Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open-loop transfer function. However, these contours have been built using non band-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers

Application of multivariable design techniques to robust control of a large-scale systems

Includes bibliographical references (leaf 12).Research supported by the National Science Foundation. Research supported by the U.S. Army Research Office. DAAL01-86-K-0171by Kelly D. Hammett, John R. Dowdle, Michael Athans and Karl D. Flueckiger

Robustness results in LQG based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, the LQ and LQG robustness results are discussed

Robustness of the Blandford-Znajek mechanism

The Blandford-Znajek mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In such mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In the current work we examine the behaviour of the BZ mechanism with respect to different boundary conditions, revealing the mechanism robustness upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.Comment: 7 pages, accepted in CQ

Development of a sensitivity analysis technique for multiloop flight control systems

This report presents the development and application of a sensitivity analysis technique for multiloop flight control systems. This analysis yields very useful information on the sensitivity of the relative-stability criteria of the control system, with variations or uncertainties in the system and controller elements. The sensitivity analysis technique developed is based on the computation of the singular values and singular-value gradients of a feedback-control system. The method is applicable to single-input/single-output as well as multiloop continuous-control systems. Application to sampled-data systems is also explored. The sensitivity analysis technique was applied to a continuous yaw/roll damper stability augmentation system of a typical business jet, and the results show that the analysis is very useful in determining the system elements which have the largest effect on the relative stability of the closed-loop system. As a secondary product of the research reported here, the relative stability criteria based on the concept of singular values were explored

Multifunction tests of a frequency domain based flutter suppression system

The process is described of analysis, design, digital implementation, and subsonic testing of an active control flutter suppression system for a full span, free-to-roll wind tunnel model of an advanced fighter concept. The design technique uses a frequency domain representation of the plant and used optimization techniques to generate a robust multi input/multi output controller. During testing in a fixed-in-roll configuration, simultaneous suppression of both symmetric and antisymmetric flutter was successfully shown. For a free-to-roll configuration, symmetric flutter was suppressed to the limit of the tunnel test envelope. During aggressive rolling maneuvers above the open-loop flutter boundary, simultaneous flutter suppression and maneuver load control were demonstrated. Finally, the flutter damping controller was reoptimized overnight during the test using combined experimental and analytical frequency domain data, resulting in improved stability robustness

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field $E$, which produces tidal forces, and the frame-drag field $B$, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of $E$) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of $E$ and $B$ on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities ($E$, $B$, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. [Abstract is abbreviated.]Comment: 19 pages, 7 figures, v2: Changed to reflect published version (changes made to color scales in Figs 5, 6, and 7 for consistent conventions). v3: Fixed Ref

Multiobjective control of a four-link flexible manipulator: A robust H∞ approach

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper presents an approach to robust H∞ control of a real multilink flexible manipulator via regional pole assignment. We first show that the manipulator system can be approximated by a linear continuous uncertain model with exogenous disturbance input. The uncertainty occurring in an operating space is assumed to be norm-bounded and enter into both the system and control matrices. Then, a multiobjective simultaneous realization problem is studied. The purpose of this problem is to design a state feedback controller such that, for all admissible parameter uncertainties, the closed-loop system simultaneously satisfies both the prespecified H∞ norm constraint on the transfer function from the disturbance input to the system output and the prespecified circular pole constraint on the closed-loop system matrix. An algebraic parameterized approach is developed to characterize the existence conditions as well as the analytical expression of the desired controllers. Third, by comparing with the traditional linear quadratic regulator control method in the sense of robustness and tracking precision, we provide both the simulation and experimental results to demonstrate the effectiveness and advantages of the proposed approach

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

Eigenvalue sensitivity minimisation for robust pole placement by the receptance method

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally