Eigenvalue Sensitivity Analysis Research Articles

Sensorless Speed Control of Induction Motor Driven Electric Vehicle Using Model Reference Adaptive Controller

Abstract This paper proposes a new sensorless speed control technique for induction motor (IM)driven electric vehicle (EV) using a model reference adaptive controller (MRAC) with a basic energy optimization technique known as golden section method. The proposed MRAC for the vector controlled IM drive utilizes instantaneous and steady state values of a fictitious resistance (R) in the reference and adaptive models respectively. The proposed scheme is immune to the variation in stator resistance (Rs). Moreover, the unique formation of the MRAC with the instantaneous and steady-state reactive power completely eliminates the requirement of any flux estimation in the process of speed estimation. Thus, the method is insensitive to integrator-related problems like drift and saturation enabling the estimation at or around zero speed quite accurately. The proposed drive's performance with the R-MRAC is validated for various speed ranges and patterns in Matlab/Simulink. Sensitivity of various motor parameters and stability studies are carried out using eigenvalues loci plots by first order eigenvalue sensitivity analysis.

Design sensitivity analysis of structures with viscoelastic dampers

In paper the design sensitivity analysis of dynamic characteristics of structures with viscoelastic (VE) dampers is considered. The dampers are modeled using the classical rheological model and the rheological model with fractional derivatives. The design sensitivity is analyzed by using direct differentiation method and adjoint variables method. The formulae enabling the calculation of sensitivity of the first and the second order with respect to chosen design parameters have been derived. Sensitivity analysis of eigenvalues, eigenvectors and dynamic characteristics such as natural frequencies and non-dimensional damping ratios are presented. The correctness of the presented formulae is illustrated in examples.

Analytical sensitivity analysis of eigenvalues and lightweight design of composite laminated beams

The paper describes an optimisation technique for the lightweight design of composite laminated beams with a big ratio of span to thickness. The optimisation model for the lightweight design is to find the fibre volume fractions to minimise the mass of the composite laminated beams under the eigenvalue (or frequency) constraints. The analytical sensitivity of the eigenvalues, with respect to the fibre volume fractions, is formulated using the Euler–Bernoulli beam theory. The analytical formulae for sensitivity analysis are suitable for the different boundary conditions (pinned–pinned, fixed–fixed, fixed–free and fixed–pinned). The eigenvalues are linearised using Taylor’s series so that optimisation model is converted to a linear programming problem. The iterative computational procedure is proposed to solve the optimisation model and eliminate the Taylor’s series approximation since the current design point maybe not near the optimum design. Finally, the lightweight designs of the composite laminated beams with different boundary conditions are performed. The merits of the proposed method and lightweight designs obtained by proposed method are discussed.

Sensitivity analysis of semi-simple eigenvalues of regular quadratic eigenvalue problems

This paper discusses the sensitivity analysis of semisimple eigenvalues and associated eigen-matrix triples of regular quadratic eigenvalue problems analytically dependent on several parameters. The directional derivatives of semisimple eigenvalues are obtained. The average of semisimple eigenvalues and corresponding eigen-matrix triple are proved to be analytic, and their partial derivatives are given. On these grounds, the sensitivities of the semisimple eigenvalues and corresponding eigenvector matrices are defined.

Stability, Receptivity, and Sensitivity Analyses of Buffeting Transonic Flow over a Profile

A transonic flow over the OAT15A supercritical profile is considered. The interaction between the shock wave and the turbulent boundary layer is investigated through numerical simulation and global stability analysis for a wide range of angles of attack. Numerical simulations are in good agreement with previous studies and manage to reproduce the high-amplitude self-sustained shock oscillations known as shock buffet. In agreement with previous results, it is found that the buffet phenomenon is driven by an unstable global mode of the linearized Navier–Stokes equations. Analysis of the adjoint global mode reveals that the flow is most receptive to harmonic forcings on the suction side of the profile, within the boundary layer upstream of the shock foot, in the recirculation bubble downstream of the shock foot, and on the right characteristic that impinges the shock foot. An eigenvalue sensitivity analysis shows that a steady streamwise force applied either in the boundary layer or in the recirculation region, a steady cooling of the boundary layer, or a steady source of eddy viscosity (a mechanical vortex generator for example) all lead to stabilization of the buffet mode. Finally, pseudoresonance phenomena have been analyzed by performing a singular-value decomposition of the global resolvent, which revealed that, besides the low-frequency shock unsteadiness, the flow also undergoes medium-frequency unsteadiness, linked to Kelvin–Helmholtz-type instability. Such results are reminiscent of the medium-frequency perturbations observed in more traditional shock wave/boundary-layer interactions.

