Computation Of Stability Regions Research Articles

Computation of stability regions for load frequency control systems including incommensurate time delays

This article studies the impact of incommensurate communication time delays on stability regions defined in proportional-integral (PI) controller parameter space for a two-area load frequency control (LFC) system. Distributed power generations and large power plants increase the complexity and control issues of interconnected power systems. In interconnected power systems, LFC systems need to have complex communication networks to exchange data between control center and geographically dispersed generations. The receiving/transmitting of remote measuring data through communication infrastructures causes inevitable time delays, which adversely affect controller performance and stability of the LFC system. Time delays introducing feedback control loops of a multiarea LFC system could exhibit incommensurate characteristics. In this study, a simple graphical method based on extracting a stability boundary locus is implemented to get PI controller parameters responsible for stabilizing the LFC system having incommensurate delay values. The boundaries of the stability regions in the PI controller parameter space are confirmed by time-domain simulations and a numerical algorithm known as the quasipolynomial mapping-based root finder algorithm. Results illustrate that incommensurate delays have remarkable effects on the stability region.

Computation of stability regions for the cylindrical ion trap with no octupole electric field as compared to the corresponding results of the Paul trap.

The cylindrical ion trap is analyzed so that the octupole component of the electric field inside the trap is set to zero. As a consequence, the diameter to height ratio is computed to be 1.20 for which the quadrupole component of the cylindrical ion trap is dominant. Afterwards, it is concluded that the electric potential inside the trap as well as the corresponding stability regions are very similar to those obtained for an ideal Paul trap with pure quadrupole electric field. Furthermore, we drew a conclusion that the stability diagrams of the cylindrical ion trap without octupole term and the stability diagrams of the Paul trap have 5.6%, 3.7%, and 2.9% discrepancy for the first, second, and third stability diagrams, respectively. It should be noted that, expansion of the electric potential inside the cylindrical ion trap in terms of the multipole electric field components and making the advantages of the octupole term elimination has not been reported in the literature previously.

Optimum Radius Size between Cylindrical Ion Trap and Quadrupole Ion Trap

Quadrupole ion trap mass analyzer with a simplified geometry, namely, the cylindrical ion trap (CIT), has been shown to be well-suited using in miniature mass spectrometry and even in mass spectrometer arrays. Computation of stability regions is of particular importance in designing and assembling an ion trap. However, solving CIT equations are rather more dif- ficult and complex than QIT equations, so, analytical and matrix methods have been widely used to calculate the stability regions. In this article we present the results of numerical simulations of the physical properties and the fractional mass resolu- tions of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) at the optimum radius size for both ion traps. Because of similarity the both results, having determining the optimum radius, we can make much easier to design CIT. Also, the simulated results has been performed a high precision in the resolution of trapped ions at the optimum radius size.

Robust prediction of chatter stability in micro milling comparing edge theorem and LMI

Machine tool chatter is detrimental to productivity and the overall quality of manufactured parts. Analytical stability models are used to predict the occurrence of chatter for a given set of machining conditions and improve productivity. Conventional chatter models typically assume that parameters are constant, which can lead to an unsuitable stability lobe prediction. System dynamics, including natural frequency and damping ratio, and cutting coefficients are the main parameters that can change during actual machining operations. Parameter variations can be taken into consideration using different robust control theory approaches. A frequency domain approach using Edge theorem, can analytically account for time invariant parameter uncertainty directly in the characteristic equation. Combined with the Zero Exclusion method, computation of stability regions can be checked graphically. Chatter stability can also be detected using a time domain approach involving Lyapunov stability theory subjected to linear matrix inequality (LMI) conditions. This paper presents two novel robust chatter stability models for predicting stability regions while accounting for three uncertain parameters. Robust stability lobes can be predicted and facilitate optimal machining parameter selection to achieve higher productivity.

Guaranteed domains of attraction for multivariable Luré systems via open Lyapunov surfaces

SUMMARY In this paper we provide guaranteed stability regions for multivariable Lure« -type systems. Specifically, using the Lure« —Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti-windup controllers for systems subject to input saturation. ( 1997 by John Wiley & Sons, Ltd.

A new frequency domain approach to certain transient stability problems in power systems analysis

The transient behaviour is considered of a synchronous generator with linear or nonlinear dumping torque, connected to an infinite bus and equipped with a fast-speed governor. Frequency criteria are presented for the non-exiatence of limit cycles in state space, and a procedure is developed for constructing new classes of stability regions, based on this property. The analysis results in sets of frequency conditions, which guarantee transient stability for the entire initial load angle range, between the unstable equilibria neighbouring the system's operating point, in the case where all other state variables are initially in equilibrium. This property guarantees asymtotically stable transients for arbitrary step changes in mechanical power input, within static stability limits, and can be checked without requiring the explicit computation of stability regions.

The computation of stability regions for systems with many singular points

A method is presented for the generation of Liapunov functions for the analysis of non-linear systems with many singular points. Criteria are given for non-oscillatory behaviour, Stability regions for all stable equilibria can be found, using a single Liapunov function of the proposed type.