Sliding mode control with adaptive vss observer

The conventional sliding mode control or variable structure control (VSC) of a nonlinear uncertain system is well known for its robust property and simplicity of control law. However, the use of either is permitted only on the assumption that the upper bound of parameter variation or nonlinearity is known and that the complete information about the state is available. Although the former has recently been solved with adaptive robust control theory, the latter does not appear to be solved. This paper attempted to solve this problem using the technique of VSS adaptive robust control theory. That is, a VSS adaptive observer and a sliding mode control incorporated with this observer was proposed. The robust stability of the closed system can be proved applying Lyapunov's second method.     

Kleene chain completeness and fixedpoint properties

Let L denote the nonscalar complexity in k(x₁,…, x_n). We prove $\text{L(?,??/?x}{}_1\text{,…,??/?x}{}_{\mathrm{n}}\text{)?3L(?)}$. Using this we determine the complexity of single power sums, single elementary symmetric functions, the resultant and the discriminant as root functions, up to order of magnitude. Also we linearly reduce matrix inversion to computing the determinant.     

Syntheses of dihydrolavandulol and its related compounds from carboxylic acids and conjugated dienes

5-Methyl-2-isopropyl-4-hexenoic acid, dihydrolavandulic acid (III) , was synthesised in 65% yield from 3-methylbutanoic acid and isoprene with sodium naphthalenide in the presence of N,N,N′,N′-tetramethylethylenediamine. Reduction of III with lithium aluminum hydride gave 5-methyl-2-isopropyl-4-hexen-l-ol, dihydrolavandulol ( IV ) (85% yield). Oxidation of IV with pyridinium chlorochromate gave 5-methyl-2-isopropyl-4-hexenal, dihydrolavandulyl aldehyde ( V ) (81 % yield).     

Oscillation frequency in hybrid stepping motors

Oscillation characteristics under constant drive pulse-rate conditions are measured on the basis of the drive pulse rate f (pps). Relationships between the oscillation frequency under rotating conditions and the single-step response are investigated. It is clarified that the main components of oscillation consist of the integral- and fractional-harmonics of f, and that they are determined from the times at the valley and peak of the single-step response, respectively. The f/4 component oscillation, which is very different from the forementioned oscillations, also is discussed.     

The Reaction of Crotonic Acid with Aldehydes Using Lithium Naphthalenide

Lithium naphthalenide reacts with crotonic acid in the presence of diethylamine to give an allylic anion of lithium crotonate. The reaction of the anion with various aldehydes gives a mixture of α and γ adducts.     

Preparation of Proton-Conducting Amorphous Films Containing Dodecamolybdophosphoric Acid by the Sol—Gel Method

Silica gel films containing dodecamolybdophosphoric acid, H₃PMo₁₂O₄₀·29H₂O (MPA), were prepared by the sol—gel method. Amorphous films were obtained for the compositions with 0 to 42 wt% MPA. Infrared spectra revealed that the skeleton of heteropolyanions PMo₁₂O³⁻₄₀ remained in the silica gel structure. The gel films exhibited considerably high proton conductivities in a highly humid atmosphere, and the conductivity increased with increasing MPA content. The value of conductance (G) at 1 kHz for these films was very sensitive to the variation of relative humidity (rh). The relation between log G and rh was almost linear and was reproducible on repeated runs for the gel films with 42 wt% MPA heat-treated at 200°C.