Frequency-domain Criterion Research Articles

LAG SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results.

On the stabilization of elastic plates with dynamical boundary control

We study the exponential stabilization of elastic plates with dynamical boundary control. We show that the corresponding system with velocity and angular velocity feedbacks control in the dynamical boundary is not exponentially stable. Our main tool is the frequency-domain criterion for exponential stability of semigroups.

Some new criteria for lag synchronization of chaotic Lur'e systems by replacing variables control

Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchronization are described. Then, based on a quadratic Lyapunov function, two new Lur‘ e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are applied to analyze the lag synchronization of general master-slave Chua's circuits so that some ranges of the parameters in which the master-slave Chua's circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.

A frequency-domain training approach for equalization and noise suppression in discrete multitone systems

In discrete multitone (DMT) transceivers, a time-domain equalizer (TEQ) is used to shorten the effective channel impulse response such that a shorter cyclic prefix can be used. In this paper, we pose the TEQ design problem completely in the frequency domain by defining a frequency-domain weighted least-squares cost function. The definition of the frequency-domain TEQ design criterion, we show, allows for the introduction of a weighting function to control the spectral shape of the TEQ, and facilitates important extensions particularly useful for the DMT system. The TEQ can be used to suppress the noise and interference in the DMT system, a feature especially useful in the frequency division multiplexing-based DMT system. Also, in the echo-cancellation-based DMT system, the TEQ can be used to jointly shorten the echo response thus reducing the complexity of the echo canceler. We present corresponding algorithms for these two objectives and simulation results, which show that the weighted frequency-domain least-squares algorithm and the two extensions we derive can achieve the shortening (channel or channel and echo) as well as noise suppression objectives effectively.

Stability of systems with several monotone nonlinearities

This paper is devoted to stability problems of automatic control systems. Frequency domain criteria for global asymptotic stability of equilibrium sets for new classes of nonlinearities are derived. Results are illustrated by examples.

Modeling and H2/H∞ MIMO Control of an Earthmoving Vehicle Powertrain

Coordination of the power distribution in a Multi-Input Multi-Output (MIMO) electro-hydraulic transmission is investigated for the case of an earthmoving vehicle powertrain. A generalized model of a representative system is presented along with the development of both H2 and H∞ MIMO controller designs. The controllers are developed based on a linearized model of the system about some nominal operating point. Multiple inputs are coordinated to control multiple load outputs simultaneously. Since typical MIMO electrohydraulic transmission systems have significant nonlinear dynamics that vary with system operating conditions, a robust controller design is paramount. The increased robustness of the H∞ controller over the H2 scheme is demonstrated qualitatively in the time domain through both disturbance rejection and trajectory tracking comparisons. A frequency domain criterion quantitatively provides quantifiable comparisons between the two methods. Hardware-in-the-Loop experiments validate the modeling and control performance on an Earthmoving Vehicle Powertrain Simulator (EVPS).

Popov's Method and its Subsequent Development

A simple proof of the quadratic criterion for absolute stability is given for the nondegenerate case. A similar result was proved earlier (for both degenerate and nondegenerate cases) by the author (1967) by using completely different methods. The proof given has some similarities with the ideas used by Popov (1959-1961) in the proof of his now widely known frequency-domain criterion of absolute stability. The new frequency-domain criterion of absolute stability is given for the system with the periodic coefficient. One illustrative example is considered.

Absolute Stability Criterion for a Class of Systems with Time Periodic Nonlinearities

The paper considers the problem of absolute stability of a system consisting of a . linear block described by a vector Volterra integral equation and a time periodic nonlineraity. The result is a frequency domain criterion. An. immediate consequence of the result is a new absolute stability criterion for stationary odd monotone nonlinearities.

State Space Extension Method in the Theory of Absolute Stability

State space extension method is applied to construct new quadratic constraints and derive new frequency domain criteria for absolute stability.

Frequency-Domain Criteria for Stability of Volterra Integral Equations with Discontinuous Nonlinear Functions

For integral Volterra equations with discontinuous periodic functions and with discontinuous functions satisfying the sector condition, frequency-domain criteria for gradient-like behaviour of averaged solution are obtained.

FREQUENCY–DOMAIN CRITERIA FOR CORRELATING AND UPDATING DYNAMIC FINITE ELEMENT MODELS

This paper discusses the use of frequency–domain criteria for finite element (FE) model correlation and updating. The criteria, which can be local or global, are either shape or amplitude based. The former are sensitive to mode shape differences but not to relative scales, and the latter depend on the actual response amplitudes. The updating objective function is formulated in such a way that two global correlation criteria are satisfied simultaneously. A sensitivity-based updating problem is expressed as a set of linear equations where the coefficient matrix contains the partial derivatives of the correlation functions with respect to the chosen design variables. The formulation has the advantage of being able to deal with incomplete measurements and there is no critical selection of updating frequency points. The correlation criteria were used successfully to quantify the initial closeness between 4 increasingly detailed FE models of an automotive oil pan. The updating of the second most detailed model, using simulated response functions from the most detailed model, exhibited quick convergence properties and yielded a very good match between the target and updated frequency response functions. However, the initial FE model was corrected in a curve-fitting/minimisation sense since actual modelling deficiencies were compensated by adjusting a small number of pre-selected design parameters.

