Robustness Of Uncertain Systems Research Articles

Robust fractional-order proportional-derivative control of unified chaotic systems with parametric uncertainties

In this paper, a robust fractional-order proportional-derivative (PDμ) control is designed for controling in integer-order unified chaotic systems with parametric uncertainties. Equivalent plant is obtained by transforming the controlled dynamic system, and then the PDμ controller as an equivalent controller is applied to the equivalent plant. In the uncertain controlled unified chaotic systems, one equation is certain, and the other two equations are uncertain . The equivalent controller for the certain system is then designed based on a fractional-order proportional-derivative controller, in which three specifications for phase margin, gain crossover frequency, and robustness should be met. On the other hand, the robustness of uncertain systems is achieved by an improved Monje-Vinagre tuning method, however, the pre-specified frequency band should be replaced by the gain crossover frequency in order to reduce the complexity in determining the controllers for the uncertain systems. Specifications related to phase margin for the lower bound of the phase, gain crossover frequency for the upper bound of the gain, and robustness for the lower bound of the phase constraints are satisfied by the uncertain system. Parameters of the equivalent controller are determined based on a graphical method. Origins of the unstable equilibrium can be asymptotically stabilized by the proposed strategy for the integer-order unified chaotic systems with parametric uncertainties. Numerical simulation examples for Chen system, L system, and Lorenz system, are given to show the effectiveness of the proposed method.

THE NYQUIST ROBUST STABILITY MARGIN—A NEW METRIC FOR THE STABILITY OF UNCERTAIN SYSTEMS

The Nyquist robust stability margin kN is proposed as a new tool for analysing the robustness of uncertain systems. The analysis is done using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability. The concept of a critical line on the Nyquist plane is defined and used to calculate a critical perturbation radius which in turn is used to produce kN. The new approach gives alternatives to computing exact stability margins in some cases of highly directional uncertainty templates where other models are not applicable. © 1997 by John Wiley & Sons, Ltd.

Semi-Active Dynamic Absorber Using the Fuzzy Theory for a Beam Subjected to Moving Loads.

This paper presents a semi-active dynamic absorber for controlling the vibration of a beam subjected to moving loads. The eigenvalues of the beam system containing moving loads vary according to position and number of loads on the beam. The eigenvalues of the semi-active dynamic absorber are also adjusted to those of the beam system. The proposed semi-active dynamic absorber is of cantilever type and the absorber mass is moved to adjust the eigenvalues. It is difficult to estimate the characteristics of the beam system, which depend on the moving loads. The fuzzy control theory has robustness for uncertain systems. Therefore, the movement of the absorber mass is determined by fuzzy inference. In this paper, the adjustment of absorber mass to the position, which is determined by the displacement responses of the beam, is performed by the fuzzy controller. It is important to decide the control rules in the fuzzy control algorithm. The rule table is produced by the simulation of analytical models. The dynamic responses and spectra of displacements at the mid-point of the beam are shown in various cases. The effectiveness of the semi-active dynamic absorber is demonstrated experimentally.

A note on two methods related to stability robustness of polynomials in a sector (relative stability)

Two recent results on the stability robustness of uncertain systems (polynomials) are addressed. One gives a vertex test for left-sector (relative) stability, where the number of the required vertices is four for a real case and eight for a complex case. The other gives an elegant frequency-domain graphical (hodograph) approach for left-plane stability, where the plotting of only one (two for a complex case) hodograph plus simple boundary conditions is both necessary and sufficient to obtain the maximum coefficient perturbation bounds. It is shown that a similar graphical test exists for the left-sector stability case. >

Eigenvalue assignment robustness: The analysis for characteristic polynomials

Abstract This paper presents new techniques for analyzing eigenvalue assignment robustness of uncertain systems. The root locus approach is used to ensure that the roots of the characteristic polynomials with coefficient variations remain in some distinct but desired regions. No restrictions are imposed on the shapes of the specified regions. An algorithm is proposed to calculate the allowable coefficient bounds. The proposed methods are applicable to the continuous‐time case as well as to the discrete‐time case.

Robustness of uncertain systems in the absence of matching assumptions

Abstract We consider a class of uncertain dynamical systems containing uncertain elements. These may be due to model-parameter uncertainty, input disturbance and measurement noise. We require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact. This paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions (which most previous results have needed). The result is applicable to non-linear systems. A specialization to linear systems is then given and a comparison is made with previous work.