Multivariable Output Error State Space Research Articles

Design of an efficient experiment for identification-based stability analysis of operating wind turbines

This paper proposes a new approach to calculate aeroelastic stability of operating wind turbines using system identification, and explores how an efficient numerical experiment can be designed. The data-driven method is based on time series including induced motion of the blades, which can stem from any fidelity simulation. While this study utilises HAWC2, the findings enable the usage of e.g. computational fluid dynamics in a fluid-structure-interaction simulation. Different forcing sequences are suitable to excite the blade, but especially the doublet and chirp show favourable characteristics and results for an application of no more than five seconds. System identification, the Multivariable Output-Error State sPace (MOESP) algorithm in particular, is used to find an algebraic equivalent of the simulated turbine. Using the output-only version, about 20 seconds of simulated time are sufficient to identify the system such that the predicted response matches the input with an R 2-score of > 99.8 %. A comparison with HAWCStab2 shows frequency differences of < 0.5% across the wind speed range, matching mode shapes but some bigger deviations in aeroelastic damping.

Development of a fed-batch-scale anaerobic co-digestion control system based on multivariable output error state space and model predictive control

This paper describes a feeding control system for fed-batch-scale anaerobic co-digestion. The proposed system is based on the multivariable output error state space and uses model predictive control to regulate the biogas flow output of anaerobic co-digestion. This control system combines predictive modeling, receding-horizon optimization, and state feedback. An accurate linear model of anaerobic co-digestion is obtained through the multivariable output error state space method using experimental data, and the accuracy of the model is evaluated using a goodness-of-fit index and the root mean square error. After augmenting the model, a predictive control system is established. The system states are observed through a Kalman filter, and the constrained receding-horizon optimization problem is solved using quadratic programming. Finally, the stability of the control system is demonstrated from both open- and closed-loop perspectives. The control system is then constructed and used in actual experiments, with the target flow output set at 100 NmL/h. The final flow output indicates that the control system achieves good control performance. This research enables the biogas output of anaerobic co-digestion to be controlled from a linear perspective through a concise control algorithm with strong practical application prospects.

Subspace Identification of Bridge Frequencies Based on the Dimensionless Response of a Two-Axle Vehicle.

As an essential reference to bridge dynamic characteristics, the identification of bridge frequencies has far-reaching consequences for the health monitoring and damage evaluation of bridges. This study proposes a uniform scheme to identify bridge frequencies with two different subspace-based methodologies, i.e., an improved Short-Time Stochastic Subspace Identification (ST-SSI) method and an improved Multivariable Output Error State Space (MOESP) method, by simply adjusting the signal inputs. One of the key features of the proposed scheme is the dimensionless description of the vehicle-bridge interaction system and the employment of the dimensionless response of a two-axle vehicle as the state input, which enhances the robustness of the vehicle properties and speed. Additionally, it establishes the equation of the vehicle biaxial response difference considering the time shift between the front and the rear wheels, theoretically eliminating the road roughness information in the state equation and output signal effectively. The numerical examples discuss the effects of vehicle speeds, road roughness conditions, and ongoing traffic on the bridge identification. According to the dimensionless speed parameter Sv1 of the vehicle, the ST-SSI (Sv1 < 0.1) or MOESP (Sv1 ≥ 0.1) algorithm is applied to extract the frequencies of a simply supported bridge from the dimensionless response of a two-axle vehicle on a single passage. In addition, the proposed methodology is applied to two types of long-span complex bridges. The results show that the proposed approaches exhibit good performance in identifying multi-order frequencies of the bridges, even considering high vehicle speeds, high levels of road surface roughness, and random traffic flows.

Subspace identification of bridge dynamics via traversing vehicle measurements

This study establishes a subspace identification scheme to estimate bridge frequencies by processing the dynamic response of a traversing vehicle for two traverses over the target bridge. Specifically, this study discusses the feasibility of the Multivariable Output Error State Space (MOESP) method for vehicles with high speed and/or bridges with short characteristic lengths. To deal with the time-varying nature of the vehicle–bridge system, the study employs the singular value decomposition (SVD) based pseudo-inverse algorithm. The proposed scheme is numerically verified on synthetic datasets, which are attained via simulation of the vehicle–bridge interaction (VBI) problem, in order to obtain the vehicle response, which serves for application of the MOESP algorithm. The numerical experiments concern both a sprung mass vehicle and a more realistic multi-degree-of-freedom (MDOF) vehicle identifying a 3-span bridge. The results demonstrate that the proposed approach succeeds in identifying structural frequencies of the bridge even under assumption of high vehicle speeds and high levels of road surface roughness.

Model predictive control for wormlike micelles (WLMs): Application to a system of CTAB and NaCl

Wormlike micelles (WLMs), which are the self-assemblies of amphiphilic surfactants, have gained attention in various applications due to their unique ‘living’ nature (i.e., union-scission). However, the industrial production of the WLMs has rarely been discussed. Moreover, given that the system hardly reaches the desired viscosity without appropriate control actions within a reasonable operation time, a model-based controller has been implemented to the production of WLMs where CTAB/NaCl in a semi-batch reactor is used as a case study. For this, a high-fidelity model was developed by integrating thermodynamic, kinetic, and rheology models and validated with experimental results. Subsequently, to alleviate the computational burden of such a high-fidelity model, the model reduction was carried out by the multivariable output error state space algorithm. The developed reduced-order model (ROM) was able to reproduce the essential features of the high-fidelity model and utilized in the formulated model predictive control (MPC) system. Herein, the manipulated variables (i.e., surfactant volume fraction, salt concentration, and temperature) are adjusted to give the desired WLM length of 3700 nm (i.e., a zero-shear viscosity of 100 Pa-s). Finally, the developed MPC scheme resulted in optimal input sequences to successfully reach the setpoint within practical constraints.

Development of parametric reduced-order model for consequence estimation of rare events

Computational fluid dynamics (CFD) models have been widely used in the chemical process industry to analyze various aspects of high-consequence rare events. However, CFD models are computationally intensive in nature, and therefore, several developments have been made in building computationally efficient models. The existing computationally efficient models in the field of high-consequence rare events are temporally static in nature and do not represent system evolution with time, which is crucial for consequence modeling of rare events. Further, the consequences depend on various parameters in addition to inputs. Since it is not affordable to construct a new model for every parameter value, incorporation of inputs and parameters is an additional challenge in developing a consequence model. Hence, to address these challenges, this work proposes a k-nearest neighbor (kNN)-based parametric reduced-order model (PROM) for consequence estimation of rare events to enhance numerical robustness with respect to parameter change. Specifically, local (with respect to parameters) ROMs are constructed based on multivariable output-error state space (MOESP) algorithm for a range of parameters, and they are linearly interpolated to estimate consequences at a new parameter value. The effectiveness of the proposed model is demonstrated through a case study of supercritical carbon dioxide release rare event.

Performance Analysis of Data-Driven Techniques for Detection and Identification of Low Frequency Oscillations in Multimachine Power System

