Showing papers on "System identification published in 1994"

Fuzzy Model Identification Based on Cluster Estimation

Abstract: We present an efficient method for estimating cluster centers of numerical data. This method can be used to determine the number of clusters and their initial values for initializing iterative optimization-based clustering algorithms such as fuzzy C-means. Here we use the cluster estimation method as the basis of a fast and robust algorithm for identifying fuzzy models. A benchmark problem involving the prediction of a chaotic time series shows this model identification method compares favorably with other, more computationally intensive methods. We also illustrate an application of this method in modeling the relationship between automobile trips and demographic factors.

Applied system identification

Abstract: 1. Introduction. 2. Time-Domain Models. 3. Frequency-Domain Models. 4. Frequency Response Functions. 5. System Realization. 6. Observer Identification. 7. Frequency Domain System ID. 8. Observer/Controller ID. 9. Recursive Techniques. Appendix A: Fundamental Matrix Algebra. Appendix B: Random Variables and Kalman Filter. Appendix C: Data Acquisition.

Modeling of dynamic systems

Abstract: I. MODELS. 1. Systems and Models. 2. Examples of Models. 3. Models for Systems and Signals. II. PHYSICAL MODELLING. 4. Basic Principles for Physical Modelling. 5. Some Basic Physical Analogies. 6. Bond-graphs. 7. Computer Support for Physical Modelling. III. SYSTEM IDENTIFICATION. 8. Estimation of Transient Response, Spectra and Frequency Functions. 9. Parameter Estimation of Dynamical Models. 10. System Identification as Tool for Modeling. IV. SIMULATION AND MODEL APPLICATIONS. 11. Simulation. 12. Simulators. 13. Model Validation and Model Use. Appendix A: Linear Systems - Description and Properties. Appendix B: Linearization. Appendix C: Signal Spectra.

Parametric identification of transfer functions in the frequency domain-a survey

Abstract: This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different approaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples. >

Adaptive control of unknown plants using dynamical neural networks

Abstract: In this paper, we are dealing with the problem of controlling an unknown nonlinear dynamical system. The algorithm is divided into two phases. First a dynamical neural network identifier is employed to perform "black box" identification and then a dynamic state feedback is developed to appropriately control the unknown system. We apply the algorithm to control the speed of a nonlinearized DC motor, giving in this way an application insight. In the algorithm, not all the plant states are assumed to be available for measurement. >

System identification using Kautz models

Abstract: In this paper, the problem of approximating a linear time-invariant stable system by a finite weighted sum of given exponentials is considered. System identification schemes using Laguerre models are extended and generalized to Kautz models, which correspond to representations using several different possible complex exponentials. In particular, linear regression methods to estimate this sort of model from measured data are analyzed. The advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters. The subsequent analysis is based on the result that the corresponding linear regression normal equations have a block Toeplitz structure. Several results on transfer function estimation are extended to discrete Kautz models, for example, asymptotic frequency domain variance expressions. >

Memory neuron networks for identification and control of dynamical systems

Abstract: This paper discusses memory neuron networks as models for identification and adaptive control of nonlinear dynamical systems. These are a class of recurrent networks obtained by adding trainable temporal elements to feedforward networks that makes the output history-sensitive. By virtue of this capability, these networks can identify dynamical systems without having to be explicitly fed with past inputs and outputs. Thus, they can identify systems whose order is unknown or systems with unknown delay. It is argued that for satisfactory modeling of dynamical systems, neural networks should be endowed with such internal memory. The paper presents a preliminary analysis of the learning algorithm, providing theoretical justification for the identification method. Methods for adaptive control of nonlinear systems using these networks are presented. Through extensive simulations, these models are shown to be effective both for identification and model reference adaptive control of nonlinear systems. >

Methodology for Optimum Sensor Locations for Parameter Identification in Dynamic Systems

Abstract: This paper provides a methodology for optimally locating sensors in a dynamic system so that data acquired from those locations will yield the best identification of the parameters to be identified. It addresses the following questions: (1) Given m sensors, where should they be placed in a spatially distributed dynamic system so that data from those locations will yield best estimates of the parameters that need to be identified?; and (2) given that we have already installed p sensors in a dynamic system, where should the next s be located? The methodology is rigorously founded on the Fisher information matrix and is applicable to both linear and nonlinear systems. A rapid algorithm is provided for use in large multi‐degree‐of‐freedom systems. After developing the general methodology, the paper goes on to develop the method in detail for a linear N‐degree‐of‐freedom, classically damped, system. Numerical examples are provided and it is verified that the optimal placement of sensors, as dictated by the met...

