Subspace State Space Research Articles

ARMAX-Based Transfer Function Model Identification Using Wide-Area Measurement for Adaptive and Coordinated Damping Control

One of the main drawbacks of the existing oscillation damping controllers that are designed based on offline dynamic models is adaptivity to the power system operating condition. With the increasing availability of wide-area measurements and the rapid development of system identification techniques, it is possible to identify a measurement-based transfer function model online that can be used to tune the oscillation damping controller. Such a model could capture all dominant oscillation modes for adaptive and coordinated oscillation damping control. This paper describes a comprehensive approach to identify a low-order transfer function model of a power system using a multi-input multi-output (MIMO) autoregressive moving average exogenous (ARMAX) model. This methodology consists of five steps: 1) input selection; 2) output selection; 3) identification trigger; 4) model estimation; and 5) model validation. The proposed method is validated by using ambient data and ring-down data in the 16-machine 68-bus Northeast Power Coordinating Council system. The results demonstrate that the measurement-based model using MIMO ARMAX can capture all the dominant oscillation modes. Compared with the MIMO subspace state space model, the MIMO ARMAX model has equivalent accuracy but lower order and improved computational efficiency. The proposed model can be applied for adaptive and coordinated oscillation damping control.

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

<p>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.</p>

Synthesis of an Optimal Dynamic Regulator Based on Linear Quadratic Gaussian (LQG) for the Control of the Relative Humidity under Experimental Greenhouse

<p><span lang="EN-US">This paper describes one practical approach that suggests a model based technique to control in real time the relative humidity under greenhouse. The humidity level is one of the most difficult environmental factors to be regulated in greenhouse. Moreover, maintaining and correcting for more or less humidity can be a challenge for even the most sophisticated monitoring and control equipment. For these raisons, a Linear Quadratic Gaussian (LQG) controller for relative humidity regulation under greenhouse turns out to be useful. Indeed a LQG controller is proposed for a relative humidity under a greenhouse control task. So, the state space model, which is best fitting the acquired data, was identified using the Numerical Subspace State Space System IDentification (N4SID) algorithm. The mathematical model that is obtained will be used for evaluating the parameters of LQG strategy. The proposed controller is implemented in two steps, in one hand, Kalman filter (KF) is used to develop an observer that estimates the state of relative humidity under greenhouse. In the other hand, the state feedback controller gain is estimated using a linear quadratic criterion function. The suggested optimal implemented controller using Matlab/Simulink environment is applied to an experimental greenhouse. We found, according to the results, that the controller is able to lead the inside relative humidity to the desired value with high accuracy, regardless of the external disturbances.</span></p>

Synthesis of an Optimal Dynamic Regulator Based on Linear Quadratic Gaussian (LQG) for the Control of the Relative Humidity under Experimental Greenhouse

<p><span lang="EN-US">This paper describes one practical approach that suggests a model based technique to control in real time the relative humidity under greenhouse. The humidity level is one of the most difficult environmental factors to be regulated in greenhouse. Moreover, maintaining and correcting for more or less humidity can be a challenge for even the most sophisticated monitoring and control equipment. For these raisons, a Linear Quadratic Gaussian (LQG) controller for relative humidity regulation under greenhouse turns out to be useful. Indeed a LQG controller is proposed for a relative humidity under a greenhouse control task. So, the state space model, which is best fitting the acquired data, was identified using the Numerical Subspace State Space System IDentification (N4SID) algorithm. The mathematical model that is obtained will be used for evaluating the parameters of LQG strategy. The proposed controller is implemented in two steps, in one hand, Kalman filter (KF) is used to develop an observer that estimates the state of relative humidity under greenhouse. In the other hand, the state feedback controller gain is estimated using a linear quadratic criterion function. The suggested optimal implemented controller using Matlab/Simulink environment is applied to an experimental greenhouse. We found, according to the results, that the controller is able to lead the inside relative humidity to the desired value with high accuracy, regardless of the external disturbances.</span></p>

Modal identification of a centrifuge soil model using subspace state space method

In this paper, modal parameters of a layered soil system comprising of a soft clay layer overlying a dense sand layer are identified from accelerometer recordings in a centrifuge test. For the first time, the subspace state space system identification (4SID) method was employed to identify the natural frequencies, damping ratios, and complex valued mode shapes while considering the non-proportional damping in a soil system. A brief review of system identification concepts needed for application of the 4SID techniques to structural modal identification is provided in the paper. The identified natural frequencies were validated against those estimated by transfer function spectra. The computed normal mode shapes were compared with closed-form solutions obtained from the one-dimensional shear wave propagation equation. The identified modal parameters were then employed to synthesize state space prediction models which were subsequently used to simulate the soil response to three successive base motions. The identified models captured acceleration time-histories and corresponding Fourier spectra reasonably well in the small and moderate shaking events. In the stronger third shaking event, the model performed well at greater soil depths, but was less accurate near the surface where nonlinearities dominated.

