Frequency-domain Criterion Research Articles

Frequency-domain criterion of global stability for dynamical systems with Prandtl hysteresis operator

Frequency-domain criterion of global stability for dynamical systems with Prandtl hysteresis operator

Frequency-domain criteria for global stability of dynamic systems with the Prandtl and play operators

The frequency criterion of the global stability of dynamic systems with the Prandtl and “play” operator is formulated. The scheme of its proof is given. The advantage of the criterion obtained as compared with the known Logemann–Ryan criterion is shown.

Singular Perturbations of Volterra Equations with Periodic Nonlinearities. Stability and Oscillatory Properties

Singularly perturbed integro-differential Volterra equations with MIMO periodic nonlinearities are considered, which describe synchronization circuits (such as phase- and frequency-locked loops) and many other “pendulum-like” systems. Similar to the usual pendulum equation, such systems are typically featured by infinite sequences of equilibria points, and none of which can be globally asymptotically stable. A natural extension of the global asymptotic stability is the gradient-like behavior, that is, convergence of any solution to one of the equilibria. In this paper, we offer an efficient frequency-domain criterion for gradientlike behavior. This criterion is not only applicable to a broad class of infinite-dimensional systems with periodic nonlinearities, but in fact ensures the equilibria set stability under singular perturbation. In particular, the proposed criterion guarantees the absence of periodic solutions that are considered to be undesirable in synchronization systems. In this paper we also discuss a relaxed version of this criterion, which guarantees the absence of “high-frequency” periodic solutions, whose frequencies lie beyond a certain bounded interval.

Model-based fractional order controller design

This paper deals with model-based fractional order controller design. The objective is identification for controller design in order to achieve the desired closed-loop performances. Firstly, the fractional order closed-loop bias-eliminated least squares method is used to identify the process model. Then, based on the numerical optimization of a frequency-domain criterion, the fractional controller is designed. If the proposed algorithm detects any changes in the process parameters, the controller is updated to keep the same performances. A numerical example is presented to show the efficiency of the proposed scheme.

Effect of spectral cross-correlation on multiaxial fatigue damage: simulations using the critical plane approach

The present paper aims to discuss a frequency-domain multiaxial fatigue criterion based on the critical plane approach, suitable for fatigue life estimations in the presence of proportional and non-proportional random loading. The criterion consists of the following three steps: definition of the critical plane, Power Spectral Density (PSD) evaluation of an equivalent normal stress, and estimation of fatigue damage. Such a frequency-domain criterion has recently been validated by using experimental data available in the literature, related to combined proportional and non-proportional bending and torsion random loading. The comparison with such experimental data has been quite satisfactory. In order to further validate the above criterion, numerical simulations are herein performed by employing a wide group of combined bending and torsion signals. Each of such signals is described by an ergodic, stationary and Gaussian stochastic process, with zero mean value. The spectrum of each signal is assumed to be represented by a PSD function with rectangular shape. Different values of correlation degree, variance and spectral content are examined.

Design of State Feedback Adaptive Fuzzy Controllers for Second-Order Systems Using a Frequency Stability Criterion

This paper proposes a design method for second-order systems that guarantees the stability of an adaptive fuzzy controller with state feedback. The system consists of a linear unstable plant, the Takagi–Sugeno controller, a nonlinear reference model, and an adaptation mechanism. In this paper, gradient-based adaptation is used to change the consequents of the controller rules so that the closed-loop system behaves like the reference model. The proposed method utilizes a frequency-domain criterion in the form of the modified circle theorem. The controller function is assumed to be a nonlinearity described by a sector condition, which means that the function lies between two planes. During the process of adaptation, this function is verified so it stays in the sector guaranteeing stability. The method described here is illustrated by an example of a control system containing an unstable plant with an unknown pole in the right half-plane. The motivation of this paper is to propose a frequency-domain method for the design of state feedback adaptive fuzzy controllers. Comparing with time-domain methods that require advanced software tools, the proposed method offers simple graphical interpretation on the Nyquist plane.