Optimal, Predictive and Adaptive Control

Abstract: 1. Introduction. I. BASIC DETERMINISTIC THEORY OF LQ AND PREDICTIVE CONTROL. 2. Deterministic LQ Regulation - I: Riccati-Based Solution. 3. I/O Descriptions and Feedback Systems. 4. Deterministic LQ Regulation - II: Solution via Polynomial Equations. 5. Deterministic Receding Horizon Control. II. STATE ESTIMATION, SYSTEM IDENTIFICATION, LQ AND PREDICTIVE STOCHASTIC CONTROL. 6. Recursive State Filtering and System Identification. 7. LQ and Predictive Stochastic Control. III. ADAPTIVE CONTROL. 8. Single-Step-Ahead Self-Tuning Control. 9. Adaptive Predictive Control. APPENDICES. A. Some Results from Linear Systems Theory. B. Some Results of Polynomial Matrix Theory. C. Some Results on Linear Diophantine Equations. D. Probability Theory and Stochastic Processes. References. Some Often Used Abbreviations. Index.

Estimation, identification, and sensorless control in motion control system

Abstract: The paper presents the state of the art of motion systems particularly emphasizing both estimation and identification of parameters and control variables of an electric-motor-driven motion system. In a modern electrical drive system, it is required to take not only the electrical aspect but also the mechanical phase into total system consideration. Improvement in electrical aspect needs a variety of information pertaining to electrical machines and power electronic circuits for improving AC variable-speed drives. Important techniques of identification or estimation of parameters and control variables in AC drives are explained. Such information includes machine parameters, flux, speed, position, and so on. Also, the paper shows that there is some theoretical limit of performance. For improvement of the mechanical phase, the disturbance torque is the most important variable to be identified. It is used in motion control systems, for example, in the feedback loop. Various applications are possible by modification of such a basic approach. As a conclusion, the paper shows that the total robustness is attained by integrating advances of control technique on the electrical aspect and the mechanical aspect. There are numerous variations of controller by possible combinations of these two aspects according to applications. >

Model identification and control strategies for batch cooling crystallizers

Abstract: The open-loop optimal control strategy to regulate the crystal-size distribution of batch cooling crystallizers handles input, output, and final-time constraints, and is applicable to crystallization with size-dependent growth rate, growth dispersion, and fines dissolution. The objective function can be formulated to consider solid-liquid separation in subsequent processing steps. A model-based control algorithm requires a model that accurately predicts system behavior. Uncertainty bounds on model parameter estimates are not reported in most crystallization model identification studies. This obscures the fact that resulting models are often based on experiments that do not provide sufficient information and are therefore unreliable. A method for assessing parameter uncertainty and its use in experimental design are presented. Measurements of solute concentration in the continuous phase and the transmittance of light through a slurry sample allow reliable parameter estimation. Uncertainty in the parameter estimates is decreased by data from experiments that achieve a wide range of supersaturation. The sensitivity of the control policy to parameter uncertainty, which connects the model identification and control problems, is assessed. The model identification and control strategies were experimentally verified on a bench-scale KNO3-H2O system. Compared to natural cooling, increases in the weight mean size of up to 48% were achieved through implementation of optimal cooling policies.

Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model

Abstract: Recursive identification algorithms, based on the nonlinear Wiener model, are presented. A recursive identification algorithm is first derived from a general parameterization of the Wiener model, using a stochastic approximation framework. Local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation. Since inversion is not utilized, noninvertible static nonlinearities can be handled, which allows a treatment of, for example, saturating sensors and blind adaptation problems. Gauss-Newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single-input/single-output case. The proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal. For FIR (finite impulse response) models, it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity. In particular, global convergence of the stochastic gradient method is obtained, provided that the nonlinearity is strictly monotone. The local analysis, performed for IIR (infinite impulse response) models, illustrates the importance of the amplitude contents of the exciting signals. >

Nonlinear Model Validation Using Correlation Tests

Abstract: New higher order correlation tests which use model residuals combined with system inputs and outputs are presented to check the validity of a general class of nonlinear models. The new method is illustrated by testing both simple and complex nonlinear system models.