Decentralised wide‐area fractional order damping controller for a large‐scale power system

This study presents the design of wide-area fractional order damping controller for low frequency inter-area oscillations in Western Electricity Coordinating Council (WECC) system. The developed wide-area damping control scheme is implemented in a decentralised manner by examining the entire system through decentralised identification at the level of each generator bus and FACTS devices in large-scale system. The decentralised identification is done by applying n4sid (Subspace State Space System Identification) algorithm to the time-domain simulated response of WECC system. The main features of the proposed approach are: (a) measurement-based control which does not require complete model of WECC; (b) minimise the communicating signals required for damping controller and incorporate practical method of time-delay compensator (TDC) design to reduce the effect of time-varying delay. The performance of wide-area control (WAC) scheme is tested on the practical WECC system and verified by non-linear time-domain simulation. The proposed decentralised WAC scheme is compared with local and centralised control scheme, which enhances the damping of inter-area oscillation effectively compared to local control scheme and more reliable compared to centralised control scheme and its robustness is verified over a wide-range of operating conditions.

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).

Estimation of interarea electromechanical modes during ambient operation of the power systems using the RDT–ITD method

Abstract An accurate awareness of the properties of the interarea electromechanical oscillation modes is essential for the secure operation of the power systems. Previously, the Ibrahim time domain (ITD) method has been applied to estimate the interarea oscillation modes using ring-down signals caused by major disturbances (such as three phase faults). In this paper, through the combination of the random decrement technique (RDT) and the ITD method, the RDT–ITD method is proposed to estimate the interarea modes during ambient operation of the power systems, using random responses caused by random changes of the loads. The estimated parameters include the frequencies, damping ratios and mode shapes. Considering the fact that both the ambient excitations and the measurement noise are stochastic in nature, Monte Carlo simulations were conducted to evaluate the performances of the RDT–ITD method in a statistical way. Simulation results in the 16 machine nonlinear power system model, as well as comparison results with the RDT-Prony method, the NExT-ERA method and the Subspace method realized by N4SID (Numerical algorithm for Subspace State Space System Identification) show that the RDT–ITD method is promising in estimating the interarea modes during ambient operation conditions. The RDT–ITD method was also validated using real PMU measurements from Sichuan power grid of China.

Controller design with model identification approach in wide area power system

Using wide area monitoring systems (WAMS) offers a possibility for an integrated measurement-based and model-based control, which suits to the operation of large electric power system (EPS), along with online analysis. This study presents studies on fixed-order controller design through model identification approach with use of synchronous measurement data. Firstly, in the study, the coherent generator in each area of large EPS is determined by the mutual information theory. Then, state-space two-input two-output model is identified for the generator that has highest participation factor and thus referred as coherent generator. The model identification algorithms; least-square, instrumental variable and subspace state-space based generalised Poisson moment function are used. Next, WAMS level model is identified between the input controllable variable and speed deviation difference of coherent generator of each area. Finally, a local controller (decentralised) in each coherent area and a centralised controller at WAMS level between two coherent areas are designed by optimisation of the several design functions; H∞ norm, H 2 norm, spectral abscissa and complex stability radius, as much as possible. These controllers feed supplementary control signal in addition to one fed by local conventionally tuned power system stabiliser. The centralised controller at WAMS level is demonstrated to stabilise the speed deviations of each generator between any two areas in the large EPS. The study is investigated with different input signal variables; ΔV ref, ΔPm excited by different pattern of disturbances.

Subspace Identification of Transfer Function Models for an Unstable Bioreactor

This work deals with the identification of transfer function model of an unstable bioreactor by a subspace-based identification method. The data set is generated from the simulated closed loop system by giving a random signal at the reference signal. The linear system matrices are estimated through the Multivariable Output Numerical algorithms for Subspace State Space System Identification (MON4SID) algorithm. The delay is estimated directly from the input–output data by the impulse response method. The identified First Order Plus Time Delay (FOPTD) model is compared with the locally linearized transfer function model derived around the unstable operating point. A Proportional Integral Derivative (PID) controller is designed for the identified model using the equating coefficient method. The closed loop servo and regulatory responses show that the model identified by MON4SID is similar to the linearized model and the optimization method.

