observer/Kalman Filter Identification Research Articles

Active Vibration Control of the Sting Used in Wind Tunnel: Comparison of Three Control Algorithms

In wind tunnel tests, cantilever stings are often used as model‐mount in order to reduce flow interference on experimental data. In this case, however, large‐amplitude vibration and low‐frequency vibration are easily produced on the system, which indicates the potential hazards of gaining inaccurate data and even damaging the structure. This paper details three algorithms, respectively, Classical PD Algorithm, Artificial Neural Network PID (NNPID), and Linear Quadratic Regulator (LQR) Optimal Control Algorithm, which can realize active vibration control of sting used in wind tunnel. The hardware platform of the first‐order vibration damping system based on piezoelectric structure is set up and the real‐time control software is designed to verify the feasibility and practicability of the algorithms. While the PD algorithm is the most common method in engineering, the results show that all the algorithms can achieve the purpose of over 80% reduction, and the last two algorithms perform even better. Besides, self‐tuning is realized in NNPID, and with the help of the Observer/Kalman Filter Identification (OKID), LQR optimal control algorithm can make the control effort as small as possible. The paper proves the superiority of NNPID and LQR algorithms and can be an available reference for vibration control of wind tunnel system.

An On-Line Tracker for a Stochastic Chaotic System Using Observer/Kalman Filter Identification Combined with Digital Redesign Method

This is the first paper to present such a digital redesign method for the (conventional) OKID system and apply this novel technique for nonlinear system identification. First, the Observer/Kalman filter Identification (OKID) method is used to obtain the lower-order state-space model for a stochastic chaos system. Then, a digital redesign approach with the high-gain property is applied to improve and replace the observer identified by OKID. Therefore, the proposed OKID combined with an observer-based digital redesign novel tracker not only suppresses the uncertainties and the nonlinear perturbations, but also improves more accurate observation parameters of OKID for complex Multi-Input Multi-Output systems. In this research, Chen’s stochastic chaotic system is used as an illustrative example to demonstrate the effectiveness and excellence of the proposed methodology.

Modeling and tracker for unknown nonlinear stochastic delay systems with positive input constraints

An approach for universal modeling and tracker design for input-constrained unknown nonlinear input time-delay stochastic sampled-data systems is newly proposed in this paper. First, the improved observer/Kalman filter identification (OKID) method, which uses the current output measurement to estimate the current state, is newly proposed in this paper and it is shown that it outperforms the traditional OKID method. In addition, it is shown that the newly proposed current output-based Kalman filter is a well-performed output estimator in the extreme case, in which it is not a filter anymore, becoming a universal way of formulating an artificial system model of a real physical process without disturbing its normal operation. Consequently, the proposed artificial system model has the following advantages: (i) It is capable of quantifying the stochastic and deterministic characteristics of the dynamical system of interest; (ii) It is capable of carrying out the analyses of various control-design methodologies to achieve the performance specifications in the pre-study phase; and (iii) It is capable of estimating missing and/or abnormal output measurements during the testing and/or practical operating phases. Furthermore, an alternative re-designed current output-based observer is newly proposed in this paper, in order to develop a modified observer-based model predictive control (MPC) with input constraints to improve the performance of the unknown nonlinear time-delay stochastic system. When the proposed artificial system model is used together with the proposed constrained MPC, a long-time prediction of future input–output sets in a closed-loop setting can be carried out. Finally, the operation of a temperature controlled real nonlinear input time-delay blast furnace process is presented as a case study in this paper, to show the effectiveness of the proposed mechanism.

Identification Technology of Modal Parameter of a Strap-on Launch Vehicle

It is generally needed to conduct ground modal tests over strap-on launch vehicle to provide modal parameters for the attitude control design and load calculating. These modal parameters can also provide basis of installing sense organs on the launch vehicle. This paper introduces a modal parameter identification method based on input-output data of the system, which can be used to check calculations of modal parameters after ground modal tests. In this paper, the double-compatible free-interface modal synthesis method is first used for the modeling of the system so as to get the input and output data of the system. Then the identification techniques of observer/Kalman filter identification (OKID) and eigensystem realization algorithm (ERA) are introduced. Finally, numerical simulations are carried out to demonstrate the validity of the presented identification method. Simulation results indicate that the modal parameter of the system can be effectively identified using OKID and ERA.

Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories

In this paper, we present adaptive iterative learning control (ILC) schemes for discrete linear time-invariant (LTI) stochastic system with batch-varying reference trajectories (BVRT). If reference trajectories change every batch, ILC shows a different convergence property from that of the identical reference trajectory. First, we derive the convergence property and propose deterministic adaptive ILC combined with iterative learning identification for LTI system with BVRT. If the state noise and measurement noise exist, convergence rate and tracking performance are degraded because the controller considers the difference arising from the noise as tracking error. To deal with such a problem, we propose two approaches. The first is based on a batch-domain Kalman filter, which uses the difference between the current output trajectory and the next reference trajectory as a state vector, while the second is based on a time-domain Kalman filter. In the second approach, the system is identified at the end of each batch in an iterative fashion using the observer/Kalman filter identification (OKID). Then, the stochastic problem is handled using Kalman filter with a steady-state Kalman gain obtained from the identification. Therefore, the second approach can track the reference trajectories of discrete LTI stochastic system using only the input–output information. Simulation examples are provided to show the effectiveness of the proposed schemes.

Digital sliding mode controller design for multiple time-delay continuous-time transfer function matrices with a long input–output delay

This paper extends the dominant eigenvector-based sliding mode control (SMC) design methodology, which was originally developed for delay-free continuous-time processes with known parameters, to the case of multiple time-delay continuous-time processes with known/unknown parameters. In addition, this paper presents a new prediction-based Chebyshev quadrature digital redesign methodology for indirect design of the digital counterpart of the analog sliding mode controller (ASMC) for multiple time-delay continuous-time transfer function matrices with either a long input delay or a long output delay. An approximated discrete-time model and its corresponding continuous-time model are constructed for multiple time-delay continuous-time stable/unstable dynamical processes with known/unknown parameters, using first the conventional observer/Kalman filter identification (OKID) method. Then, an optimal ASMC is developed using the linear quadratic regulator (LQR) approach, in which the corresponding sliding surface is designed using the user-specified eigenvectors and the scalar sign function. For digital implementation of the proposed non-augmented low-dimensional ASMC, a digital counterpart is designed based on the existing prediction-based digital redesign method and the newly developed prediction-based Chebyshev quadrature digital redesign method. Finally, a non-augmented low dimensional digital observer with a long input or output dead time is constructed for the implementation of the digitally redesigned sliding mode controller, to improve the performances of multiple time-delay dynamical processes. The effectiveness of the proposed method has been verified by means of two illustrative examples.

Altitude tracking controller design for a small unmanned aerial vehicle based on linear-quadratic-Gaussian-integral control

This paper presents the design procedure of a digital altitude tracking controller based on optimal control theory. The controller governs the longitudinal dynamics of a small-scale fixed-wing unmanned aerial vehicle (UAV) via an inner-outer loop control structure. In particular, the inner feedback loop maintains the aircraft's longitudinal stability and controls the climb rate (vertical velocity) while the outer-loop tracks the desired altitude through barometric altitude feedback. The inner-loop controller is designed based on the linear-quadratic-Gaussian-integral (LQGI) approach which necessitates the aircraft's longitudinal model to be expressed by a state-space representation. In this work, the model is obtained via a system identification technique called the observer/Kalman filter identification (OKID) method. Actual flight test data is collected and used in the system identification algorithm. On the other hand, the outer-loop controller simply features a proportional-gain control which eliminates the error between a reference altitude and the aircraft's altitude measured in real-time. The proposed altitude tracking controller is implemented on the National Cheng Kung University's Swallow UAV system and has been validated through a series of successful flight tests.

Algorithm 945

We describe a new parallelized Python library for model reduction, modal analysis, and system identification of large systems and datasets. Our library, called modred, handles a wide range of problems and any data format. The modred library contains implementations of the Proper Orthogonal Decomposition (POD), balanced POD (BPOD) Petrov-Galerkin projection, and a more efficient variant of the Dynamic Mode Decomposition (DMD). The library contains two implementations of these algorithms, each with its own advantages. One is for smaller and simpler datasets, requires minimal knowledge to use, and follows a common matrix-based formulation. The second, for larger and more complicated datasets, preserves the abstraction of vectors as elements of a vector space and, as a result, allows the library to work with arbitrary data formats and eases distributed memory parallelization. We also include implementations of the Eigensystem Realization Algorithm (ERA), and Observer/Kalman Filter Identification (OKID). These methods are typically not computationally demanding and are not parallelized. The library is designed to be easy to use, with an object-oriented design, and includes comprehensive automated tests. In almost all cases, parallelization is done internally so that scripts that use the parallelized classes can be run in serial or in parallel without any modifications.

