Discrete modelling of uncertain continuous systems having an interval structure using higher-order integrators

A higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Thanks to simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients of exponential nature in the exact discrete-time transfer function is therefore circumvented. Furthermore, interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulas to obtain the lower and upper bounds for the discrete interval system are derived, so that existing robust results in the discrete-time domain can be easily applied to the discretized system. Digital simulation and design for the continuous-time interval plant can then be performed based on the obtained discrete-time interval model.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

This paper addresses some approaches to modeling of uncertain systems. The model used to describe these uncertain systems is the linear fractional transformation (LFT). Definitions of robust models and optimization of robust models are introduced. Techniques and experimental examples to construct robust models are described, which include additive-error, relative/multiplicative-error, combinations of additive-error and multiplicative-error, and weighted-error techniques.

In this paper, an evolutionary approach is proposed to obtain a discrete-time state-space interval model for uncertain continuous-time systems having interval uncertainties. Based on a worst-case analysis, the problem to derive the discrete interval model is first formulated as multiple mono-objective optimization problems for matrix-value functions associated with the discrete system matrices, and subsequently optimized via a proposed genetic algorithm (GA) to obtain the lower and upper bounds of the entries in the system matrices. To show the effectiveness of the proposed approach, roots clustering of the characteristic equation of the obtained discrete interval model is illustrated for comparison with those obtained via existing methods.

Transfer function estimation of turboalternator from practical operating data by spectral analysis

This paper discusses the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design problem for non-linear two-dimensional (2-D) uncertain continuous systems with state delays and saturation. The non-linear function under consideration is assumed to satisfy the Lipschitz condition while the saturation term is being dealt by using a memory-less sector region methodology. A suitable Lyapunov-Krasovskii functional is considered, and the Wirtinger-based integral inequality method is used to derive some sufficient conditions which ensure that the resultant filtering error system is robustly asymptotically stable along-with the specified L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbance attenuation level γ. A suitable example explains the derived results' usefulness.

An approximation, valid over a limited region of the s plane, is given to a single path in a multivariable system. The inference of system instability from instability of this approximate transfer function is discussed, and it is shown that it is not sufficient for the approximation to be valid over a region of the real-frequency axis alone. This point is demonstrated by an example.

In this work, a mathematical model for stochastic uncertain systems where the system uncertainty is handled by polynomial chaos method is developed. For uncertain systems where the system uncertainty is modeled by a first order polynomial chaos expansion, the estimation of the system states are done by an augmented Kalman filter equations developed by averaged least square method. The performance of the proposed robust estimation algorithm is shown by an uncertain system used as a framework example in previous works.

A new method for digital model conversion of a continuous-time uncertain system and a new digital redesign method for robust control of a sampled-data uncertain system are presented. The concept of the principle of equivalent areas together with interval arithmetic is utilised for finding the discrete-time uncertain model and the digital robust control law from the continuous-time uncertain state equation and the analogue robust control law, respectively. Using the newly digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.

COSMOS is a new simulation language for description of continuous, discrete or combined continuous/discrete models. For continuous models, the COSMOS language definition constitutes a superset of CSSL with many additional structuring elements being incorporated, e.g. for convenient modelling of piecewise continuous models and variable structure systems. Discrete models are coded according to the process interaction world view. The design of the language constructs makes it possible to write simulation programs in accordance with modem software engineering methodology. The model and experiment description, for example, are totally separated. In addition, models can be separated into submodels.

The problems of vibration-attenuation controller design for uncertain mechanical systems with time-varying input delay are of concern in this paper. Firstly, based on matrix transformation, the mechanical system is described as a state-space model. Then, in terms of introducing the linear varying parameters, the uncertain system model is established. Secondly, the LMI-based sufficient conditions for the system to be stabilizable are deduced by utilizing the LMI technique. By solving the obtained LMIs, the controllers are achieved for the closed-loop system to be stable with a prescribed level of disturbance attenuation. Finally, numerical examples are given to show the effectiveness of the proposed theorems.

On the second-order slow drift force spectrum

New fractional-order LADRC scheme based on a novel filtered-Bode’s ideal transfer function for integer-order systems

Choice of Basis Functions for Continuous and Discrete System Modelling

Many dynamic systems in physics, chemistry, biology, engineering and information sciences can be characterized by impulsive dynamics caused by abrupt jumps at certain instants during the process. These complex dynamic behaviour can be modelled by singular and impulsive differential systems. This paper formulates and studies a model of singular and impulsive interval uncertain dynamic systems with time delay. Several fundamental issues such as global exponential robust stability of such systems are established. A numerical example is given for illustration and interpretation of the theoretical results.