Adaptive quantification of model uncertainties by rational approximation (original) (raw)
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Identification of uncertainty bounds in robust control design is known to be a critical issue that attracts the attention of research in robust control field recently. Nevertheless, the practical implementation involves a trial and error procedure, which depends on the designer prior knowledge and the available information about the system under study. Artificial intelligent techniques provide a suitable solution to such a problem. In this paper a new intelligent identification method of uncertainty bound using an adaptive neuro-fuzzy inference system (ANFIS) in an enhanced feedback scheme is proposed. The proposed ANFIS structure enables accurate determination of the uncertainty bounds and guarantees robust stability and performance. In our proposed technique, the validation of the intelligent identified uncertainty weighting function is based on the measurement of both the v-gap metric and the stability margin that result from the corresponding robust controller design. Additionally, these two indices are used to improve the accuracy of the intelligent estimation of uncertainty bound in conjunction with the robust control design requirements. The enhanced intelligent identification of uncertainty bound is demonstrated on a servo positioning system. Simulation and experimental results prove the validity of the applied approach; more reliable and highly efficient estimation of the uncertainty weighting function for robust controller design.
Uncertainty remodeling for robust control of linear time-invariant plants^1
Periodica Polytechnica Electrical Engineering, 2009
The paper proposes a measure of robust performance based on frequency domain experimental data that allows nonconservative modeling of uncertainty. Given the nominal model of the plant and closed-loop performance specifications the iterative control design and remodeling of model uncertainty based on that measure leads to a controller with improved robust performance. The structured dynamic uncertainty is allowed to act on the nominal model in a linear fractional transformation (LFT) form. The proposed method is a modification of the structured singular value with implicit constraints on model consistency. The usefulness of the method is demonstrated on a vehicle control simulation example.
Robust rational function approximation algorithm for model generation
Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361)
The problem of computing rational function approximations to tabulated frequency data is of paramount importance in the modeling arena. In this paper we present a method for generating a state space model from tabular data in the frequency domain that solves some of the numerical difficulties associated with the traditional fitting techniques used in linear least squares approximations. An extension to the MIMO case is also derived.
An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
Journal of Uncertainty Analysis and Applications, 2015
Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 "Test Uncertainty" and the ISO Guide for the "Expression of Uncertainty in Measurement," has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method.
Time-Domain Robust Stability Test Under Plant and Controller Interval Uncertainty
IFAC Proceedings Volumes, 2000
Once a controller has been designed for a certain plant with any method available, one would like to know if that controller will perform well despite structured uncertainty in the plant. Furthermore, as controller implementation is concerned, one is also interested in its fragility (Keel and Bhattacharyya, 1997). In this paper, interval parametric uncertainty is considered. As an alternative to testing robust stability by polynomial methods (Bhattacharyya et al., 1995; Ackermann, 1993), one can perform a robust simulation of the time domain response of the closed loop taking into account plant and controller uncertainties. It is shown that, based on this simulation, it is possible to test the closed loop robust stability.
Parameterised controller synthesis for SISO-LTI uncertain plants using frequency domain information
This paper extends the results of a new model-free approach which has been applied to guarantee nominal stability and performance. In this paper, using a particular controller structure, the robust stability (RS) and robust performance (RP) criteria for single input single output linear time invariant (SISO-LTI) plants with multiplicative uncertainty are transformed to affine functions in terms of controller parameters. It is shown that solving the feasibility problem of these new criteria will lead to controllers that guarantee the RS and performance. There is no need for a plant mathematical model. The required data for controller synthesis are just the frequency responses corresponding to limited samples of the uncertain plant. Also, there is no need for exact data at each frequency for the whole set of frequency responses. The approach is also applicable for designing both low- and high-order controllers. The effectiveness of the proposed technique is illustrated by simulation results.
Rational Basis Functions for Robust Identification from Frequency and Time-Domain Measurements
Automatica, 1998
This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two-parameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown, that by using a min-max criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to re-parameterise the model structures into new ones with equivalent fixed poles, but for which the basis functions are orthonormal in ¢ ¤ £ .