Uncertainty Quantification of the Eigensystem Realization Algorithm Using the Unscented Transform

The Unscented Transformation (UT) is used in this paper to provide a systematic procedure to perform identified model parameter uncertainty quantification. The statistics of signal space uncertainties (input output I/O experimental data) are first mapped into the I/O model space using the Observer Kalman/Filter Identification (OKID) theory. The statistics of the state space model parameters are then computed by an application of the unscented transform on the statistics of the system Markov parameters. Numerical simulations and comparisons with Monte-Carlo error statistics demonstrate the efficacy of UT for model parameter uncertainty calculations presented in this paper. The algorithm is applied to quantify uncertainties associated with the pitch dynamics model of a 2 degree of freedom helicopter model. It is also applied to quantify the error statistics associated with the dynamics of a flexible beam.

Health monitoring of an instrumented SRMF building using earthquake data

SUMMARYThis paper is a study of a six‐story welded steel moment‐resisting frame instrumented by California Strong Motion Instrumentation Program. Several earthquakes had shaken the building, and its response of strong motion data recorded during the earthquakes were made available. In particular, the Whittier Narrows (October 1987), Sierra Madre (June 1991), Northridge (January 1994) and Chino Hills (July 2008) earthquakes were considered in the studies reported here.The paper investigates the capability of input–output system identification methods, namely eigensystem realization algorithm with data correlation, and observer Kalman filter identification, in identifying dynamic characteristics of typical office building structures subjected to strong ground motion. It explores the possibility to extend the above system identification procedures to near‐real‐time estimation of the building response under future earthquakes in order to estimate the likelihood of brittle damage in welded beam to column connections. The modal identification results are compared with those obtained using the spectral analysis and the deterministic‐stochastic subspace identification method to verify the accuracy of the identified modal parameters. Copyright © 2013 John Wiley & Sons, Ltd.

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...

Fault-tolerant tracker for a class of unknown interconnected large-scale sampled-data nonlinear systems with input constraint and actuator failure

Based on the model predictive control (MPC), the soft switching method, and the observer/Kalman filter identification (OKID) method, this paper presents the decentralized fault-tolerant trackers for a class of unknown interconnected large-scale multi-input multi-output sampled-data nonlinear systems with input constraint, actuator failure, and closed-loop decoupling properties. The off-line OKID method is utilized to determine decentralized appropriate (low-) order discrete-time linear models for the class of unknown interconnected large-scale sampled-data systems by using known input–output sampled data. Then, to overcome the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach will be presented. So, decentralized multiple MPC controllers are designed beforehand by using the identified linear models. Once a fault is detected in each decentralized controller, one of the backup control configurations in each decentralized subsystem is switched to using the soft switching approach. Thus, the decentralized fault-tolerant control with the closed-loop decoupling property can be achieved through the above approach with a high-gain property decentralized observer/tracker.

Dynamic modeling and active control of flexible plate based on the input-output data

This paper studies the low-order dynamic modeling and active control of a flexible plate and provides experimental verification. First based on the input-output data of the system, the Markov parameters of the system are identified using the method of observer/Kalman filter identification (OKID). Then a low-order state-space model is built using the eigensystem realization algorithm (ERA). Finally, a linear quadratic Gaussian (LQG) controller is designed based on the low-order state-space model. Experimental results have proved the effectiveness and feasibility of the research.

Identification of discrete-time bilinear systems through equivalent linear models

This paper presents a novel method for identification of discrete-time, time-invariant state-space models of bilinear dynamical systems using the steady-state portion of a single input/multiple output time-history measurements. These measurements are recorded by exciting the system with a linear combination of sine and cosine functions of user-selected frequencies enriched by a subtle amount of random component. The proposed method relies on conversion of the bilinear system into an equivalent linear model (ELM) by an accurate approximation of the state in the bilinear term using a set of sine and cosine basis functions whose frequencies are obtained as combinations of the input frequencies. Observer/Kalman Filter Identification (OKID), a linear time invariant (LTI) system identification algorithm, is used to identify the aforementioned ELM from which the original bilinear model is recovered. A numerical example is also provided.

System identification and active vibration control of a flexible structure

The aim of this paper is to illustrate the active control of vibration of a flexible structure using a model-based digital controller. The state-space model of the system is derived using a system identification technique known as the Observer/Kalman Filter Identification (OKID) method together with Eigensystem Realization Algorithm (ERA). Based on the measured response of the structure to a random input, an explicit state-space model of the equivalent linear system is determined. The model is used in a Linear Quadratic Regulator (LQR) to control the first two modes of vibration of a cantilever beam using a piezoelectric actuator/sensor pair. Experimental results demonstrate the efficacy of the proposed approach.

