Linearization of nonlinear dynamic systems
19 Jul 2004-IEEE Transactions on Instrumentation and Measurement (IEEE)-Vol. 53, Iss: 4, pp 1245-1248
TL;DR: This paper proposes a method to linearize a nonlinear dynamic system: the nonlinear distortions are reduced, and the linear dynamics are corrected to a flat amplitude and linear phase in a user defined frequency band.
Abstract: In this paper we propose a method to linearize a nonlinear dynamic system: the nonlinear distortions are reduced, and the linear dynamics are corrected to a flat amplitude and linear phase in a user defined frequency band.
Citations
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01 Jan 2005
TL;DR: In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.
Abstract: Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models. More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system. In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented. In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs. It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem.
122 citations
TL;DR: This paper describes a new autocalibration methodology for nonlinear intelligent sensors based on artificial neural networks, ANN, and shows that the proposed method turned out to have a better overall accuracy than the other two methods.
Abstract: The development of smart sensors involves the design of reconfigurable systems capable of working with different input sensors. Reconfigurable systems ideally should spend the least possible amount of time in their calibration. An autocalibration algorithm for intelligent sensors should be able to fix major problems such as offset, variation of gain and lack of linearity, as accurately as possible. This paper describes a new autocalibration methodology for nonlinear intelligent sensors based on artificial neural networks, ANN. The methodology involves analysis of several network topologies and training algorithms. The proposed method was compared against the piecewise and polynomial linearization methods. Method comparison was achieved using different number of calibration points, and several nonlinear levels of the input signal. This paper also shows that the proposed method turned out to have a better overall accuracy than the other two methods. Besides, experimentation results and analysis of the complete study, the paper describes the implementation of the ANN in a microcontroller unit, MCU. In order to illustrate the method capability to build autocalibration and reconfigurable systems, a temperature measurement system was designed and tested. The proposed method is an improvement over the classic autocalibration methodologies, because it impacts on the design process of intelligent sensors, autocalibration methodologies and their associated factors, like time and cost.
43 citations
TL;DR: This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system.
Abstract: This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system To this end, competing Volterra structures of different sizes are employed in a hierarchical combination scheme so as to find the best configuration of the second-order kernel memory, using the already known diagonal-coordinate representation The length and number of required quadratic kernel diagonals can be concurrently estimated by monitoring the combination performance Subsequently, the memory size of the involved models is dynamically increased or decreased, following a set of intuitive rules Since this automatic memory adaptation is performed along with the coefficient updates, an efficient Volterra filter is realized, offering great flexibility and minimizing the risk of under- or overmodeling any given quadratic nonlinearity Besides the straightforward scheme, a simplified version is presented, greatly reducing the algorithmic demands This efficient version is based on a virtualization of the competing Volterra filters by jointly using common coefficients and hence exhibits a computational complexity suitable for practical implementations The robust estimation performance of the approach is demonstrated by various examples for a nonlinear acoustic echo cancellation scenario, involving stationary noise, real speech signals and realistic Volterra kernels
42 citations
Cites background from "Linearization of nonlinear dynamic ..."
...have addressed the problem of finding the best (inverse) model for approximate linearization in [28]....
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TL;DR: Zhelin reservoir, a multi-purpose reservoir designed mainly for hydropower generation, is located in Xiushui watershed in Jiangxi Province, China as mentioned in this paper, where three optimization algorithms including progressive optimization algorithm (POA), particle swarm optimization (PSO), and genetic algorithm (GA) are applied.
31 citations
TL;DR: This article explains the applications of DSP measurand reconstruction and defines and illustrates three classes of elementary problems: scalar nonlinear problems of static reconstruction, scalar linear problems of dynamic reconstruction, and scalarNonLinear problems of quasi-dynamic reconstruction.
Abstract: A digital signal processing (DSP) based stand-alone measurement system is capable of making decisions in control. This article explains the applications of DSP measurand reconstruction and defines and illustrates three classes of elementary problems: scalar nonlinear problems of static reconstruction, scalar linear problems of dynamic reconstruction, and scalar nonlinear problems of quasi-dynamic reconstruction.
15 citations
References
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Book•
01 May 2000
TL;DR: Inversion and time series analysis of polynomial systems has been studied in this article, with a focus on frequency-domain methods for Volterra system identification, as well as adaptive truncated VOLTERRA filters.
Abstract: Volterra Series Expansions. Realization of Truncated Volterra Filters. Multidimensional Volterra Filters. Parameter Estimation. Frequency-Domain Methods for Volterra System Identification. Adaptive Truncated Volterra Filters. Recursive Polynomial Systems. Inversion and Time Series Analysis. Applications of Polynomial Filters. Some Related Topics and Recent Developments. Appendices. References. Index.
586 citations
"Linearization of nonlinear dynamic ..." refers background in this paper
...It was realized that nonlinear systems can be approximated by parallel structures [12]....
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DOI•
01 Nov 1980TL;DR: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way as discussed by the authors, where the limitations, relationships and applicability of the methods are discussed throughout.
Abstract: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory and included. The limitations, relationships and applicability of the methods are discussed throughout.
491 citations
TL;DR: A well chosen, general nonlinear model structure is proposed that is identified in a two-step procedure and not only includes Wiener and Hammerstein systems but is also suitable to model nonlinear feedback systems.
133 citations
"Linearization of nonlinear dynamic ..." refers background or methods in this paper
...However, since the cost to check this is very restricted (this is the whole idea beyond the procedure), it is not a disaster if the method fails [10]....
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...A detailed description is given in [10]....
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...The identification of this nonlinear model can be very easily done using a two step procedure starting from a single experiment [10]....
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TL;DR: This paper discusses the design and properties of two trajectory tracking controllers for linear time-invariant systems, and compares their implementation and experimental results on a flexible one-link robot equipped with a velocity-controlled actuator.
Abstract: This paper discusses the design and properties of two trajectory tracking controllers for linear time-invariant systems, and compares their implementation and experimental results on a flexible one-link robot equipped with a velocity-controlled actuator. High positioning accuracy and low tracking errors within a specified bandwidth are their performance specifications. Both controllers use the same state feedback controller, but have a different feedforward design approach. Both feedforward methods design stable prefilters which approximate the unstable inverse system model. The first method designs a stable prefilter using the extended bandwidth zero phase error tracking control (EBZPETC) method. The second feedforward method adds delay to the inverse model and then uses common filter design techniques to approximate this delayed frequency response.
82 citations
"Linearization of nonlinear dynamic ..." refers background in this paper
...is designed to correct the undesired behavior [1]–[3]....
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25 Apr 1989
TL;DR: In this paper, a method for compensating in real time for a nonideal transfer function of a data acquisition channel by means of a digital IIR (infinite impulse response) filter is presented.
Abstract: A method is presented for compensating in real time for a nonideal transfer function of a data acquisition channel by means of a digital IIR (infinite impulse response) filter. Real-time compensation of the amplitude and phase characteristics of an acquisition channel so that the long-term error is less than +or-0.01 dB and +or-0.1 degrees , respectively, has been obtained experimentally. It is shown that stability and linearity are the main requirements for the components of the data acquisition channel. Careful selection of the components and outlining of the antialias filter and the programmable amplifier is no longer necessary. >
51 citations