In power systems, identification and damping of low-frequency oscillations(LFO) is very crucial to maintain the small signal stability. Hence the computation of eigenvalues, eigenmode shapes, participation factors, and coherency of generators are essential parameters of critical LFO modes. The existing data-driven approaches explore either one or two aspects of modal parameters from the dynamic pattern of the measurement data. In the present work, two approaches i) Iterative Approach(IA) ii) Non-Iterative Subspace(SS) method of data-driven techniques are used to estimate the state-space model of the system under study from the measurement data in a holistic framework. Based on the estimated system model, the eigenvalues of LFO, eigenmode shapes, participation factor, and coherency of associated generators participating in electromechanical oscillations are computed. Finally, from the estimated participation factors for the Inter-area oscillation mode (IAM), the Static Synchronous Compensator (STATCOM) damping controller is designed and placed at the generator with the highest participation factor for damping of inter-area oscillation. The enhancement of damping ratio of inter area mode with STATCOM damping controller is estimated and verified using IA & SS data driven approaches for the first time. In this work, IA uses prediction-error minimization algorithm (PEM) & Parallel computing techniques and SS method uses Multivariable Output Error State Space (MOESP) algorithm for the estimation of Hankel matrix from the measured data. The effectiveness of data-driven approaches are demonstrated by the simulation of a IEEE 4-machine,10-bus power system using MATLAB / Simulink. IA & SS methods incorporating wavelet based denoising techniques are very effective in identifying the LFO modes even with noisy measurement. The efficacy of the denoising to suppress the effect of noise is demonstrated by comparing with noiseless environment. The results of data-driven approaches indicate their high degree of accuracy and efficiency in being consistent with Eigenvalue analysis (EA) performed on the system.

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.

Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.

A Comparison Study of Subspace Identification of Blast Furnace Ironmaking Process

Blast Furnace (BF) iron making process is an extremely complex industrial process. The molten iron silicon content is considered as an important indicator of the thermal status of the blast furnace. The stabilization control of blast furnace depends on the molten iron silicon content. Three classic subspace identification methods including MOESP (Multivariable Output-Error State sPace), CVA (Canonical Variate Analysis) and SSARX (Subspace identification method ARX) are considered to establish the state space model of blast furnace ironmaking process. The inputs to the model are the most responsible and easily measured variables for the fluctuation of thermal state in blast furnace while the output to the model is the molten iron silicon content. The identified state space models are then tested on datasets obtained from No.1 BF in LiuGang Iron and Steel Group Co. of China. Experiment results show that the blast furnace ironmaking process can be reliably modeled by these subspace identification methods. Further, the SSARX method outperforms over the other two subspace identification methods with closed loop data.

Fractional-Order System Identification and Equalization in Massive MIMO Systems

In this paper, a new methodology for the identification and equalization of massive Multiple-Input Multiple-Output (MIMO) channels in fifth generation (5G) wireless communications is proposed. Channel equalization is performed in state-space, having estimated the channel using the fractional-order Multivariable Output Error State Space (MOESP) system identification algorithm. The proposed fractional-order algorithm is an improvement over its integer-order counterpart that is currently used for state-space channel identification/estimation and state-space channel equalization. When dealing with fractional-order calculus our work adopts the Riemann-Liouville definition. Our numerical results of channel identification having used a chirp signal to excite our massive MIMO system show a lower mean square error (MSE) in channel estimation using the proposed fractional-order MOESP identification algorithm when compared to integer-order MOESP identification algorithm of increased order. Furthermore, following equalization, transmission using Binary phase shift keying (BPSK), Quadrature phase shift keying (QPSK) and 256-Quadrature amplitude modulation (256-QAM) signals show that the symbol error rate (SER) as a function of signal to noise ratio (SNR) performance of the fractional-order equalization algorithm compares to that of the integer-order equalization algorithm. The proposed channel identification algorithm also provides a more parsimonious solution for modelling multipath fading, thus enabling the design of fractional-order equalizers. In addition, they may be used in other applications where high order filtering and more complex control algorithms which are difficult to tune would be needed. Finally, the work has other technological applications where there is a requirement for modelling and control of propagation processes in dispersive media.

