new model is validated against measurement data and other dynamic stall models in Bladed for various flow conditions and airfoils. It is demonstrated that the new model is able to reproduce the measured dynamic polar accurately without airfoil specific parameter calibration and has a superior performance compared to the incompressible Beddoes–Leishman model and the Øye model in Bladed.

Time-Series Prediction of Long-Term Sustainability of Grounds Improved by Chemical Grouting

In the field of geotechnical engineering, the problems of liquefaction and land subsidence are of major concern. In order to mitigate or prevent damage from liquefaction, the chemical injection method is actively used as one of the countermeasures for ground improvement. However, a complete understanding of the long-term sustainability of improved grounds is still unavailable due to a lack of knowledge of the influencing parameters. Thus, the chances of chemical injection accidents cannot be ruled out. In this study, the compressive strength of improved grounds by the granulated blast furnace slag (GBFS), one of the grouting materials used in the chemical injection method, was evaluated and used for a time-series prediction of long-term sustainability. The objective of this study was to evaluate the accuracy and validity of the prediction method by comparing the prediction results with the test results. The study was conducted for three different models, namely, the autoregressive integrated moving average (ARIMA) model, the state-space representation (SSR) model, and the machine learning predictive (MLP) model. The MLP model produced the most reliable results for the prediction of long-term data when the input information was sufficient. However, when the input data were scarce, the SSR model produced more reliable results overall. Meanwhile, the ARIMA model generated the highest degree of errors, although it produced the best results compared to the other models depending on the criteria. It is advised that studies should be continued in order to identify the parameters that can affect the long-term sustainability of improved grounds and to simulate various other models to determine the best model to be used in all situations. However, this study can be used as a reference for the selection of the best prediction model for similar patterned input data, in which remarkable changes are observed only at the beginning and become negligible at the end.

A stabilizing predictive controller with implicit feedforward compensation for stable and time-delayed systems

Predictive controllers stand out as a realizable solution concerning disturbance rejection in comparison to classical feedforward compensators. However, stability attributes are still scarce in studies of predictive model controllers with implicit disturbance compensation. Therefore, this paper proposes a nominal stable model predictive control with implicit feedforward action for stable and time-delayed systems. The control formulation is presented based on the state-space model representation, considering the control inputs and measured disturbances increments. The control law results in a one-layer optimization problem providing optimal input moves that lead the process output to the desired reference rejecting the measured disturbances in a stable closed-loop response. The nominal stability properties are guaranteed by proving that the control cost function is a Lyapunov function. A solar collector field is used as a case study to show the disturbance rejection and overall performance characteristics of the proposed control strategy. Simulation results demonstrate the advantages and progress of the novel control algorithm and its capabilities to circumvent common issues that arise from disturbance rejection with classical feedforward structures.

State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

State space model representation is widely used for the estimation of nonobservable (hidden) random variables when noisy observations of the associated stochastic process are available. In case the state vector is subject to constraints, the standard Kalman filtering algorithm can no longer be used in the estimation procedure, since it assumes the linearity of the model. This kind of issue is considered in what follows for the case of hidden variables that have to be non-negative. This restriction, which is common in many real applications, can be faced by describing the dynamic system of the hidden variables through non-negative definite quadratic forms. Such a model could describe any process where a positive component represents “gain”, while the negative one represents “loss”; the observation is derived from the difference between the two components, which stands for the “surplus”. Here, a thorough analysis of the conditions that have to be satisfied regarding the existence of non-negative estimations of the hidden variables is presented via the use of the Karush–Kuhn–Tucker conditions.

Primary frequency support from local control of large-scale heat pumps

Increasing penetration of volatile renewable sources in the electric power system increases the need of new sources of balancing capacity. As a power-to-x technology, heat pumps (HPs) couple the electricity and heating systems, while offering a potential source of regulating capacity. This paper presents new findings on primary frequency support from large-scale HPs through local droop and synthetic inertia control methods with the objective of improving the system frequency control performance following a disturbance. The complexity and operation of large-scale HPs are different from the common model representation of HPs as thermostatically controllable load, which makes the existing studies and HP frequency support methods inaccurate. This work applies a state space model representation of the large-scale HPs, which enables a performance evaluation of existing local frequency control methods. Simulation results show the improved grid frequency control performance following a disturbance supported by large-scale HPs. Simultaneously, the heat and power response of large-scale HPs with frequency control support is compared to that of small-scale HPs.

