Adaptive backstepping control of wheeled inverted pendulum with velocity estimator

In this paper, we introduce a backstepping control design of a wheeled inverted pendulum. Based on a second-order motion equation of the body angle, an adaptive integral backstepping controller is designed to stabilize the body angle. It is shown that the σ-modification rule in the adaptive update law guarantees the boundedness of the errors in estimating the time-varying signal that is an output of a linear system with every bounded input signal. Then, the stabilizing controller for the wheel angle is constructed by a PD-type positive feedback. The derived controller requires the full-state measurements. In the output feedback case, the K filter or the observer backstepping is needed. However, the structure of the controller becomes complicated. We propose a non-model-based differentiator based on the adaptive update law. Since the non-model-based differentiator does not require any knowledge of the dynamic structure of the signal, we can use it as a velocity estimator for unknown nonlinear systems. Therefore, we replaced the velocity measurement with the estimates by the non-model-based differentiator. Finally, simulation results for the proposed controller are presented.     

Effects of Gd Substitution on Sintering and Optical Properties of Highly Transparent (Y0.95−xGdxEu0.05)2O3 Ceramics

Highly transparent (Y_0.95?xGd_xEu_0.05)₂O₃ (x = 0.15–0.55) ceramics have been fabricated by vacuum sintering at the relatively low temperature of 1700°C for 4 h with the in‐line transmittances of 73.6%–79.5% at the Eu³⁺ emission wavelength of 613 nm (~91.9%–99.3% of the theoretical transmittance of Y_1.34Gd_0.6Eu_0.06O₃ single crystal), whereas the x = 0.65 ceramic undergoes a phase transformation at 1650°C and has a transparency of 53.4% at the lower sintering temperature of 1625°C. The effects of Gd³⁺ substitution for Y³⁺ on the particle characteristics, sintering kinetics, and optical performances of the materials were systematically studied. The results show that (1) calcining the layered rare‐earth hydroxide precursors of the ternary Y–Gd–Eu system yielded rounded oxide particles with greatly reduced hard agglomeration and the particle/crystallite size slightly decreases along with increasing Gd³⁺ incorporation; (2) in the temperature range 1100°C–1480°C, the sintering kinetics of (Y_0.95?xGd_xEu_0.05)₂O₃ is mainly controlled by grain‐boundary diffusion with similar activation energies of ~230 kJ/mol; (3) Gd³⁺ addition promotes grain growth and densification in the temperature range 1100°C–1400°C; (4) the bandgap energies of the (Y_0.95?xGd_xEu_0.05)₂O₃ ceramics generally decrease with increasing x; however, they are much lower than those of the oxide powders; (5) both the oxide powders and the transparent ceramics exhibit the typical red emission of Eu³⁺ at ~613 nm (the ⁵D₀→⁷F₂ transition) under charge transfer (CT) excitation. Gd³⁺ incorporation enhances the photoluminescence and shortens the fluorescence lifetime of Eu³⁺.     

Research and Development of the Coprecipitation Process for Lanthanum Germanate Oxyapatite

Although lanthanum germanate oxyapatite (La–Ge–O) has shown good potential for use as a solid electrolyte in energy storage applications, its synthesis has been challenging by either solid‐ or solution‐state methods. In this study, a new synthesis of La–Ge–O was developed through a coprecipitation technique, in which a highly concentrated homogeneous aqueous solution of La and Ge was prepared from aqueous ammonium germanate and lanthanum nitrate solutions with the addition of dilute nitric acid. Several precipitates were formed by pH manipulation, including an amorphous material obtained at pH > 3. Compared to the individual precipitation behaviors of the parent compounds, the amorphous precipitate was formed only from the aqueous two‐component mixture, and appeared to contain both metals. This material was transformed into crystalline mixtures upon heating at 1273 K. The crystalline phases were La₂Ge₃O₉ and hexagonal‐type GeO₂ when the precipitate was formed below pH 8, and the La–Ge–O and La₂Ge₂O₇ phases when the precipitate was formed around pH 8. Product formation from the coprecipitate was discussed based on X‐ray diffraction and thermal analyses. The improved availability of La–Ge–O will allow more extensive investigations of its useful properties.     

