Robustness analysis using singular value sensitivities

Introduction. 1.1 Linear Time-Invariant Systems. 1.2 Nonlinear Systems. 1.3 Equilibrium Points. 1.4 First-Order Autonomous Nonlinear Systems. 1.5 Second-Order Systems: Phase-Plane Analysis. 1.6 Phase-Plane Analysis of Linear Time-Invariant Systems. 1.7 Phase-Plane Analysis of Nonlinear Systems. 1.8 Higher-Order Systems. 1.9 Examples of Nonlinear Systems. 1.10 Exercises. Mathematical Preliminaries. 2.1 Sets. 2.2 Metric Spaces. 2.3 Vector Spaces. 2.4 Matrices. 2.5 Basic Topology. 2.6 Sequences. 2.7 Functions. 2.8 Differentiability. 2.9 Lipschitz Continuity. 2.10 Contraction Mapping. 2.11 Solution of Differential Equations. 2.12 Exercises. Lyapunov Stability I: Autonomous Systems. 3.1 Definitions. 3.2 Positive Definite Functions. 3.3 Stability Theorems. 3.4 Examples. 3.5 Asymptotic Stability in the Large. 3.6 Positive Definite Functions Revisited. 3.7 Construction of Lyapunov Functions. 3.8 The Invariance Principle. 3.9 Region of Attraction. 3.10 Analysis of Linear Time-Invariant Systems. 3.11 Instability. 3.12 Exercises. Lyapunov Stability II: Nonautonomous Systems. 4.1 Definitions. 4.2 Positive Definite Functions. 4.3 Stability Theorems. 4.4 Proof of the Stability Theorems. 4.5 Analysis of Linear Time-Varying Systems. 4.6 Perturbation Analysis. 4.7 Converse Theorems. 4.8 Discrete-Time Systems. 4.9 Discretization. 4.10 Stability of Discrete-Time Systems. 4.11 Exercises. Feedback Systems. 5.1 Basic Feedback Stabilization. 5.2 Integrator Backstepping. 5.3 Backstepping: More General Cases. 5.4 Examples. 5.5 Exercises. Input-Output Stability. 6.1 Function Spaces. 6.2 Input-Output Stability. 6.3 Linear Time-Invariant Systems. 6.4 Lp Gains for LTI Systems. 6.5 Closed Loop Input-Output Stability. 6.6 The Small Gain Theorem. 6.7 Loop Transformations. 6.8 The Circle Criterion. 6.9 Exercises. Input-to-State Stability. 7.1 Motivation. 7.2 Definitions. 7.3 Input-to-State Stability (ISS) Theorems. 7.4 Input-to-State Stability Revisited. 7.5 Cascade Connected Systems. 7.6 Exercises. Passivity. 8.1 Power and Energy: Passive Systems. 8.2 Definitions. 8.3 Interconnections of Passivity Systems. 8.4 Stability of Feedback Interconnections. 8.5 Passivity of Linear Time-Invariant Systems. 8.6 Strictly Positive Real Rational Functions. Exercises. Dissipativity. 9.1 Dissipative Systems. 9.2 Differentiable Storage Functions. 9.3 QSR Dissipativity. 9.4 Examples. 9.5 Available Storage. 9.6 Algebraic Condition for Dissipativity. 9.7 Stability of Dissipative Systems. 9.8 Feedback Interconnections. 9.9 Nonlinear L2 Gain. 9.10 Some Remarks about Control Design. 9.11 Nonlinear L2-Gain Control. 9.12 Exercises. Feedback Linearization. 10.1 Mathematical Tools. 10.2 Input-State Linearization. 10.3 Examples. 10.4 Conditions for Input-State Linearization. 10.5 Input-Output Linearization. 10.6 The Zero Dynamics. 10.7 Conditions for Input-Output Linearization. 10.8 Exercises. Nonlinear Observers. 11.1 Observers for Linear Time-Invariant Systems. 11.2 Nonlinear Observability. 11.3 Observers with Linear Error Dynamics. 11.4 Lipschitz Systems. 11.5 Nonlinear Separation Principle. Proofs. Bibliography. List of Figures. Index.

This paper presents a method for designing a dynamic compensator based on artificial neural networks (ANN). The ANN is trained to give the proper compensator parameters (X, Tz) so as to always assign certain eigenvalues to desired locations in the output feedback system. The eigenvalues of concern are those associated with the angle /spl delta/ and speed /spl omega/. These eigenvalues are to be assigned to the specified locations under variations in several system parameters [static nonlinear load parameters A/sub p/ and A/sub q/, transmission line reactance, x/sub e/, and generated real power, P/sub G/]. The exact and ANN's results of compensator's parameters are plotted. In addition speed response is provided for the compensated and uncompensated systems. Results show that the ANN can be used on line once the off line training is performed to determine the compensator data so as to maintain the desired response of the system under variations in system parameters.