Optimal experimental design for linear time invariant state–space models

The linear time invariant state–space model representation is common to systems from several areas ranging from engineering to biochemistry. We address the problem of systematic optimal experimental design for this class of model. We consider two distinct scenarios: (i) steady-state model representations and (ii) dynamic models described by discrete-time representations. We use our approach to construct locally D-optimal designs by incorporating the calculation of the determinant of the Fisher Information Matrix and the parametric sensitivity computation in a Nonlinear Programming formulation. A global optimization solver handles the resulting numerical problem. The Fisher Information Matrix at convergence is used to determine model identifiability. We apply the methodology proposed to find approximate and exact optimal experimental designs for static and dynamic experiments for models representing a biochemical reaction network where the experimental purpose is to estimate kinetic constants.

State-Space Model Representation to Characterize an Energy-Harvesting Circuit

This paper presents a method to model an energy harvesting circuit and a propagation channel as parts of a wireless power transfer (WPT) system. Previously , an original solution was proposed by the authors to maximize the collected DC power level, implying to model the different parts of the system by using state space representation and using convex optimization algorithms to calculate multi carrier signal weights. Firstly, a state-space model of the radio channel is obtained by the use of multivariable output-error state space (MOESP) algorithm. Then, by the vector fitting method a state-space representation is obtained in order to model the linear part of the energy harvesting circuit. At last, by the polynomial-nonlinear state-space (PNLSS) method, the non-linear part of the rectifier is also modeled.

Constructing the Singular Roesser State-Space Model Description of 3D Spatio-Temporal Dynamics From the Polynomial System Matrix

This paper considers systems theoretic properties of linear systems defined in terms of spatial and temporal indeterminates. These include physical applications where one of the indeterminates is of finite duration. In some cases, a singular Roesser state-space model representation of the dynamics has found use in characterizing systems theoretic properties. The representation of the dynamics of many linear systems is obtained in terms of transform variables and a polynomial system matrix representation. This paper develops a direct method for constructing the singular Roesser state-space realization from the system matrix description for 3D systems such that relevant properties are retained. Since this method developed relies on basic linear algebra operations, it may be highly effective from the computational standpoint. In particular, spatially interconnected systems of the form of the ladder circuits are considered as the example. This application confirms the usefulness and effectiveness of the proposed method independently of the system spatial order.

Estimation of Equation Coefficients of Free and Forced String Vibrations in Continuous Medium with Consideration of Dynamic Noise and Measurement Noise

Abstract Linear hyperbolic differential equation of partial derivatives, that sets string vibration, as well as other oscillatory processes in continuous medium and electrodynamics, is also used in many areas of theoretical physics. This article considers estimation problems of equation coefficients of free and forced string vibrations with fixed ends with consideration of additive dynamic and measurement noises. Use of a finite-difference method allowed solving partial differential equations with consideration of additive dynamic and measurement noise by solving systems of linear stationary stochastic, finite-difference and algebraic equations, expressed as state-space models. State-space model representation of string vibration equation makes it possible to use Kalman filter algorithm to make accurate estimates of string vibrations’ coordinates.

Graph-theoretic approach for structural controllability of two-dimensional linear systems

Abstract The aim of this work is to present some criteria of structural-controllability relative to a certain structural two-dimensional linear systems. The most important property of two-dimensional systems is that the information is spread in two independent directions. To study their structural-controllability, we considered a new structural digraph associated with the different structural two-dimensional linear systems. The construction of this structural digraph is based on the disjoint-union graph notion, which translates the independence of the two dynamics, and consider separately the horizontal and vertical part of the state space model representation of two-dimensional systems. We define the two-dimensional disjoint-union digraph of structural Givone–Roesser model, and determine the two-dimensional disjoint-union digraph of structural Fornasini–Marchesini model, finally we derive a criteria based on the two-dimensional disjoint-union digraph.

