Frequency-domain Uncertainty Research Articles

An Operator-Theoretic Approach to Robust Event-Triggered Control of Network Systems With Frequency-Domain Uncertainties

In this paper, we study the robustness of the event-triggered consensus algorithms against frequency- domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain L2-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicative uncertainties are considered, respectively. In both cases, quantitative relationships among the parameters of the controllers, the Laplacian matrix of the network topology, and the robustness against aperiodic event triggering and frequency-domain uncertainties are unveiled. Furthermore, the event-triggered dynamic average consensus (DAC) problem is also investigated, wherein the sampling errors are shown to be images of nonlinear finite-gain operators. The robust performance of the proposed DAC algorithm is analyzed, which indicates that the robustness and the performance are negative

Finite frequency fault estimation and fault-tolerant control for dynamics of high-speed train based on descriptor systems

In this paper, novel fault estimation and fault-tolerant control methods are proposed for dynamics of high-speed train based on descriptor systems with uncertainties in finite frequency domain. Dynamics of high-speed train is established based on multi-particle model considering that basic resistance is seen as the coefficient of state variables, and additive resistance and the operating noise are seen as multi-source disturbance. Concurrent actuator, sensor faults, and wind gust are considered simultaneously; wind gust is modeled as a disturbance generated by the exogenous system, and an uncertain descriptor system with actuator fault and the exogenous disturbance is established by seeing the sensor fault of high-speed train as the state variables. A robust disturbance-observer-based fault estimation method is proposed to decouple the non-linearity of the descriptor system, so that the combining estimation of the fault and wind gust is implemented. This observer has an unknown input structure, and its gain matrices are formulated as linear matrix inequalities. The observer not only guarantees the augmented state estimation error is asymptotic stable but also the actuator fault estimation and wind gust estimation errors are robust to the multi-source disturbance and the uncertainties. Based on the estimation results, the fault-tolerant controller associated with the state estimation, faults estimation, and wind gust estimation results is proposed to implement a stable close-loop fault-tolerant control for dynamics of high-speed train. Simulation examples are given to illustrate the effectiveness of this method.

A Unified Frequency-Domain Model for Automatic Generation Control Assessment Under Wind Power Uncertainty

High frequency uncertainty of wind power is highly stochastic and unpredictable. It can have considerable impacts on automatic generation control (AGC) for power systems. This paper proposes a novel frequency-domain model to evaluate AGC performances under wind power uncertainty in frequency domain. High frequency volatilities are accurately described by the frequency model of wide-sense stationary stochastic process. The newly introduced frequency tools enable the variations of power/energy units and network variables to be represented by the generalized transfer functions of the independent or joint stochastic processes of wind power fluctuations. The time-domain operation constraints and performance criteria of CPS1 and CPS2 are successfully transformed into frequency domain on basis of a theorem and its corollary related to the calculation of cross correlation functions proved in this paper. In general, this paper proposes a unified way of modeling volatility sources, system operations, and AGC performance assessments in frequency domain. Case studies on an isolated system and IEEE 118 interconnected system demonstrate the effectiveness and the conveniences of the proposed frequency domain model.

Noise Reduction Based on Soft Masks by Incorporating SNR Uncertainty in Frequency Domain

The binary mask approach has been studied recently to reduce the background noise and improve the speech intelligibility and quality in the noisy surroundings. This mask is usually applied at the time–frequency illustration of a noisy speech and discards portions of a speech below a signal-to-noise-ratio (SNR) threshold, whereas allowing others to pass over intact. The threshold, however, is normally very low, and considerable residual noise would exist. Moreover, the precise estimate of local instantaneous SNR in practical applications is a difficult task. By modeling the local instantaneous SNR as Fisher–Snedecor distributed random variable, the soft masks for noise reduction are derived by incorporating SNR uncertainty in the frequency domain. Instead of finding a different method to estimate the local instantaneous SNR, the probability of local instantaneous SNR is computed higher than the threshold. The results indicated that soft masks yielded significantly better speech quality in terms of speech distortion and residual noise.

H∞filter design for linear time-invariant systems with polytopic uncertainties in finite frequency domain

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

A new method for robust fixed-order H∞ controller design for uncertain time-delay systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Systems with uncertain dead-time and with multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. Furthermore, it is shown that the design method can also be extended to design of robust gain-scheduled dead-time compensators. The performance of the method is illustrated by simulation examples.