Traditional digital distance relaying scheme is used to protect the transmission lines against various abnormal conditions/faults. In this paper, the authors have discussed the adverse effects of fault and system parameters, such as fault resistance, fault location, power transfer angle etc., on the performance of the protection scheme. Further, a modified protection algorithm is developed to mitigate the effect of weak sources/non-homogeneous network on the protection of shunt-compensated doubly-fed transmission line. It also improves the performance of the protection scheme during all the aforesaid variations in system and fault parameters. The modified protection scheme is based on the mathematical analysis of the sequence components of voltage, current and impedance of the network components. An equivalent impedance vector for each of the above-stated fault and system parameters is obtained and the relationship between these vectors is represented in vectorial form. With the help of this vector diagram and the mathematical analysis, the actual impedance of faulted part of the line is calculated. Since the algorithm is derived mathematically, it is simple to understand and user-friendly. A negligible error is observed while simulating the modified protection algorithm considering all the severe variations in fault and system parameters. MATLAB/Simulink software is used to verify the developed algorithm using 50 Hz frequency of the power system.

Sensitivity analysis, i.e., the analysis of the effect of small variations in system parameters on the output measures, can be studied by computing the derivatives of the output measures with respect to the parameter. An algorithm for parametric sensitivity analysis of Markov regenerative stochastic Petri nets (MRSPN) is presented. MRSPNs are a true generalization of stochastic Petri nets, in that they allow for transitions to have generally distributed firing times (under certain conditions). The expressions for the steady state probabilities of MRSPNs were developed by H. Choi et al. (1993). The authors extend the steady state analysis and present equations for sensitivity of the steady state probabilities with respect to an arbitrary system parameter. Sensitivity functions of the performance measures can accordingly be expressed in terms of the sensitivity functions of the steady state probabilities. The authors present an application of our algorithm by finding an optimizing parameter for a vacation queue. >

Fault identification in electrical power distribution system using combined discrete wavelet transform and fuzzy logic

A position controller, considering the effects of system dead-time and parameter variations, for induction motor servo drives is proposed in this paper. First a DSP-based computer controller indirect field-oriented induction motor servo drive is implemented and its dynamic model at the nominal case is estimated from measurements. Based on this model, an integral plus proportional (IP) controller is quantitatively designed to match the prescribed position tracking specifications. Then a dead-time compensator (DTC) and a simple robust controller (RC) are designed and augmented to reduce the effects of system dead-time on the stability and the performance degradation due to parameter variations. The prescribed drive tracking specifications can be preserved under parameter variations. Rather good load regulating response can also be obtained. Some experimental results are provided to demonstrate the effectiveness of the proposed controllers. >

Implementation of Adaptive Controllers Using Digital Signal Processor Chips

In this paper, we propose a framework for analyzing the effects of circuit parameter variations on high level system specifications in a hierarchical manner. The effects of parameter variations in one level of design hierarchy on those of the next are mapped through linear and piecewise linear sensitivity functions. The models allow computation of the statistical distributions of the circuit parameters and their correlations. This data is used to determine the critical circuit specifications that must be measured and those that may be eliminated from the testing process.

Application of series compensation in extra high voltage (EHV) transmission line makes the protection job difficult for engineers, due to alteration in system parameters and measurements. The problem amplifies with inclusion of electronically controlled compensation like thyristor controlled series compensation (TCSC) as it produce harmonics and rapid change in system parameters during fault associated with TCSC control. This paper presents a pattern recognition based fault type identification approach with support vector machine. The scheme uses only half cycle post fault data of three phase currents to accomplish the task. The change in current signal features during fault has been considered as discriminatory measure. The developed scheme in this paper is tested over a large set of fault data with variation in system and fault parameters. These fault cases have been generated with PSCAD/EMTDC on a 400 kV, 300 km transmission line model. The developed algorithm has proved better for implementation on TCSC compensated line with its improved accuracy and speed.

Cascaded linear systems based modeling techniques have been used in the past to predict important system parameters that have a direct impact on image quality. Such models are also useful in optimizing system parameters to improve image quality. In this work, detailed analysis of a solid-state fluoroscopic imaging system intended for high-resolution angiography is presented with the use of such a model. The imaging system analyzed through this model uses four 8 x 8 cm three-side buttable interlined charge-coupled devices (CCDs) specifically designed for high-resolution angiography and tiled in a seamless fashion to achieve a field of view (FOV) of 16 x 16 cm. Larger FOVs can be achieved by tiling more CCDs in a similar manner. The system employs a CsI:Tl scintillator coupled to the CCDs by straight (nontapering) fiberoptics and can potentially be operated in 78, 156, or 234 microm pixel pitch modes. The system parameters analyzed through this model include presampling modulation transfer function, noise power spectrum, and detective quantum efficiency (DQE). The results of the simulations performed indicate that DQE(0) in excess of 0.6 is achievable, with the imager operating at 156 microm pixel pitch, 30 frames/s, and employing a 450-microm-thick CsI:Tl scintillator, even at a low fluoroscopic exposure rate of 1 microR/frame. Further, at a nominal fluoroscopic exposure rate of 2.5 microR/frame there was no noticeable degradation of the DQE even at the 78 microm pixel pitch mode suggesting that it is feasible to perform high-resolution angiography hitherto unattainable in clinical practice.