Mechanism of Catalytic Effects on AMMO/HMX Composite Propellants Combustion Rates

Thermal decomposition and the burning properties of AMMO/HMX propellants have been investigated. The heat generated by the AMMO decomposition initiated and accelerated the thermal decomposition of HMX, and the reaction between decomposed AMMO and HMX depended upon the heating rate. The rate determining step of the reaction path was different in higher and lower heating rate conditions. 2,2-bis(ethylferrocenyl)propane (CFe) and copper chromite (CuC) significantly altered the mechanisms of the thermal decomposition and the burning properties. CFe showed an increase in burning rate with a slight increase in burning rate exponent. However, CuC yielded high values for the burning rate exponent. The combined additive yielded the highest burning rate with the lowest burning rate exponent. The influence of CuC on the burning rate exponent disappeared by the combination with CFe. Though CFe and the combination additive improved the ignitability of the propellants, the propellant with CuC was difficult to ignite because of the relatively small quantity of heat feedback and/or heat released by the decomposition.     

Burning Rate Augmentation of BAMO Based Propellants

Thermal decomposition and the burning properties of BAMO based propellants with HMX or AN/HMX have been investigated. The heat generated by the azide binder decomposition initiated and accelerated the thermal decomposition of HMX and AN. Ammonium perchlorate (AP) and lead stearate with carbon black significantly altered the mechanisms of the thermal decomposition and the burning properties of the HMX based propellants. AP showed an increase in burning rate with a slight decrease in burning rate pressure exponent. The lead catalyst yielded high value of the burning rate with the lowest pressure exponent. The ammonium dichromate also influenced the mechanisms of the thermal decomposition and the burning properties of the AN/HMX samples. The combination of ammonium dichromate and copper chromite was the most effective on the burning rate augmentation of AN/HMX based propellants. AN sublimed and evaporated from the condensed phase and mainly reacted exothermically in the gas phase HMX and AN/HMX based propellants showed smokeless burning characteristics in the small rocket motor combustion tests.     

Am1 MO Study of Benzene Nitro Derivatives

Molecular properties of benzene nitro derivatives were investigated by using semi-empirical MO calculations. As the results, the molecular structures and the rotational barrier of the nitro group calculated by AM1 showed a good agreement with the experimental values. The heats of formation in gaseous and condensed phases were obtained by considering isodesmic reactions. By this procedure, the heat of formation of hexanitrobenzene in solid phase was calculated to be +22.7 kcal/mol. The detonation parameters were also calculated by using four equations of state. The predicted detonation velocities showed a good agreement with the experimental values.     

Combustion Characteristics of High Burn Rate Azide Polymer Propellant

The combustion characteristics of high burn rate azide polymer composite propellant were examined by using a chimney type strand burner, a Ø 80 mm × 140 mm small rocket motor and a L/D = 16 of Ø 70 mm heavy-wall rocket motor. The propellant, BAMO/NMMO copolymer was used as a fuel binder and AP as an oxidizer, burned approximately 29 mm/s at a pressure range of 7 MPa to 20 MPa with a plateau-mesa burning behavior. However, the pressure exponent rapidly increased at above the pressure of 20 MPa and was 0.52 between 20 MPa and 25 MPa. The low pressure exponent and high burn rate of the azide polymer propellant are suitable to the short burn time at the maximum expected operating pressure range of 15 MPa to 20 MPa. The high L/D heavywall rocket motor with volumeric mass fraction of 83% showed stable combustion without any pressure oscillation and severe erosive burning. The average burn rate in the high L/D motor was 10% larger than that estimated from the strand data. The theoretically calculated pressure-vs-time and thrust-vs-time curves were well consistent with the measured data. α = 20 and β = 180 for the Lenoir-Robillard equation were used to estimate the burn rate.