The state space extension method in the theory of absolute stability

This paper shows how the state space extension method can be used to derive frequency domain criteria for stability of systems with different kinds of uncertainties. The main result is illustrated by a number of examples.

Concepts of Strict Positive Realness and the Absolute Stability Problem of Continuous-Time Systems

After the conditions for absolute stability and positive realness are reviewed, it is shown that the current definition of positive realness is inadequate to establish less conservative criteria for absolute stability. In this paper, the concepts of wide positive realness (WPR) and wide strict positive realness (WSPR) are proposed. Both WPR and WSPR functions may have poles in the open left and right half-planes, and WPR functions may have single poles on the imaginary axis including ±j∞. Using the concepts of WPR and WSPR, less conservative criteria, including algebraic and frequency domain criteria, are presented for absolute stability of slope-restricted multiple nonlinearity feedback systems. Refined results for non-slope-restricted nonlinearity feedback systems are also proposed. It is pointed out that there is no spectral factorization for WPR and WSPR functions if they have poles at both j∞ and −j∞, this can be used to explain the deficiencies of algebraic criteria presented in previous publications.

Multivariable process identification for mpc: the asymptotic method and its applications

In this work we will introduce the asymptotic method (ASYM) of identification and provide two case studies. The ASYM was developed for multivariable process identification for model based control. The method calculates time domain parametric models using frequency domain criterion. Fundamental problems, such as test signal design for control, model order/structure selection, parameter estimation and model error quantification, are solved in a systematic manner. The method can supply not only input/output model and unmeasured disturbance model which are asymptotic maximum likelihood estimates, but also the upper bound matrix for the model errors that can be used for model validation and robustness analysis. To demonstrate the use of the method for model predictive control (MPC), the identification of a Shell benchmark process (a simulated distillation column) and an industrial application to a crude unit atmospheric tower will be presented.

Optimal MISO Repetitive Control System Design Using Mixed Time and Frequency Domain Criteria

This paper presents an optimal repetitive controller design approach when both frequency and time domain criteria are considered. These criteria include limited control force, convergence rate, and robustness. In particular, the design formulation is based on MISO (multiple-input-single-output) plants which aim at solving nodal point problems encountered in flexible dynamic systems. Nodal points represent physical constraints for feedback control, especially when their frequencies are within the control bandwidth. If multiple control paths with distinct nodal frequencies are available, the proposed method is able to design controllers to compensate the effect and reach certain design objectives. The ellipsoid algorithm is used to calculate controllers’ parameters. Experiments were conducted to demonstrate the proposed method.

Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

AbstractStability is the most important attribute of any system. A prerequisite for all stability criteria of control systems is the existence of a mathematical model. In contrast, fuzzy control systems are often designed based on heuristic human knowledge and without a mathematical model, hence, it has been a difficult task to determine stability of fuzzy control systems under such restrictions. This paper uses the Takagi/Sugeno type of fuzzy rules whose consequences are analytical, and singletons are used as a basis for a number of sufficiency conditions for stability. The schemes considered here are time-domain, but a brief survey which proceeds the main results considers frequency domain as well. Both Lyapunov and interval matrix criteria are presented with some proofs and numerical examples.

Frequency domain criteria for cellular neural networks

A dynamical system is called globally asymptotically stable if it has a unique equilibrium point which attracts every trajectory in state space. As a consequence its steady state response is insensitive to initial conditions and then depends only on the input. In this paper some criteria are presented for the global asymptotic stability of cellular neural networks (CNNs), concerning both discrete-time and continuous-time dynamics. The proposed criteria represent necessary and sufficient conditions that can easily be checked by computing the discrete Fourier transform of the template elements. For this reason they have been called frequency domain stability criteria. These criteria provide milder constraints on the template coefficients than required in existing results for general recurrent neural network models. © 1997 by John Wiley & Sons, Ltd.

Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions

In this paper, the problem of robust stability of systems subject to parametric uncertainties is considered. Sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion which is reminiscent of, but less conservative than, Popov's stability criterion. An equivalent frequency-domain criterion is demonstrated. The relative sharpness of the proposed test and existing stability criteria is then discussed. The use of parameter-dependent Lyapunov functions for robust controller synthesis is then considered. It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant. A possible synthesis procedure and a numerical example are then discussed.

Optimal Repetitive Control System Design Using Mixed Time and Frequency Domain Criteria

This paper presents an optimal repetitive controller design approach when both frequency and time domain criteria are considered. These criteria include limited control force, convergence rate and robustness. In particular, the design formulation is based on MISO (multiple-input-single-output) plants which aim at solving nodal point problems encountered in flexible dynamic systems. Nodal points represent physical constraints for feedback control, especially when their frequencies are within the control bandwidth. If multiple control padis with distinct nodal frequencies are available, the proposed method is able to design controllers to compensate the effect and reach certain design objective. The ellipsoid algorithm is used to calculate controllers' parameters. Simulation examples are also given to demonstrate the proposed method.

Absolute stability of sampled-data systems with a sector nonlinearity

This paper studies the absolute stability problem of sampled-data systems with a sector nonlinearity. Using the FR-operator technique, a frequency-domain criterion with a Nyquist-like plot is derived. It can be regarded as a sampled-data version of the circle criterion. It is shown that the “absolute-stability gain margin” can be read directly from the plot.