Impact of forced and unforced system parameter variations on network stability and system economics of radial MTDC networks

In this paper, a hybrid system that combines the advantages in terms of robustness of the fractional control and the Sliding Mode Control (SMC) will be proposed. The proposed fractional order SMC is applied to a level control in a nonlinear coupled tank, as a case study. To investigate the capability of the method, a Sliding Mode Controller is alternatively designed. Primarily a sliding surface based on linear compensation networks PD or PID is designed. The work is followed by designation of a fractional form of these networks, PDμ or PIλDμ. Finally, the performance of the proposed technique is also investigated under disturbance and variation in parameters of system. The simulation results indicate the significance of the fractional order sliding mode controllers.

This paper investigates the problem of designing a single linear static feedback control to simultaneously stabilize a family of multi-input linear dynamical systems. The family of systems Σ(A(q), B(q)); q∈Q, represented by their state space matrices, may be uncountable thus allowing for the possibility of a continuum of variations in system parameters. Sufficient conditions related to the given state space matrices A(q) and B(q) are given under which there does exist a single robust controller stabilizing the family of systems. A recursive algorithm is also provided to compute a desired constant feedback gain matrix K.

Using current estimates of the celestial and atmospheric background emission, infrared source crowding, and detector performance, we estimate expected point source sensitivities for possible future infrared and sub-millimeter observatories on the ground, in the air, and in space. Our goal is to evaluate the effects of variations in basic observatory system parameters for typical operation over the wavelength range labmda ~3 - 1000 microns. For the first time in a general astronomical journal, we evaluate mission design goals for the wavelength range identified as the premier for this decade. Here we emphasize the effects of telescope temperature, aperture, and emissivity upon detectable point source signal level using diffraction-limited instrumentation, along with approximations to improvements in sensitivities using the new generation of array detectors. We find that [1] for broadband imaging, a larger aperture is more important than extremely low optical system temperature in detecting weak sources in two situations: (1) at short wavelengths, where a telescope need only be cooled to several tens of kelvins for the optical system emission to fall below that of the celestial background, and (2) at far-infrared and sub-millimeter wavelengths, where interstellar "cirrus" and extragalactic confusion eventually determine the limits to sensitivity, which, below some critical temperature, can only be improved upon by increasing the effective angular resolution. [2] for moderate-resolution spectroscopy (lambda/delta-lambda ~30 - 2000), the faintest signal level is always achieved when the telescope temperature is low enough so that the optical system contributes less than the celestial background. This temperature declines as the wavelength increases, so, for example, T <~ 10 K for lbmad >~ 100 microns. However, for sub-millimeter wavelengths, on or near the Rayleigh-Jeans side of the optical system emission, sensitivity increases less strongly with declining temperature. Consequently, large, warm (ground-based and airborne) sub-millimeter telescopes compete favorably with small cold ones in space and those windows accessible from within the Earth's atmosphere. [3] for high-resolution spectroscopy {lambda/delta-lambda >~ 105+), the thermal background from sky and optical system can be low enough that detector noise limits achievable sensitivity. If so, the telescope temperature need not be extremely low and light-gathering aperature is relatively more important. However, to take full advantage of reduced thermal background via high spectral resolution, detector performance may need to be near optimum. [4] conversely, in many circumstances, current and near-future detectors are over-specified in key aspects of operation compared to the high background of the far-infrared. Under such circumstances, detectors may be operated in non-optimum conditions without significant adverse effects upon overall system sensitivity.

This paper proposes a vehicle-to-grid (V2G) system interfaced with a microgrid that is effective at regulating frequency on a microgrid over a 24-h cycle. A microgrid is designed and divided into four components. The first component is a diesel generator, which is used to act as the base power generator. The second component consists of renewable energy (RE) power plants, which include solar photovoltaic (PV) and wind plants. The third component is a V2G system. The last component is the load connected to the microgrid. A microgrid is designed to be of sufficient size to represent a community of one thousand households during the day period of low consumption in the spring or fall seasons. A hundred electric vehicles (EVs) are modeled as base models to realize a 1:10 ratio for cars to households, which indicates a possible scenario in the near future. Detailed analysis of the active power, reactive power, voltage, frequency, and current is carried out. It is established that the proposed design of the V2G and microgrid effectively maintains system parameters such as frequency and voltage within permissible limits with an error of less than 1%. Further, transient deviations in these parameters are limited to within 5%. A microgrid with V2G devices regulates the system frequency by mitigating load demand through coordinated control of conventional generation, solar PV plant generation, wind plant generation, power exchange with the microgrid network, and electric vehicles. The proposed microgrid and V2G are efficient for energy management and mitigation of intermittency and variability of RE power with improved performance. Variations in system parameters have been investigated by changing the operating scenario, and it has been determined that the error is limited to less than 5%. The study is effectively realized in the MATLAB/Simulink environment.