N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper, an analysis for ill conditioning problem in subspace identification method is provided. The subspace identification technique presents a satisfactory robustness in the parameter estimation of process model which performs control. As a first step, the main geometric and mathematical tools used in subspace identification are briefly presented. In the second step, the problem of analyzing ill-conditioning matrices in the subspace identification method is considered. To illustrate this situation, a simulation study of an example is introduced to show the ill-conditioning in subspace identification. Algorithms numerical subspace state space system identification (N4SID) and multivariable output error state space model identification (MOESP) are considered to study, the parameters estimation while using the induction motor model, in simulation (Matlab environment). Finally, we show the inadequacy of the oblique projection and validate the effectiveness of the orthogonal projection approach which is needed in ill-conditioning; a real application dealing with induction motor parameters estimation has been experimented. The obtained results proved that the algorithm based on orthogonal projection MOESP, overcomes the situation of ill-conditioning in the Hankel's block, and thereby improving the estimation of parameters.

Least squares algorithm for an input nonlinear system with a dynamic subspace state space model

For a Hammerstein input nonlinear system with a subspace state space linear element, this paper transforms the system into a bilinear identification model by using the property of the shift operator to the state space model and presents a recursive and an iterative least squares algorithms to generate parameter estimates and state estimates by using the hierarchical identification principle and by replacing the unknown state variables with their estimates. The proposed approaches are computationally more efficient than the over-parameterization model based least squares method.

Observer Kalman Filter Identification for Output-Only Systems Using Interactive Structural Modal Identification Toolsuite

AbstractSeveral modal identification techniques have been developed in the past few decades, and their use is rapidly expanding due to new focus on the instrumentation of major structures. This paper focuses on the expansion of the eigenvalue realization algorithm (ERA)–observer Kalman filter identification (OKID) to identify modal parameters of output-only systems (OO) by splitting the state-space model into deterministic and stochastic subsystems (ERA-OKID-OO). The performance is then compared with other output-only identification methods in terms of the level of accuracy and efficiency. A newly developed software package [Structural Modal Identification Toolsuite (SMIT)] is used to provide a uniform and convenient way of utilizing several system identification (SID) methods, including variations of ERA, auto-regressive with exogenous terms (ARX) models, system realization using information matrix (SRIM), and numerical algorithms for subspace state space system identification (N4SID). The main purpose o...

Mode shape estimation algorithms under ambient conditions: A comparative review

This paper provides a comparative review of five existing ambient electromechanical mode shape estimation algorithms, i.e., the Transfer Function (TF), Spectral, Frequency Domain Decomposition (FDD), Channel Matching, and Subspace Methods. It is also shown that the TF Method is a general approach to estimating mode shape and that the Spectral, FDD, and Channel Matching Methods are actually special cases of it. Additionally, some of the variations of the Subspace Method are reviewed and the Numerical algorithm for Subspace State Space System IDentification (N4SID) is implemented. The five algorithms are then compared using data simulated from a 17-machine model of the Western Electricity Coordinating Council (WECC) under ambient conditions with both low and high damping, as well as during the case where ambient data is disrupted by an oscillatory ringdown. The performance of the algorithms is compared using the statistics from Monte Carlo simulations and results from measured WECC data, and a discussion of the practical issues surrounding their implementation, including cases where power system probing is an option, is provided. The paper concludes with some recommendations as to the appropriate use of the various techniques.

Improved subspace identification with prior information using constrained least squares

Subspace identification incorporating prior information has been proven to be effective in obtaining state-space models with improved accuracy. Available algorithms, however, can require prohibitively demanding computations. The incorporation of prior information, for example, steady-state gain, time constant and zero transfer functions, in subspace identification is investigated using constrained least squares (CLS). The method exploits the interpretation of subspace identification as an optimal multi-step ahead predictor and reduces the identification to solve an optimisation problem with equality constraints describing the prior information. The standard multivariable output-error state-space subspace algorithm is further examined using the same CLS approach to incorporate dc gain information. Simulation results show that the proposed algorithm provides computationally efficient approach for subspace identification with satisfactory parameter variances, and the method is equally applicable to both single-input single-output and multiple-input multiple-output systems.