Stability analysis of rotary power flow controller

SummaryThis paper deals with the stability analysis of a rotary power flow controller (RPFC). RPFC is a newly presented flexible alternating current transmission system device based on the rotary phase shifting transformer (RPST) configuration. This device comprises a shunt and a series transformer and two RPSTs. In this paper, a linear model is developed for RPFC in the dq‐reference frame. The model includes two RPSTs, shunt, and series transformers. Stability of the device is studied using eigenvalues of the state matrix. Effects of system parameters such as resistance, reactance, and phase difference of the shunt and series transformers and RPSTs on stability are investigated using eigenvalue sensitivity analysis. Simulation results using PSCAD/EMTDC software and analytical results based on eigenvalue analysis are presented to evaluate effects of different parameters on stability of RPFC. Copyright © 2014 John Wiley & Sons, Ltd.

Linear stability of piezoelectric-controlled discrete mechanical systems under nonconservative positional forces

Discrete models of piezoelectric controlled mechanical systems, subjected to follower forces, are derived in this paper. A targeted strategy of control is first discussed, leading to detect three novel linear controllers resembling, in the order, the Tuned Mass Damper with large and small mass, respectively, and Energy Sink, used in the literature for controlling linear and nonlinear oscillations. Here, however, and differently from those systems, coupling between the controller and the main structure is of gyroscopic type, whose magnitude is governed by an electro-mechanical parameter. Based on an eigenvalue sensitivity analysis, carried out via suitably selected perturbation methods, the effectiveness of the three controllers is investigated. As an application, the two-degree-of-freedom Ziegler column, undergoing Hopf bifurcation triggered by a follower force, equipped with piezoelectric controllers, is studied, and the different strategies proposed numerically compared.

Can a semi-simple eigenvalue admit fractional sensitivities?

We perform high-order sensitivity analysis of eigenvalues and eigenvectors of linear systems depending on parameters. Attention is focused on double not-semi-simple and semi-simple eigenvalues, undergoing perturbations, either of regular or singular type. The use of integer (Taylor) or fractional (Puiseux) series expansions is discussed, and the analysis carried out both on the characteristic polynomial and on the eigenvalue problem. It is shown that semi-simple eigenvalues can admit fractional sensitivities when the perturbations are singular, conversely to the not-semi-simple case. However, such occurrence only manifests itself when a second-order perturbation analysis is carried out. As a main result, it is found that such over-degenerate case spontaneously emerges in bifurcation analysis, when one looks for the boundaries of the stability domain of circulatory mechanical systems possessing symmetries. A four degree-of-freedom system under a follower force is studied as an illustrative example.

Numerical Study of a Seivr Epidemic Model among Infants with Vaccination and Temporary Immune Protection

In this work, the numerical study of a deterministic mathematical model of an SEIVR (Susceptible-Exposed- Infected-Vaccinated-Recovered) epidemic model among infants was carried out. This model incorporates a temporary immune recovery class which involves subsequent dose vaccination for the infants. Hypothetical values were chosen for the parameters to test the validity of the mathematical model. The parameter with the greatest impact on the model was computed using the eigenvalue elasticity and sensitivity analyses and it was found that the parameter of the rate at which the vaccine wanes in the infants (ω) has the greatest impact on the mathematical model.

Open-loop control of noise amplification in a separated boundary layer flow

Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is the largest in the shear layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on these results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Linear calculations on controlled base flows confirm that optimal gains can be drastically reduced at all frequencies. Nonlinear direct numerical simulations also show that this control allows the flow to withstand a higher level of stochastic noise without becoming nonlinearly unstable, thereby postponing bypass transition. In the supercritical regime, sensitivity analysis of eigenvalues supports the choice of this control design. Full restabilization of the flow is obtained, as evidenced by direct numerical simulations and linear stability analysis.

A new unconditionally stable condition based on singular perturbation analysis

Decentralised configuration with integral control action is the most commonly used control strategy in engineering practice. For decentralised integral control, a desired design target is to achieve closed-loop unconditional stability. Campo and Morari presented steady-state conditions, which can be applied to analyse unconditional stability for most multivariable processes. However, they also showed some processes for which the unconditional stability cannot be determined by only investigating the steady-state gain matrices of the processes. This paper presented an easy to use criterion to determine unconditional stability by using singular perturbation analysis and eigen-value sensitivity analysis. Based on the proposed criterion, the unconditional stability of all the examples presented by Campo and Morari can be easily determined. In the meantime, we proved a conjecture proposed by Campo and Morari (a necessary and sufficient condition for Integral Controllability) for up to all Three-Input and Three-Output systems. For higher dimensional systems, we proposed a new conjecture to simplify the verification of Campo and Morari’s conjecture.

Finite Element Model Updating of a Prestressed Concrete Continuous Bridge Based on Dynamic Monitoring

The finite element model modified technique based on optimization principle is benefit for the model updating of the large bridge structures. By the ambient vibration test information provided by health monitoring system of huanghe bridge II in baotou , this article adopted corrected parameter based on structural eigenvalue sensitivity analysis to update the bridge dynamic model.The fundamental vibrational frequency of updated finite element model is more closer to the measured result under ambient excitation, which indicates that the optimization algorithm provided by large-scale general software can carry out the model updating effectively.

Proportional-Integral Control of First-Order Time-Delay Systems via Eigenvalue Assignment

A new design method is presented for proportional-integral (PI) controllers of first-order plants in the presence of time delays. In general, time delays can limit and degrade the achievable performance of the controlled system, and even induce instability. Thus, the PI gains should be selected carefully considering such effects of time delays. Unlike existing methods, the design method presented in this paper is based on solutions to delay differential equations, which are derived in terms of the Lambert W function. PI controllers for first-order plants with time delays are designed by obtaining the rightmost (i.e., dominant) eigenvalues in the infinite eigenspectrum of time-delay systems and assigning them to desired positions in the complex plane. The process is possible due to a novel property of the Lambert W function. The controllers designed using the presented method can improve the system performance and successfully stabilize an unstable plant. Also, sensitivity analysis of the rightmost eigenvalues is conducted, and the results compare favorably with those of a prediction-based method for eigenvalue assignment. Extension to design of PI-differential controllers is discussed with examples.

Performance-oriented communication topology design for distributed control of interconnected systems

Communication networks provide a larger flexibility for the control design of interconnected systems by allowing the information exchange between the local controllers of the subsystems which can be used to improve the overall system performance. However, the interconnected systems may become unstable due to permanent communication link failures. This article presents a novel two-layer control architecture that allows to jointly improve the system performance which is the decay rate and guarantee the stability of the interconnected system under permanent communication link failures. As a novelty, the design of communication topology between the local controllers is also taken into account. On the other hand, it is still not well understood how significant the role of each possible communication link is in improving the system performance. Another novelty of this article is thus to propose a method based on eigenvalue sensitivity analysis in order to characterize the influence of each possible communication link in improving the performance of the overall system. In addition, for a special class of systems and physical interconnection topology, explicit solutions on communication topology design are derived for the first time. The solutions provide some insights into how the heterogeneity of the subsystem local dynamics, the strength of interconnection and the size of the network affect the optimal communication topology.

Modal Sensitivity Analysis for Parallel Harmonic Resonance in Power System

Parallel harmonic resonance is closely related to the singularity of a node admittance matrix. It was found that the smallest eigenvalue of the matrix defines the mode of parallel harmonic resonance. This paper applies eigenvalue theory and modal sensitivity analysis method to determine which network components contribute significantly to a harmonic resonance phenomenon. Case study results further confirm the theoretical correctness and effectiveness. Thus, this practical method not only provides significant measures for harmonic resonance manage, but also support theoretical and experimental bases for the component parameter design.

Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues

This paper considers the computation of eigensolution sensitivity of viscously damped eigensystems with distinct and repeated eigenvalues. To simplify the computation, a combined normalization, which combines two traditional normalizations, is presented. Based on the combined normalization, a method for sensitivity analysis of eigenvalues and eigenvectors is studied. In the case of distinct eigenvalues, the proposed method can determine the eigenvector derivatives directly and is robust since the components of coefficient matrices are all of the same order of magnitude. The computational cost of the second-order sensitivities of eigenvectors can be reduced remarkably since the matrix decomposition of the coefficient matrix is available from the computation process of the first-order eigensensitivities. In the case of repeated eigenvalues, an algorithm is presented for computing the eigensolution sensitivities. The algorithm maintains N-space without using state-space equations such that the computational cost is reduced. The method is accurate, compact, numerically stable and easy to be implemented. Finally, three numerical examples have demonstrated the validity of the proposed method. The capacity of predicting the changes of eigensolutions with respect to the changes of design parameters in terms of the first- and second-order eigensensitivities is studied with application to the analysis of a two-stage floating raft isolation system.

Stability analysis of power system with doubly fed induction generator-based wind farm connected through series flexible AC transmission SYSTEM device compensated line

Wind farm may be remotely located due to the availability of wind. Therefore, series compensation may be required to evacuate large wind power to a distant power system. The impact of series compensation on the stability of power system with wind farm is of concern for transmission and system operation. This paper investigates the stability issues of power system with remote wind farm. The studied power system network is connected to a remote wind farm through a series Flexible AC Transmission System device, Static Synchronous Series Compensator, compensated transmission line. The small signal stability and transient stability issues are studied for uncompensated and compensated system. The results show that damping ratio is increased for most of the oscillatory modes showing increase in small signal stability with series compensation. The eigenvalue sensitivity analysis is performed with the degree of compensation and voltage gain as sensitivity parameters. Transient analysis is performed for a three-phase fault, and the results show improvement in transient stability of compensated power system.

DC Motor Control Using the Lambert W Function Approach

A new design method for proportional-plus integral (PI) and proportional-plus velocity (PV) control for DC motors to regulate angular velocity and position considering time-delays, is presented. Time-delays inherent in plants can arise from signal processing and actuation and can lead to undesired system performance including instability. Thus, time-delays should be considered in designing controllers. In this paper, a method based on the Lambert W function is used to address such problems caused by time-delays. The method enables one to find the rightmost (i.e., dominant) characteristic roots in the infinite eigenspectrum. Then, PI and PV control gains are obtained by assigning the rightmost eigenvalues to desired positions in the complex plane. The assignment can be achieved thanks to a novel property of the Lambert W function. System performance can be improved as well as successfully stabilized. Effectiveness of the presented method is verified through simulations and experiments. Also, sensitivity analysis of the rightmost eigenvalues with respect to delay mismatches is conducted to compare the proposed approach to a prediction-based method.

Modal Sensitivity Analysis for Series Harmonic Resonance in Power System

Harmonic resonance is composed of series and parallel harmonic resonance. It is closely related to the singularity of a network loop impedance matrix or node admittance matrix. It was found that such resonance phenomenon is associated with the singularity of the network matrix. The smallest eigenvalue of the matrix defines the mode of series harmonic resonance. This paper applies this eigenvalue theory and modal sensitivity analysis method to determine which network components contribute significantly to a series harmonic resonance phenomenon. Case study results further confirm the theoretical correctness and effectiveness. Thus, this practical method not only provides significant measures for series harmonic resonance manage, but also support theoretical and experimental bases for the component parameter design.

Parameter tuning of power system stabilizer using eigenvalue sensitivity

Abstract This paper proposes a method for PSS parameter tuning. The proposed method is based on the system identification using a Kalman filter. To eliminate the influence of inaccuracies of the mathematical model due to incomplete data of the system parameters, this paper proposes a procedure for identifying system parameters based on a Kalman filter. The identified system is the basis for determining the eigenvalue sensitivity function. PSS tuning is carried out based on the eigenvalue sensitivity analysis of changes of PSS parameters. In order to obtain the eigenvalue sensitivity function on the PSS parameter in a wider range of parameter values, it has been proposed to determine eigenvalues on the basis of the Bairstow method for solving polynomial equations. The entire procedure can be applied on-line, so the PSS structure and settings can be adaptive. Experimental tests carried out on a synchronous generator connected to an AC system demonstrate the effectiveness of the proposed method. Performance of the PSS tuned by using the proposed method was compared with the performance of the PSS tuned by using eigenvalue sensitivity.