Model-free adaptive fractional order control of stable linear time-varying systems

This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency-domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example.

On the convergence of iterative learning control

We derive frequency-domain criteria for the convergence of linear iterative learning control (ILC) on finite-time intervals that are less restrictive than existing ones in the literature. In particular, the former can be used to establish the convergence of ILC in certain cases where the latter are violated. The results cover ILC with non-causal filters and provide insights into the transient behaviors of the algorithm before convergence. We also stipulate some practical rules under which ILC can be applied to a wider range of applications.

Frequency-domain stability criteria for SISO and MIMO nonlinear feedback systems with constant and variable time-delays

New frequency-domain criteria are proposed for the L2-stability of both nonlinear single-input-single-output (SISO) and nonlinear multiple-input-multiple-output (MIMO) feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities (FATQNs) with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i) zero, ii) a constant, iii) variable-time and iv) fixed-history (only for SISO systems).

A critical analysis of the Mises stress criterion used in frequency domain fatigue life prediction

Multiaxial fatigue failure criteria are formulated in time and frequency domain. The number of frequency domain criteria is rather small and the most popular one is the equivalent von Mises stress criterion. This criterion was elaborated by Preumont and Piefort on the basis of well-known von Mises stress concept, first proposed by Huber in 1907, and well accepted by the scientific community and engineers. It is important to know, that the criterion was developed to determine the yield stress and material effort under static load. Therefore the direct use of equivalent von Mises stress criterion for fatigue life prediction can lead to some incorrectness of theoretical and practical nature. In the present study four aspects were discussed: influence of the value of fatigue strength of tension and torsion, lack of parallelism of the SN curves, abnormal behaviour of the criterion under biaxial tensioncompression and influence of phase shift between particular stress state components. Information contained in this article will help to prevent improper use of this criterion and contributes to its better understanding. KEYWORDS. Mises stress; Frequency domain; Multiaxial fatigue.

Frequency Domain Criterion of Appearance of an Electromagnetic Surface Wave Above the Laminar Ice—Salt Water Structure

We propose a frequency domain criterion for appearance of an electromagnetic surface wave above the laminar ice—salt water structure and substantiate it theoretically and experimentally. It is found that an ice layer on the ocean surface increases the surface impedance modulus and shifts its phase to the domain corresponding to strongly inductive impedances (with a phase of up to −88°). We show that due to the presence of a thin low-conductivity ice layer on the ocean surface, an additive component appears in the ocean water impedance, which depends on the thickness of the ice layer linearly and shifts the impedance phase to the region corresponding to strong inductance. In this case, electric properties of the ice layer have almost no influence on the change in the impedance. The ice layer has a great influence on the electromagnetic field, which can be greater over the ice-covered ocean compared with the field over an infinitely conducting plane. The field increase effect is due to the electromagnetic surface wave.

Consensus for Linear Multiagent Systems With Time-Varying Delays: A Frequency Domain Perspective.

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.

Simplex Guided Extremum Seeking Control With Convergence Detection to Improve Global Performance

This paper presents a novel approach to improve the global performance of extremum seeking control (ESC). This algorithm employs perturbation-based ESC to find local extrema and a simplex-based algorithm to search for the global extremum. The two methods are employed in an iterative switching manner. We propose a novel frequency-domain criterion to detect when the state of a system under ESC has converged to a local optimum. Switching from ESC to the simplex method is triggered when this criterion is satisfied. We prove that this criterion will be met within finite time, under conditions on the ESC law. Simulations and experiments demonstrate and statistically prove that this algorithm outperforms ESC or simplex-based algorithms for optimizing objective functions with multiple extrema.

Frequency-domain criteria for the global stability of phase synchronization systems

New criteria for the global stability of phase synchronization systems are formulated and proved. The efficiency of the criteria for phase-locked loops is demonstrated.