A Comparison of Methods for Forecasting Emergency Department Visits for Respiratory Illness Using Telehealth Ontario Calls

Objectives: Anticipating increases in hospital emergency department (ED) visits for respiratory illness could help time interventions such as opening flu clinics to reduce surges in ED visits. Five different methods for estimating ED visits for respiratory illness from Telehealth Ontario calls are compared, including two non-linear modeling methods. Daily visit estimates up to 14 days in advance were made at the health unit level for all 36 Ontario health units.Methods: Telehealth calls from June 1, 2004 to March 14, 2006 were included. Estimates generated by regression, Exponentially Weighted Moving Average (EWMA), Numerical Methods for Subspace State Space Identification (N4SID), Fast Orthogonal Search (FOS), and Parallel Cascade Identification (PCI) were compared to the actual number of ED visits for respiratory illness identified from the National Ambulatory Care Reporting System (NACRS) database. Model predictor variables included Telehealth Ontario calls and upcoming holidays/weekends. Models were fit using the first 304 days of data and prediction accuracy was measured over the remaining 348 days.Results: Forecast accuracy was significantly better (p<0.0001) for the 12 Ontario health units with a population over 400,000 (75% of the Ontario population) than for smaller health units. Compared to regression, FOS produced better estimates (p=0.03) while there was no significant improvement for PCI-based estimates. FOS, PCI, EWMA and N4SID performed worse than regression over the remaining smaller health units.Conclusion: Telehealth can be used to estimate ED visits for respiratory illness at the health unit level. Non-linear modeling methods produced better estimates than regression in larger health units.

Active Damping Using N4SID Model Referenced Predictive Anti-Phase Pitch Driving Method

Vibration suppression control considering elastic part deformation is one of the indispensable issues in the precision engineering field and a high-density LSI circuit processing[1]. This study aims at suppressing the induced vibration at rapid positioning operation using the N4SID (Subspace State Space model Identification) Model Referenced predictive Anti-phase pitch Driving Active Damping (N4SID-MRAD) and improve the positioning performance limit generated by conventional PID feedback control with existing actuator, which has low dynamic characteristics with a time lag. This control method consists of reduced order model identification (model order reduction using N4SID concept: offline process) and predictive control using the counter pitch driving based on the model output (: on-line process). This method was applied to principal axis vibration suppression of three axes positioning machine driven by a ball screw feeding mechanism to control the probe tip end positioning in feeding rod axis. The result showed that amplitude of residual vibration at the probe tip end suppressed with conventional PI controlled and the 77% performance improvement under low stable conditions that Balanced Realization could not be applied.

Coordinated control design of multiple HVDC links based on model identification

This paper presents a method for designing a centralized coordinated controller for several HVDC links. The controller increases the damping of the power oscillations by modulating the current through the HVDC links in a coordinated fashion. To design a centralized coordinated controller a reduced order open system model is estimated. The open system model of the power system is estimated using the Numerical Algorithms for Subspace State-Space System Identification (N4SID) algorithm which is a black-box system identification technique. The current set-point change through the HVDC links is the set of input signals and the speeds of the generators are the set of outputs. This controller design method increases the damping significantly, which is shown for a small power system.

Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this technical brief, a new subspace state space system identification algorithm for multi-input multi-output bilinear systems driven by white noise inputs is introduced. The new algorithm is based on a uniformly convergent Picard sequence of linear deterministic-stochastic state space subsystems which are easily identifiable by any linear deterministic-stochastic subspace algorithm such as MOESP, N4SID, CVA, or CCA. The key to the proposed algorithm is the fact that the bilinear term is a second-order white noise process. Using a standard linear Kalman filter model, the bilinear term can be estimated and combined with the system inputs at each iteration, thus leading to a linear system with extended inputs of dimension <formula formulatype="inline"><tex Notation="TeX">$m(n+1)$</tex></formula>, where <formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula> is the system order and <formula formulatype="inline"> <tex Notation="TeX">$m$</tex></formula> is the dimension of the inputs. It is also shown that the model parameters obtained with the new algorithm converge to those of the true bilinear model. Moreover, the proposed algorithm has the same consistency conditions as the linear subspace identification algorithms when <formula formulatype="inline"><tex Notation="TeX">$i\rightarrow\infty$</tex> </formula>, where <formula formulatype="inline"><tex Notation="TeX">$i$</tex> </formula> is the number of block rows in the past/future block Hankel data matrices. Typical bilinear subspace identification algorithms available in the literature cannot handle large values of <formula formulatype="inline"> <tex Notation="TeX">$i$</tex></formula>, thus leading to biased parameter estimates. Unlike existing bilinear subspace identification algorithms whose row dimensions in the data matrices grow exponentially, and hence suffer from the “curse of dimensionality,” in the proposed algorithm the dimensions of the data matrices are comparable to those of a linear subspace identification algorithm. A case study is presented with data from a heat exchanger experiment. </para>