Nonlinear Parameter Variations Research Articles

Design of Sampled-Data High-Gain PD Control Systems

Proportional and derivative (PD)control is a simple and effective control technique for a wide class of dynamic systems. System uncertainties due to nonlinearity distortions, parameter variations, or external disturbances can be suppressed by increasing the feedback gains. In practice, however, there are limits to the PD gains without causing instability. The instability is usually attributed to measurement noise or high-frequency unmodeled dynamics excited by the high feedback gains. In this paper we show that the sample-and-hold effect in a digital control system may cause instability in an otherwise stable PD control system. With proper approximations, explicit and practical stability criteria are derived relating the magnitudes of the feedback gains to the sampling period and other system parameters. Basides the sampling period, the stability of the closed-loop system is also significantly affected by the computation time, which is often neglected in theoretical analyses or numerical simulations. Case studies are presented to illustrate the use of the stability criteria in the design of high-gain PD control systems.

Active panel flutter suppression using self-sensing piezoactuators

Nonlinear flutter of flat and slightly curved panels in high supersonic flow is investigated based on a von Karman plate model for the structure and on linear piston theory for aerodynamics. A finite element formulation of adaptive structures with piezoelectric material layers is developed using classical laminate theory. Sensor equations are derived for sell-sensing piezoactuators. The paper briefly discusses linear and nonlinear flutter analysis techniques. Dynamic feedback control is used to suppress flutter of adaptive panels. Linear observer-based state feedback is shown to fail in the face of structural nonlinearity and flight parameter variations. Therefore, a novel control approach using output feedback from a pair of collocated or self-sensing piezoactuators is proposed. This new control methodology based on active compensation of aerodynamic stiffness terms is investigated regarding robustness and design limits.

Comparison of linear and nonlinear elastic moduli for reservoir rock by use of a granular medium model

The variations of linear and nonlinear elastic parameters as a function of initial stress and material structure are considered using a model of a granular medium with fluid pore filling. Examples of such variations for some geological conditions interesting for seismoprospecting are presented. It is demonstrated that the nonlinear parameter may be used in exploration seismology as a much more sensitive characteristic compared with conventionally exploited linear moduli.

Atomic and magnetic structure of YBa 2(Cu 1− x57Fe x) 3O 6+ y studied by neutron diffraction on isotope enriched samples

The YBa 2(Cu 1− x 57Fe x ) 3O 6+ y system was studied by neutron diffraction in a wide range of iron concentration in both oxygen-saturated, y≈1, and oxygen-deficient, y≈0.5, states. Detailed data about the atomic and magnetic structure were obtained. The dependence of both atomic coordinates and long-range magnetic order displays some specific features which are quite different from those in the Y123-Cu/Co system. In contrast with this system, a marked amount of Fe atoms occupies Cu(2) sites for x≥0.7, the Cu(2)-O(1) interatomic distance does not depend on iron concentration, and there is no long-range magnetic order in oxygen-saturated samples whatever the iron concentration. A temperature study of 3 deoxygenated samples with x = 0.07, 0.10 and 0.15, confirms the existence of a collinear AF structure, involving a strong coupling between the iron spin and the copper lattice and a rather strong moment induced on the Cu(1) sites. We also observed a non linear variation of the lattice parameters in the T-range 8–400 K, without any abrupt change of slope.

Inequality of temperature increments ofn-alkane homologs as one of the reasons for the nonlinear variation of sorption parameters of substances in temperature-programmed gas chromatography

GC behavior of C6-C17n-alkanes has been investigated at different temperatures of isothermal analysis and under temperature programming conditions using two capillary columns coated with OV-101 and OV-351 stationary phases. Temperature increments have been calculated for the homologs and their inequality has been demonstrated for each member of then-alkane series. It was shown that the nonlinear individual temperature variation of the energy of dispersive interaction ofn-alkane homologs with the stationary phase, which was observed under isothermal conditions, may be one of the main reasons for the nonlinear change in sorption parameters ofn-alkanes in temperature-programmed gas chromatography.

Application of an Adaptive Control Method to the Guide Roll Force Control for Ring Rolling Processes

In spite of several advantages and increasing application of the ring rolling process, analytical design method for controlling the process has been little investigated. This paper considers the ring rolllng process control and treats the problem of controlling the guide roll force which is critical to the stability of the rolling process. There are difficult control problems associated with this process due to the nonlinear characteristics and parameter variation of the process dynamics. In order to control the guide roll force to track a desired profile as close as possible durIng the rolling cycle, an adaptive controller was designed taking into consIderation these fundamental properties of the rolling process. Simulation studies were conducted to verify the effectiveness of this controller. The results show that the proposed adaptive controller is fairly InsensitIve to the parameter variation, and yields desirable performance of tracking guIde roll force throughout the rolling time.

A new approach to the method of nonlinear variation of parameters for a perturbed nonlinear neutral functional differential equation

In this paper we present a nonlinear variation of parameters method for a neutral functional differential equation, without the help of the associated variational equation. An application is made to the study of the asymtotic behavior of solutions of perturbed equations.

A new approach to the method of nonlinear variation of parameters

A nonlinear variation of parameters method for ordinary differential equations is obtained, which generalizes existing techniques. The versatility of the method is demonstrated by studying the asymptotic behavior of solutions of perturbed equations.

Variation of nonlinear parameters to compute decay-constants and their standard deviation

A computer method was develop for fitting a decay curve, which does not require good initial estimates for the nonlinear parameters. It is only necessary to declare intervals in which their values are included. For a net of half-life-combinations, taken the intervals, the best linear parmeters and a “goodness of fit”-quantity are computed. This quantity, as a function of the nonlinear parameters, is used to compute the values of the “best” parameters and their standard deviation by means of parabolic interpolation. The sharpness of a chi-squarred-test, depending on the number of] data points, is investigated and a general, halfermpiric formular for the relative error of the half life of a single component with back-ground using equidistant dta points is deduced by analyzing suitable sysnthetic data. Under certain conditions the computer method can be generalized to any nonlinear curve fit.

Rydberg Terms of Acetylene

It is assumed that two observed Rydberg series in acetylene correspond to (ns) and (nd) orbital excitation. Calculations in a one-electron approximation support the assumption in both cases. The core is assumed to be frozen and linear and interatomic distances unchanged from normal state values in the Rydberg states and in the lowest state of the ion. The terms agree well with experimental values. The Rydberg functions are obtained as linear combinations of Slater functions and energies are stable to variation of both linear and nonlinear parameters.

Ab initio calculation on the H3 activated complex

A full configuration interaction treatment has been carried out for linear, symmetrical H3 activated complex, with a limited basis set of Slater orbitals. A similar calculation is performed on H2 in order to obtain an estimate of the activation energy of the reaction H+H2=H2+H. The variation of nonlinear parameters in the basis set is studied and the different behaviour of the H3 and H2 resulting wave functions examined. — A larger basis set is needed.