Model Predictive Control Method of Simulated Moving Bed Chromatographic Separation Process Based on Subspace System Identification

Simulated moving bed (SMB) chromatographic separation is a new type of separation technology based on traditional fixed bed adsorption operation and true moving bed (TMB) chromatographic separation technology, which includes inlet‐outlet liquid, liquid circulation, and feed liquid separation. The input‐output data matrices were constructed based on SMB chromatographic separation process data. The SMB chromatographic separation process was modeled by utilizing two subspace system identification algorithms: multivariable output‐error state‐space (MOESP) identification algorithm and numerical algorithms for subspace state‐space system identification (N4SID), so as to obtain the 3rd‐order and 4th‐order state‐space yield models of the SMB chromatographic separation process, respectively. The model predictive control method based on the established state‐space models is used in the SMB chromatographic separation process. The influence of different control indicators on the predictive control system response performance is discussed. The output response curves of the yield models were obtained by changing the related parameters so that the yield model parameters are optimized set meanwhile. Finally, the simulation results showed that the yield models are successfully controlled based on the each control period and given yield range.

A new Hammerstein model control strategy: feedback stabilization and stability analysis

This paper treats the identification, the control and the stability analysis of the discrete Hammerstein structure which is composed by a static nonlinearity gain associated with a linear dynamic subsystem. Its parameters are obtained from the subspace identification using the multivariable output error state space algorithm. The stabilization of this class of systems is generally leaded by a nonlinear control law, including an exact inverse of the static nonlinearity. Then, it is possible to use a linear state feedback controller to stabilize the Hammerstein system in closed-loop and to track the reference input. Thus, the performances of this method become limited when the considered static nonlinearity is approximately invertible. In this context, an approximate inverse of this component is investigated. Furthermore, based on the Lyapunov method, the stability conditions are obtained by solving a set of linear matrix inequalities constraints. The case of a coupled two-tank system is considered in order to illustrate the validity of the proposed approach.

Subspace-Based Fractional Order Systems Identification in Presence of Outliers

This paper aims at identifying the commensurate fractional order systems when output signal is corrupted by noise and outliers. A new outliers detection method via nuclear norm and infinite norm is proposed, which can detect outliers exactly and estimate noise at the same time. With the adoption of recovered “clean” output signal, the multivariable output error state space method is used to estimate system parameters. The effectiveness and superiority of proposed method are verified by detailed numerical examples.

A Physical Model Suggests That Hip-Localized Balance Sense in Birds Improves State Estimation in Perching: Implications for Bipedal Robots.

In addition to a vestibular system, birds uniquely have a balance-sensing organ within the pelvis, called the lumbosacral organ (LSO). The LSO is well developed in terrestrial birds, possibly to facilitate balance control in perching and terrestrial locomotion. No previous studies have quantified the functional benefits of the LSO for balance. We suggest two main benefits of hip-localized balance sense: reduced sensorimotor delay and improved estimation of foot-ground acceleration. We used system identification to test the hypothesis that hip-localized balance sense improves estimates of foot acceleration compared to a head-localized sense, due to closer proximity to the feet. We built a physical model of a standing guinea fowl perched on a platform, and used 3D accelerometers at the hip and head to replicate balance sense by the LSO and vestibular systems. The horizontal platform was attached to the end effector of a 6 DOF robotic arm, allowing us to apply perturbations to the platform analogous to motions of a compliant branch. We also compared state estimation between models with low and high neck stiffness. Cross-correlations revealed that foot-to-hip sensing delays were shorter than foot-to-head, as expected. We used multi-variable output error state-space (MOESP) system identification to estimate foot-ground acceleration as a function of hip- and head-localized sensing, individually and combined. Hip-localized sensors alone provided the best state estimates, which were not improved when fused with head-localized sensors. However, estimates from head-localized sensors improved with higher neck stiffness. Our findings support the hypothesis that hip-localized balance sense improves the speed and accuracy of foot state estimation compared to head-localized sense. The findings also suggest a role of neck muscles for active sensing for balance control: increased neck stiffness through muscle co-contraction can improve the utility of vestibular signals. Our engineering approach provides, to our knowledge, the first quantitative evidence for functional benefits of the LSO balance sense in birds. The findings support notions of control modularity in birds, with preferential vestibular sense for head stability and gaze, and LSO for body balance control,respectively. The findings also suggest advantages for distributed and active sensing for agile locomotion in compliant bipedal robots.