OKID-based Identification and Control of Unmanned Ducted-Fan Helicopter

This paper presents system identification and control of unmanned helicopter(UH) with ducted fan. The plant is an unstable multi-input multi-output (MIMO) system. Four identification methods have been considered in this work. Two of these methods studied the identification of the system as a set of transfer functions relating different inputs and outputs namely least square with QR-factorization (LS-QR) and recursive least square method (RLS). On the other hand, subspace method and observer/Kalman filter identification (OKID) methods have been used to identify the system in state space representation. The results of the identifications are presented and benchmarked based on degree of fitness. Comparison between output and methods are conducted and analyzed. OKID proves to be the best method for such system and subsequently serves as the basis for the design of LQGI-based velocities tracking controllers.

Detection of Sensor Faults in Small Helicopter UAVs Using Observer/Kalman Filter Identification

Reliability is a critical issue in navigation of unmanned aerial vehicles (UAVs) since there is no human pilot that can react to any abnormal situation. Due to size and cost limitations, redundant sensor schemes and aeronautical‐grade navigation sensors used in large aircrafts cannot be installed in small UAVs. Therefore, other approaches like analytical redundancy should be used to detect faults in navigation sensors and increase reliability. This paper presents a sensor fault detection and diagnosis system for small autonomous helicopters based on analytical redundancy. Fault detection is accomplished by evaluating any significant change in the behaviour of the vehicle with respect to the fault‐free behaviour, which is estimated by using an observer. The observer is obtained from input‐output experimental data with the Observer/Kalman Filter Identification (OKID) method. The OKID method is able to identify the system and an observer with properties similar to a Kalman filter, directly from input‐output experimental data. Results are similar to the Kalman filter, but, with the proposed method, there is no need to estimate neither system matrices nor sensor and process noise covariance matrices. The system has been tested with real helicopter flight data, and the results compared with other methods.

A Novel Tracker for a Class of Sampled-data Nonlinear Systems

In this paper, a novel observer/Kalman filter identification (OKID) based iterative learning control (ILC) for a class sample-data nonlinear system is proposed and supplies a good tracking performance in both the transient and steady-state phase. The proposed observer-based digital redesign tracker can suppress the uncertainties and the nonlinear perturbations. First, even without resetting the identical initial condition the optimal linear model of the analog nonlinear system is constructed at the operating point. The operating point is generated due to the analog observer updated by the well-designed analog OKID-ILC nonlinear system. Thereafter, the linear quadratic regulator design technique with a high-gain property is applied to design an analog observer-based tracker of the optimal linear model. Finally, the proposed approach for the analog system is then extended to the case for a class of sampled-data nonlinear systems.

Observer Kalman filter identification and multiple-model adaptive estimation technique for classifying animal behaviour using wireless sensor networks

The identification of a mathematical model capable of describing the behaviour of animals given input such as feed has great potential for behavioural control purposes. Such models will allow to make predictions which are fundamental to any closed loop control such as control of the feeding. This paper investigates the problem of mathematically modelling animal behaviour. An observer Kalman filter identification method was successfully applied to input–output data and two models representing the hypotheses that animals are actively feeding and the hypotheses that animals are inactive were identified. The input and output of each of the identified models were feed dry matter offer and the pitch angle of the neck, respectively. The pitch angle of the neck of the animal was successfully measured and aggregated by a ZigBee-based wireless sensor network. Two fourth-order models describing the dynamics of an animal in the active and inactive behaviour modes showed good performance in terms of prediction error, cross-correlation between the residual and the output as well as cross-correlation between the residual and the input with 99% confidence interval. A multiple-model adaptive estimation approach was applied to determine the likelihood of each of the two models being the correct model for a specific input of dry matter feed. The average classification success rate was 87.2% for the whole experiment.

Application of Genetic Algorithms to Observer Kalman Filter Identification

In this paper several applications of genetic algorithm (GA) as an aid to the system identification process are presented. First, GAs are used in a set of covariance-based optimum input signal algorithms using a proposed architecture suitable for online system identification. The optimal signals are computed recursively using a predictive filter. The efficiency of these algorithms are compared based on a set of simulations. Second, a novel input design for a two-step identification scheme is presented. Constraint systems, such as commonly found in structural and biomedical engineering applications, are considered for the input design algorithm. This paper presents a novel approach that induces a learning scheme into the input design computation and allows for considerations of the given constraints of the system. The optimization of the new input signal is accomplished using a simple elitism based genetic algorithm. Simulation results indicate the proposed piecewise adaptive input design algorithm performs well compared to the general white-noise-based estimation results. In the third portion of this paper proof is given that no dynamic controller can reduce the noise influence in linear system identification. A new selection scheme of the corresponding singular values is proposed for the eigensystem realization portion of the Observer Kalman filter IDentification algorithm in noisy systems. The selection is done using a GA. Simulation results of the proposed algorithm in comparison with the traditional used method are presented. The results indicate an improved ability to extract system models from highly noise corrupted data.