Consensus in nonlinear stationary networks with identical agents

For the multiagent networks with arbitrary-order identical agents and nonlinear uncertain couplings, satisfying the sector inequalities consideration was given to the problem of reaching consensus (asymptotic synchronization) The network topology was assumed to be time-invariant. A frequency-domain consensus criterion extending the Popov criterion for the absolute stability of Lurie systems with one scalar-valued nonlinearity was proposed.

Frequency-domain criterion for the chaos synchronization of time-delay power systems under linear feedback control

This paper studies the global synchronization of non-autonomous, time-delay, chaotic power systems via linear state-error feedback control. The frequency domain criterion and the LMI criterion are proposed and applied to design the coupling matrix. Some algebraic criteria via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. The effectiveness of the new criteria is illustrated with numerical examples.

Multiaxial Fatigue Criteria for Random Stress Response – Theoretical and Experimental Comparison

Randomly excited structures are exposed to random stress loads that can result in fatigue failure. Prediction of such failure requires good structural dynamics and fatigue models. This study researches the multiaxial criteria which reduce the multiaxial stress state to an equivalent uniaxial stress. Several frequency-domain criteria can be found in literature. However, experimental comparison studies are scarce. This research presents and then theoretically and experimentally compares selected frequency-domain multiaxial criteria, namely: maximum normal stress, maximum shear stress and the C-S criterion. Time-to-failure results are compared across multiaxial criteria and with experimental data. Results show that selected methods give reliable estimates.

Convergence-based Analysis of Robustness to Delay in Anti-windup Loop of Aircraft Autopilot

The windup phenomenon is interpreted as a consequence of the convergent property absence for system with a saturation. This makes it possible to use the frequency-domain criterion for analysis of anti-windup augmentation in the case of stable and marginally stable plants. Based on this approach, robustness of the systems with respect to time delay in the anti-windup loop is examined and the approach for an optimal choice of the static anti-windup gain is proposed. An application of the convergence-based anti-windup control strategy to aircraft flight control for the case of time-delay in the anti-windup loop is described and studied by simulations.

A new extension of the infinite-dimensional KYP lemma in the coercive case

The Kalman-Yakubovich-Popov (KYP) Lemma, giving the frequency-domain criteria for solvability of LQR problems and feasibility of related LMIs and Lur'e-Riccati equations, is undoubtedly one of the cornerstone results in modern control theory. Numerous applications of the KYP lemma in nonlinear and robust control motivated its extension to systems with distributed parameters. Unlike the finite-dimensional case, where the KYP lemma admits elegant proofs by means of algebraic techniques and methods from convex analysis, a prerequisite for its infinite-dimensional extensions is feasibility of the corresponding LQR problem, resulting on assumptions of exponential or L2-stabilizability. This property is restrictive and not easily verifiable for general infinite-dimensional systems. Being quite natural in the problems of absolute stability, it seems unnecessary in other applications of the KYP lemma which require only solvability of the operator inequality, but not positivity of its solution, such as e.g. instability or dichotomy criteria. In the present paper we show, that in the “strict” or coercive case the KYP lemma retains its validity, replacing stabilizability assumption with some technical assumption which holds, for instance, whenever the linear system is exponentially dichotomic.

Asymptotic Properties of Nonlinear Singularly Perturbed Volterra Equations

In this paper we examine asymptotic behavior of dynamics systems in the Lur'e form, that can be decomposed into feedback interconnection of a linear part and a time-varying nonlinearity. The linear part obeys a singularly perturbed integro-differential Volterra equation of the convolutional type, whereas the nonlinearity is sector-bounded. For such a system we propose frequency-domain criteria of the stability and the “gradient-like” behavior, i.e. the attraction of any solution to one of equilibria points. Those criteria, based on the V.M. Popov's method of a priori integral indices, are uniform with respect to the small parameter.