An Alternative Approach to the Inference of the Extended Observability Matrix, and Its Relation With the PO-MOESP Algorithm

The subspace identification methods (SIMs), such as past outputs multivariable output-error state space (PO-MOESP), numerical algorithms for subspace state-space system identification, and canonic correlation analysis, build state-space models from a set of input–output data of a linear time invariant system. In these algorithms, the key step is the computation of the extended observability matrix, which is done via an orthogonal projection between spaces generated by the input–output data. However, the PO-MOESP algorithm, unlike the others subspace methods, uses a different space for computing such projection. This fact hinders the analysis and direct comparison with other algorithms. In this paper, we introduce a modified version of the PO-MOESP algorithm, which is conceptually simpler, requires fewer steps for computing the model parameters, and enables the comparison with other SIMs. Three numerical examples are provided in order to show the effectiveness of the proposed approach.

Subspace Identification of 2-D CRSD Roesser Models With Deterministic-Stochastic Inputs: A State Computation Approach

In this brief, we present a subspace system identification framework for 2-D separable-in-denominator systems with deterministic-stochastic inputs in the Roesser form. The advantage of the proposed framework is that it is based on the computation of state matrices, as opposed to current algorithms that compute the system parameter matrices from Markov parameters and the observability matrix. As such, it does not require solving specialized Toeplitz or Hankel systems of equations while computing the system parameter matrices. In addition, the problem is broken down into two simple oblique projection computations—one in the horizontal direction and one in the vertical direction. Within this framework, Numerical algorithms for Subspace State Space System IDentification (N4SID), Past-Output Multivariable Output-Error State-sPace (PO-MOESP), and Canonical Variate Analysis (CVA) type algorithms are obtained. Simulation results show that the algorithms are accurate and provide new alternatives for modeling and identifying 2-D causal, recursive, and separable-in-denominator Roesser models.

Recursive Subspace Identification Algorithm using the Propagator Based Method

&lt;p&gt;Subspace model identification (SMI) method is the effective method in identifying dynamic state space linear multivariable systems and it can be obtained directly from the input and output data. Basically, subspace identifications are based on algorithms from numerical algebras which are the QR decomposition and Singular Value Decomposition (SVD). In industrial applications, it is essential to have online recursive subspace algorithms for model identification where the parameters can vary in time. However, because of the SVD computational complexity that involved in the algorithm, the classical SMI algorithms are not suitable for online application. Hence, it is essential to discover the alternative algorithms in order to apply the concept of subspace identification recursively. In this paper, the recursive subspace identification algorithm based on the propagator method which avoids the SVD computation is proposed. The output from Numerical Subspace State Space System Identification (N4SID) and Multivariable Output Error State Space (MOESP) methods are also included in this paper.&lt;/p&gt;

IDENTIFICATION OF ON-AND OFF-LINE LINEAR STATE SPACE MODELS USING SUBSPACE METHODS

In this paper, subspace identification methods are proposed to analyze the differences between On-And Off-Line Linear State Space Models Using Subspace Methods. There are several ways that can estimate the order of the system. For this paper, Singular Value Decomposition (SVD) is used to estimate the order of the system. Comparing with the others methods, this method only need a limited number of input and output data for the determination of the system matrices. Two methods of the subspace algorithm are used which is N4SID (Numerical algorithm for Subspace State Space System Identification) and MOESP (Multivariable Output-Error State-Space model identification).

Subspace-based continuous-time identification of fractional order systems from non-uniformly sampled data

This work focuses on the identification of fractional commensurate order systems from non-uniformly sampled data. A novel scheme is proposed to solve such problem. In this scheme, the non-uniformly sampled data are first complemented by using fractional Laguerre generating functions. Then, the multivariable output error state space method is employed to identify the relevant system parameters. Moreover, an in-depth property analysis of the proposed scheme is provided. A numerical example is investigated to illustrate the effectiveness of the proposed method.