Identification and Observability of Lumped Kinetic Models for Vacuum Gas Oil Hydrocracking

The so-called “lumping approach” is widely used to study complex processes such as hydrocracking of vacuum residue. In order to describe the composition changes in such systems, not only must the kinetic parameters be determined, but the lumped reactions that occur should also be identified. In this study, the modeling of catalytic hydrocracking of vacuum gas oil has been carried out using six component lumps. Three different identification strategies have been developed to determine the reaction subnetwork containing a given number of reaction pathways that provides the data fit. The strategies were compared according to their tendency to provide increasingly better results, as a function of the number of reactions present. Although, in this way, 40% of the original reaction superstructure was eliminated from the system, the kinetic parameters of the remaining reactions still could not be identified with complete certainty. Hence, the linearized state-space model representations of the reaction networks ...

A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Levy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same Levy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p−1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Levy process, and show simulations and applications to real data.

Continuous-time identification of periodically parameter-varying state space models

This paper presents a new frequency domain identification technique to estimate multivariate Linear Parameter-Varying (LPV) continuous-time state space models, where a periodic variation of the parameters is assumed or imposed. The main goal is to obtain an LPV state space model suitable for control, from a single parameter-varying experiment. Although most LPV controller synthesis tools require continuous time state space models, the identification of such models is new. The proposed identification method designs a periodic input signal, taking the periodicity of the parameter variation into account. We show that when an integer number of periods is observed for both the input and the scheduling, the state space model representation has a specific, sparse structure in the frequency domain, which is exploited to speed up the estimation procedure. A weighted non-linear least squares algorithm then minimizes the output error. Two initialization methods are explored to generate starting values. The first approach uses a Linear Time-Invariant (LTI) approximation. The second estimates a Linear Time-Variant (LTV) input–output differential equation, from which a corresponding state space realization is computed.

Design and Implementation of an FPGA-based Real-time Simulator for a Dual Three-Phase Induction Motor Drive

This paper presents a digital hardware implementation of a real-time simulator for a multiphase drive using a field-programmable gate array (FPGA) device. The simulator was developed with a modular and hierarchical design using very high-speed integrated circuit hardware description language (VHDL). Hence, this simulator is flexible and portable. A state-space representation model suitable for FPGA implementations was proposed for a dual three-phase induction machine (DTPIM). The simulator also models a two-level 12-pulse insulated-gate bipolar transistor (IGBT)-based voltage-source converter (VSC), a pulse-width modulation scheme, and a measurement system. Real-time simulation outputs (stator currents and rotor speed) were validated under steady-state and transient conditions using as reference an experimental test bench based on a DTPIM with 15 kW-rated power. The accuracy of the proposed digital hardware implementation was evaluated according to the simulation and experimental results. Finally, statistical performance parameters were provided to analyze the efficiency of the proposed DTPIM hardware implementation method.

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation.

We present a framework for the identification of spatiotemporal linear dynamical systems. We use a state-space model representation that has the following attributes: 1) the number of spatial observation locations are decoupled from the model order; 2) the model allows for spatial heterogeneity; 3) the model representation is continuous over space; and 4) the model parameters can be identified in a simple and sparse estimation procedure. The model identification procedure we propose has four steps: 1) decomposition of the continuous spatial field using a finite set of basis functions where spatial frequency analysis is used to determine basis function width and spacing, such that the main spatial frequency contents of the underlying field can be captured; 2) initialization of states in closed form; 3) initialization of state-transition and input matrix model parameters using sparse regression-the least absolute shrinkage and selection operator method; and 4) joint state and parameter estimation using an iterative Kalman-filter/sparse-regression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model.

Latent state-space models for neural decoding.

Ensembles of single-neurons in motor cortex can show strong low-dimensional collective dynamics. In this study, we explore an approach where neural decoding is applied to estimated low-dimensional dynamics instead of to the full recorded neuronal population. A latent state-space model (SSM) approach is used to estimate the low-dimensional neural dynamics from the measured spiking activity in population of neurons. A second state-space model representation is then used to decode kinematics, via a Kalman filter, from the estimated low-dimensional dynamics. The latent SSM-based decoding approach is illustrated on neuronal activity recorded from primary motor cortex in a monkey performing naturalistic 3-D reach and grasp movements. Our analysis show that 3-D reach decoding performance based on estimated low-dimensional dynamics is comparable to the decoding performance based on the full recorded neuronal population.

