State-feedback-controllers and state-estimators (filters) are designed for the roll-pitch-horizontal motions of a helicopter near hover, using a new quadratic synthesis technique. One model (tenth order) uses a dynamic model of the rotor, whereas the other model (sixth order) assumes the rotor can be tilted instantaneously. It is shown that, for tight control, neglecting the rotor dynamics in designing the autopilot can produce unstable closed-loop response on the model that includes rotor dynamics. Two filters are designed to use only fuselage sensors and two are designed to use both fuselage and rotor sensors. It is shown that rotor states can be estimated with sufficient accuracy using only fuselage sensors so that it does not seem worthwhile to use rotor sensors. The mean square response of the vehicle to a gusty, random wind, using several different filter/state-feedback compensators, is shown to be satisfactory.
NomenclatureA = matrix of state weighting coefficients (i.e., weighting of OF = ABF) C = matrix of control gains F = open loop (controls fixed) dynamics matrix G = control distribution matrix H = measurement distribution matrix K = matrix of Kalman filter gains P = covariance matrix of error estimate Q = spectral density matrix of process noise R = spectral density matrix of measurement noise X = mean square response matrix of state responses X = mean square response matrix of state estimates p = roll rate q = pitch rate u, v = longitudinal and lateral velocities of vehicle center of mass u = control vector w = wind vector 6 = pitch angle B c = lateral cyclic pitch 0s = longitudinal cyclic pitch T C -correlation time of wind
Aryliodine(III) difluorides represent an interesting and relatively little studied class of fluorinating agents. Early studies were conducted on the generation of phenyliodine (III) difluoride and its reactions with a few selected alkenes.2 3"4 Carpenter developed an improved method for the preparation of phenyliodine(III) difluoride from the dichloride and studied its reaction with arylethenes.5
The reactions in water of 21 primary and secondary amines with phthalic and succinic anhydrides were examined. Each reaction was first order in both anhydride and amine neutral molecule concentrations, and product analysis showed that the amines did not significantly catalyze the hydrolysis reactions of the anhydrides. Plots of the logarithms of the aminolysis rate constants against the pAfa values of the amine cations were not linear and revealed that the reactions with weakly basic amines were considerably more sensitive to the basicity of the amine than were the reactions with the strong bases. The results suggest that a considerable amount of N-C bond formation has occurred in the rate-determining transition state for reactions with the weakly basic amines and that very little rate facilitation is brought about by hydrophobic bonding between reactants or in the transition state. This behavior thus contrasts markedly with the structure-reactivity relationships exhibited by strongly basic amines which were discussed in part I of this series.
This paper considers an application of the Frequency Domain Input Synthesis procedure reference [12] for identifying the stability and control derivatives of an aircraft. In previous studies, the input design has mostly been carried out in the time-domain. However, by using a frequency-domain approach, one can handle criteria that are not easily handled by the time-domain approaches. Numerical results are presented for optimal elevator deflections to estimate the longitudinal stability and control derivatives subject to root-mean square constraints on the input. The applicability of the steady state optimal inputs to finite duration flight testing is investigated. It is shown that the steady state approximation of frequency-domain synthesis is good for data lengths greater than two time cycles for the short period mode of the aircraft longitudinal motions. For data lengths shorter than this, the phase relationships between different frequency components becomes important. The frequency domain inputs are shown to be much better than the conventional doublet inputs.
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