Structural damage detection and identification using neural networks

Abstract: A novel methodology is presented for on-line damage identification of discrete structural systems. The damage characteristic (location and severity) of the system first can be detected and then identified from the change of its dynamic properties (eigenvalues and mode shapes) through a backward-propa gation neural network. The neural network is constructed by three multilayer subnets that perform the tasks of input pattern generation, damage location identification, and damage severity determination, respectively. The methodology is demonstrated on two spring-mass systems. The effectiveness and limitations of the methodology are discussed. Nomenclature C = damping matrix of the discrete structural system di = dynamic residual vector K = stiffness matrix of the discrete structural system M = mass matrix of the discrete structural system \//» vdj = generalized eigenvalue and eigenvector of damaged system

Application of higher order spectral analysis to cubically nonlinear system identification

Abstract: In this study, digital higher-order spectral analysis and frequency-domain Volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time-invariant systems up to third order. The primary focus is on consideration of random excitation of nonlinear systems and, thus, the approach makes extensive use of higher-order spectral analysis to determine the frequency-domain Volterra kernels, which correspond to linear, quadratic, and cubic transfer functions. Although the Volterra model is nonlinear in terms of its input, it is linear in terms of its unknown transfer functions. Thus, a least squares approach is used to determine the optimal (in a least squares sense) set of linear, quadratic, and cubic transfer functions. Of particular practical note, is the fact that the approach of this paper is valid for non-Gaussian, as well as Gaussian, random excitation. It may also be utilized for multitone inputs. The complexity of the problem addressed in this paper arises from two principal causes: (1) the necessity to work in a 3D frequency space to describe cubically nonlinear systems, and (2) the necessity to characterize the non-Gaussian random excitation by computing higher-order spectral moments up to sixth order. A detailed description of the approach used to determine the nonlinear transfer functions, including considerations necessary for digital implementation, is presented. >

Element-level system identification with unknown input

Abstract: A finite element‐based time domain system identification procedure is proposed to evaluate existing large structural systems at the element level. The procedure does not need any information on the input excitation forces. Since the input exciting forces are not required, there is no restriction on the type of exciting force, only a small number of observation time points are required and no information is required on the modal properties of the structure. The unknown exciting forces can be applied at the ground level representing the seismic excitation. The procedure is particularly applicable to identifying an existing structure. The method is verified using three examples. For verification purposes, both the noise‐free and noise‐included output responses are considered. In all cases, the proposed method identified the structural parameters very well. The errors in the estimation of the parameters are considerably smaller than those in the other methods currently available in the literature. The propose...

On the time complexity of worst-case system identification

Abstract: In this paper we treat a general worst-case system identification problem. This problem is worst-case with respect to both noise and system modeling uncertainty. We consider this problem under various a priori information structures. We determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst-case error bound. Our results are algorithm independent. We show that this minimum duration is prohibitively long. Based on our results, we suggest that worst-case (with respect to noise) system identification requires unrealistic amounts of experimental data. >

An unbiased equation error identifier and reduced-order approximations

Abstract: The equation error (EE) identification technique is modified to remove the parameter bias problem induced by uncorrelated measurement errors. The modification replaces a "monic" constraint with a "unit-norm" constraint; the asymptotic solution replaces a normal equation with an eigenequation. The resulting algorithm is simpler than previous schemes, while at the same time preserving the desirable properties of the conventional EE method: simplicity of an on-line algorithm, unimodality of the performance surface, and consistent identification in the sufficient-order case. In the more realistic undermodeled case, a robustness result shows that the mean optimal parameter values of both the monic and unit-norm EE schemes correspond to a stable transfer function for all degrees of undermodeling, and for all stationary output disturbances, provided the input sequence satisfies an autoregressive constraint; otherwise an unstable model may result. Model approximation properties for the undermodeled case are exposed in detail for the case of autoregressive inputs; although both the monic and unit-norm variants provide Pade approximation properties, the unit-norm version is capable of autocorrelation matching properties as as well, and yields the optimal solution to a first- and second-order interpolation problem. Finally, the mismodeling error for the undermodeled case is shown to be a well-behaved function of the Hankel singular values of the unknown system. This modification allows EE methods to be admitted to the class of unbiased identification and approximation techniques. >

High performance drive of DC brushless motors using neural network

Abstract: In this paper, a multi-layer neural network (NN) architecture is proposed for the identification and control of DC brushless motors operating in a high performance drives environment. The NN in the proposed structure performs two functions. The first is to identify the nonlinear system dynamics at all times. Hence, detailed and elaborate models for the DC brushless machines are not needed. Furthermore, unknown nonlinear dynamics that are difficult to model such as load disturbances, system noise and parameter variations can be recognized by the trained neural network. The second function of the NN is to control the motor voltage so that the speed and position are made to follow pre-selected tracks (trajectories) at all times. The control action emulated by the NN is based on the indirect model reference adaptive control. A hardware laboratory setup is utilized to test and evaluate the proposed neural network structure. The paper shows, based on the laboratory test results, that the proposed neural network structure performance was good: the tracking accuracy was very high and the system robustness was quite evident even in the presence of random and severe disturbances. >