Stability Analysis of Chatter in Tandem Rolling Mills—Part 1: Single- and Multi-Stand Negative Damping Effect

Many different modes of chatter in rolling and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been fully established and accepted. In this two-part paper, stability of tandem mills is investigated. In Part 1, state-space models of single- and multi-stand chatter are formulated in a rigorous and comprehensive mathematical form. Then, the stability of the rolling system is investigated in the sense of the single- and multi-stand negative damping effects. First, a single-stand chatter model in state-space representation is proposed by coupling a dynamic rolling process model with a structural model for the mill stand. Subsequently, a multi-stand chatter model is developed by incorporating the inter-stand tension variations and the time delay effect of the strip transportation based on the single-stand chatter model. Stability criteria are proposed and stability analyses are performed to create corresponding stability charts in terms of the single- and multi-stand negative damping mechanism through numerical simulations. Particularly, the effect of friction conditions on chatter is examined and an explanation is given for the existence of an optimum friction condition. In Part 2, the regenerative effect and resulting instabilities are examined. Suitable stability criteria for each mechanism are established and stability charts are demonstrated in terms of relevant rolling process parameters.

Elimination of one dc voltage source in stacked multicell converters

This study presents a novel configuration for stacked multicell (SM) converters. The main advantage of the proposed converter, in comparison with the conventional one, is that the number of required dc voltage sources is reduced from two to one in the proposed topology which results in decreasing the cost and size of the converter. This progress is achieved by adding four low-frequency switches to the conventional configuration of SM converter whereas the number and voltage rating of high-frequency switches and clamping capacitors as well as the number of high-frequency switchings during a full cycle are kept constant. This converter is controlled by phase shifted carrier-sinusoidal pulse width modulation technique; therefore the self-balancing phenomenon of clamping capacitors' voltages is maintained. This study also presents a state-space representation model to analyse the dynamic of clamping capacitor's self-balancing phenomenon in the proposed SM converter by obtaining the switching instants of the pulse width modulation in terms of the Kapteyn series. Numerical solution of obtained state-space representation model of the proposed converter and simulation results as well as measurements taken from an experimental set-up are presented in order to validate the effectiveness and advantages of the proposed configuration as well as its control strategy and state-space model.

A Revised State Space Modelling Approach and Improved Fault Detection Using Combined Index Monitoring for Dynamic Processes

Larimore's state space model derivation and stochastic estimation algorithm, first published in 1983, have been the adopted standard for deriving the state variables and parameters of the five (5) matrices state space model representation which continues to be applied extensively in the literature for applications ranging from controls, system identification and process monitoring. This paper presents an alternate derivation and stochastic estimation algorithm. The paper also discusses how strategic classification of the process inputs may, for some applications, facilitate the use of a simplified stochastic estimation algorithm. The alternative state space modeling approaches demonstrated better fault monitoring statistic performance for specific types of faults simulated. The canonical variate based state space modeling approaches were evaluated on a simulate CSTR process – with recycle through a heat exchanger. The results demonstrates the potential benefits to be derived from using a combined monitoring index based upon monitoring statistics derived from independent state space models for improved overall fault detecting capabilities and reliability of the fault monitoring scheme.

누적방지 무충돌전환을 위한 새로운 통합형 기법

In many real applications, the discrepancy problem between controller outputs and plant inputs or the abrupt variation problem of controller outputs can occur. These problems have a negative effect on control performance and stability. It is well-known that two phenomena called 'windup' and 'bump' cause these problems. So far these problems have been studied separately in each side of the anti-windup and the bumpless transfer. This paper proposes a new unified method combines the anti-windup and the bumpless transfer method using the linear quadratic minimization and a proper state space model representation for the anti-windup controller. The proposed method has a feature that it takes account of both the anti-windup and the bumpless transfer in one formula. Finally, we exemplify the performance of the proposed method via numerical examples using the controller switching between the anti-windup PID controller and the anti-windup LQ controller.