Path-connectedness of frequency-domain uncertainty sets in the graph topology⋆

AbstractPath-connectedness with respect to the topology induced by the gap metric underpins a recent robustness result for uncertain feedback interconnections of transfer functions in the Callier-Desoer algebra; i.e. possibly distributed-parameter with only finitely many unstable poles. In this paper, we establish path-connectedness of the following uncertainty sets of such transfer functions: diagonally structured sets with path-connected entries; arbitrarily large H∞-norm balls; and sufficiently small gap metric balls. Proof of the latter relies on the existence of a certain J-spectral factorisation, which is also established herein.

Fixed-order [formula omitted] controller design for nonparametric models by convex optimization

A new approach for robust fixed-order H ∞ controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by nonparametric models in the frequency domain are considered. It is shown that the H ∞ robust performance condition can be represented by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Systems with time-delay and with multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. The proposed method is compared with the standard H ∞ control problem by a simulation example on an unstable system.

Monotonic Convergence of Iterative Learning Control for Uncertain Systems Using a Time-Varying Filter

Iterative learning control (ILC) is a learning technique used to improve the performance of systems that execute the same task multiple times. Learning transient behavior has emerged as an important topic in the design and analysis of ILC systems. In practice, the learning control is often low-pass filtered with a ldquoQ-filterrdquo to prevent transient growth, at the cost of performance. In this note, we consider linear time-invariant, discrete-time, single-input single-output systems, and convert frequency-domain uncertainty models to a time-domain representation for analysis. We then develop robust monotonic convergence conditions, which depend directly on the choice of the Q-filter and are independent of the nominal plant dynamics. This general result is then applied to a class of linear time-varying Q-filters that is particularly suited for precision motion control.

Robust controller design by linear programming with application to a double-axis positioning system

A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A lower bound on the crossover frequency and a new linear stability margin which guarantees lower bounds for the classical robustness margins are defined. Two optimization problems are proposed and solved by linear programming. In the first one the robustness margin is maximized for a given lower bound on the crossover frequency, whereas in the second one the closed-loop performance in terms of the load disturbance rejection is optimized with constraints on the new stability margin. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach.

Quantification of frequency domain error bounds with guaranteed confidence level in prediction error identification

This paper considers prediction error identification of linearly parametrized models in the situation where the system is in the model set. For such situation it is easy to construct a confidence ellipsoid in parameter space in which the true parameter lies with an a priori fixed probability level, α . Surprisingly perhaps, the construction of a corresponding uncertainty set in the frequency domain, to which the true system belongs with probability α , is still an open problem. We show in this paper how to construct such frequency domain uncertainty set with a probability level of at least α .

Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.

Inner loop control of supersonic aircraft in the presence of aeroelastic modes

Longitudinal control system design is considered for a linearized dynamic model of a supersonic transport aircraft concept characterized by relaxed static stability and significant aeroelastic interactions. Two LQG-type controllers are designed using the frequency-domain additive uncertainty formulation to ensure robustness to unmodeled flexible modes. The first controller is based on a fourth-order model containing only the rigid-body modes, while the second controller is based on an eighth-order model that additionally includes the two most prominent flexible modes. The performance obtainable from the fourth-order controller is not adequate, while the eighth-order controller is found to provide better performance. Frequency domain and time-domain (Lyapunov) methods are subsequently used to assess the robustness of the eighth-order controller to parametric uncertainties in the design model.

Exploiting ellipsoidal parameter set estimates in H robust control design

The focus of this investigation is the exploitation of knowledge of an ellipsoidal bound on system parameters for the identification of modeling uncertainty information vital to the H robust control designer, a time to frequency domain uncertainty transformation. The characterizations of parametric uncertainty as coprime factor and additive perturbations to a nominal plant model are addressed in worst-case analyses. A Kharitonov type analysis provides sufficient conditions for the use of an additive plant perturbation uncertainty characterization. Original optimization results for the coprime factor perturbation enable the essential task of loopshaping to be conducted in the control design phase. A novel scheme is introduced to interpolate magnitude samples of the perturbation bounding function and is further developed into a technique for identification of reduced-order perturbation weightings, vital for practical control design. An example serves to illustrate the success of the developed techniques.

Integrated Identification and Robust Control

Abstract A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller-performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.

Mapping circular bounds on frequency responses to bounds on time responses

Although considerable work has been done in the area of translating time-domain uncertainty into frequency-domain uncertainty, little has been done on translating frequency-domain uncertainty into time-domain uncertainty. It has been shown here that when there are known bounds on the system frequency response, it is possible to calculate the analytically exact corresponding boundaries of the system time response for a periodic input. This is then extended to give less conservative results for step responses than those obtained using periodic inputs.

Frequency domain uncertainty and the graph topology

A new metric on linear, time-invariant systems is defined. This metric is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds. Unlike other known metrics which induce the graph topology, it has a clear frequency response interpretation. This allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>