Construction of Lur'e Type Lyapunov Function with Effect of Magnetic Flux Decay

In this paper a generalized stability criterion for a system with multi-argument non-linearities is derived. The new criterion is based on M. A. Pai's work, and is proved along B. D. O. Anderson's criterion. The new criterion enables us to construct a Lur'e type Lyapunov function in a systematic way. The new criterion is applied to a multi-machine power system with magnetic flux decays of generators. A new Lyapunov function is constructed in a well known manner established by J. L. Willems and other researchers. The new Lyapunov function is similar to the one which has already been obtained for a system without the magnetic flux decays, except for a few points which will affect a transient stability of the system

Applications of frequency domain stability criteria in the design of nonlinear feedback systems

The Popov criterion for absolute stability of nonlinear feedback systems is applied to several example problems. Model transformations such as pole shifting and zero shifting extend the class of systems to which the criterion applies. Extensions of the criterion having simple graphical interpretations yield stronger results for systems with constant monotonic slope-bounded nonlinearities. Additional extensions lacking simple graphical interpretations in the complex plane are also demonstrated by example. Stability throughout a region in parameter space is discussed, and the Kalman conjecture is verified for a new class of systems. The Popov criterion is also used to prove BIBO stability, process stability, and degree of stability. The conservatism of the criterion, i. e., the margin of actual performance beyond guaranteed performance, is discussed in the light of simulation results. An interactive computer program is developed to make the Popov criterion, along with two of its extensions, a convenient tool for the design of stable systems. The user has the options of completely automatic parameter adjustment or intervention at any stage of the procedure --Abstract, page ii

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds

State Space Application To System Design.

http://www.archive.org/details/statespaceapplic00moc

Single link flexible beam testbed project

This thesis describes the single link flexible beam testbed at the CLaMS laboratory in terms of its hardware, software, and linear model, and presents two controllers, each including a hub angle proportional-derivative (PD) feedback compensator and one augmented by a second static gain full state feedback loop, based upon a synthesized strictly positive real (SPR) output, that increases specific flexible mode pole damping ratios w.r.t the PD only case and hence reduces unwanted residual oscillation effects. Restricting full state feedback gains so as to produce a SPR open loop transfer function ensures that the associated compensator has an infinite gain margin and a phase margin of at least (-90, 90) degrees. Both experimental and simulation data are evaluated in order to compare some different observer performance when applied to the real testbed and to the linear model when uncompensated flexible modes are included

Relationships between digital signal processing and control and estimation theory

Bibliography: leaves 83-97.NASA Grant NGL-22-009-124 and NSF Grant GK-41647.Alan S. Willsky