1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

CVXGEN is a software tool that takes a high level description of a convex optimization problem family, and automatically generates custom C code that compiles into a reliable, high speed solver for the problem family. The current implementation targets problem families that can be transformed, using disciplined convex programming techniques, to convex quadratic programs of modest size. CVXGEN generates simple, flat, library-free code suitable for embedding in real-time applications. The generated code is almost branch free, and so has highly predictable run-time behavior. The combination of regularization (both static and dynamic) and iterative refinement in the search direction computation yields reliable performance, even with poor quality data. In this paper we describe how CVXGEN is implemented, and give some results on the speed and reliability of the automatically generated solvers.

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CVXGEN: a code generator for embedded convex optimization

This paper is a pragmatic tutorial review of the cepstrum literature focusing on data processing. The power, complex, and phase cepstra are shown to be easily related to one another. Problems associated with phase unwrapping, linear phase components, spectrum notching, aliasing, oversampling, and extending the data sequence with zeros are discussed. The advantages and disadvantages of windowing the sampled data sequence, the log spectrum, and the complex cepstrum are presented. The influence of noise upon the data processing procedures is discussed throughout the paper, but is not thoroughly analyzed. The effects of various forms of liftering the cepstrum are described. The results obtained by applying whitening and trend removal techniques to the spectrum prior to the calculation of the cepstrum are discussed. We have attempted to synthesize the results, procedures, and information peculiar to the many fields that are finding cepstrum analysis useful. In particular we discuss the interpretation and processing of data in such areas as speech, seismology, and hydroacoustics. But we must caution the reader that the paper is heavily influenced by our own experiences; specific procedures that have been found useful in one field should not be considered as totally general to other fields. It is hoped that this review will be of value to those familiar with the field and reduce the time required for those wishing to become so.

The cepstrum: A guide to processing

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Analysis of Dynamic Behaviour of Electric Power Systems with Large Amount of Wind Power

A unified PID tuning method for load frequency control (LFC) of power systems is discussed in this paper. The tuning method is based on the two-degree-of-freedom (TDF) internal model control (IMC) design method and a PID approximation procedure. The time-domain performance and robustness of the resulting PID controller is related to two tuning parameters, and robust tuning of the two parameters is discussed. The method is applicable to power systems with non-reheated, reheated, and hydro turbines. Simulation results show that it can indeed improve the damping of the power systems. It is shown that the method can also be used in decentralized PID tuning for multi-area power systems.

Unified Tuning of PID Load Frequency Controller for Power Systems via IMC

The load-frequency control problem for interconnected systems is considered from the viewpoint of optimal stochastic system theory. A control algorithm is developed which provides improved power system performance in both large and small signal modes of operation. An especially attractive feature of the proposed control scheme is that it requires as inputs only the variables currently used, i. e., frequency deviations and scheduled interchange deviations. The classical two-area power system is used as a base system for comparative studies relating the response of an interconnected power system using the new control algorithm to the response obtained using conventional control strategy.

An Optimal Linear Systems Approach to Load-Frequency Control

The power invariant, nonlinear differential equations, that describe the behavior of a two-phase equivalent of a balanced three-phase induction motor, are linearized about an arbitrary nominal point. Under the assumption that terminal voltage and system frequency can be approximated by a straight line segment over any interval of time, solutions of these small perturbation equations are used to give expressions for active and reactive power delivered tb the motor during transient conditions. These newly developed expressions for power, which turn out to be implicit functions of voltage and frequency, and explicit functions of time and the rates of change of voltage and frequency, are proposed as a load model represeptation of an induction motor for use in transient stability studies. An intuitively appealing, corrective technique, which reduces the error introduced by the use of a linearized model, is presented. Eigenvalues of the linearized system of equations for a group of typical induction motors are given. For a small low voltage motor, a sensitivity study of the dominant eigenvalue to changes in nominal point quantities and parameters is made. Values of active and reactive power calculated by a numericzal solution of the motor nonlinear differential equations are compared with those values of power predicted by the model for certain specific rates of change of voltage and frequency.

Transient Load Model of an Induction Motor

Computational algorithms are given for the design of optimal, finite-length, convolutional filters with finite-length input sequences. Design techniques are developed for minimum-weighted-mean-square-error filters (MWMSE), for minimum-weighted-absolute-error filters (MWAE), and for filters which minimize the maximum output error (minimax). It is shown that the coefficients of the MWAE and minimax filters can be obtained by using standard linear programming methods. Next, the problem of developing a filter whose function is to "sharpen" a particular input waveform is considered. The filter input sequence is assumed to be derived from a Ricker wavelet of the velocity type and the desired output is the Dirac delta function. Convolutional filters are developed for this problem using each of the three performance criteria described above. The output sequences of each of the three optimal filters are discussed. It is shown that the minimax filter gives significantly better discrimination than can be obtained from either the MWAE or MWMSE filters.

The Design of Optimal Convolutional Filters via Linear Programming

This short paper considers the problem of designing a compensating control scheme for an observable linear multivariable plant using partial state feedback so that the impulse response matrix of the resulting system exactly corresponds to the impulse response matrix of a prespecified linear model. A procedure is given for the synthesis of the compensator that does not require a separate realization for the plant observer. A sufficient condition is given for the internal stability of the model following system.

Model following using partial state feedback

The authors review some of the properties of the pseudoinverse and oblique pseudoinverse of a linear transformation T from one finite-dimensional inner-product space into another, and then use these properties and a theorem of Milne (1968), which states that the oblique pseudoinverse can be expressed in terms of a weak generalized inverse and two projection operators, in order to compute a mean-axis influence coefficient matrix for the dynamic analysis of an elastic body. Some eigenvalue invariance properties of the mean-axis structural dynamics equations are demonstrated, and on the simple example of a uniform beam, it is shown that the finite frequencies and mode shapes of the mean axis structural system are identical to the nonzero frequencies and mode shapes of the free structure.

Ralph K. Cavin

Papers

An Optimal Linear Systems Approach to Load-Frequency Control

Transient Load Model of an Induction Motor

The Design of Optimal Convolutional Filters via Linear Programming

Model following using partial state feedback

Eigenvalue properties of structural mean-axis systems