In the design of a control system for a multivariable linear plant using the optimal control theory which minimizes a quadratic performance index, the optimal control law results in a linear combination of the state of the plant to be controlled. Although all the regulator and tracking problems which were formulated by the above procedure have the assumption that the complete state vector should be measured accurately, this assumption becomes often unrealistic. It is then required for the controller implementation to include the observers which reconstruct the state vector or find the approximation to the state vector from the observed variables. In this paper, perfect model following problems, in which the aircraft (Convair C-131 B) to be controlled follows a model aircraft (Boeing SST) satisfying a desired flying quality when angle of attack can not be measured, are discussed. The approaches employed in this study have the following two steps. The first is the design of an optimal control law for perfect model following assuming that all the state vector can be measured. The second is the synthesis of a scheme which reconstructs the unaccessible states from the measured input and output informations of the plant. Then model following controller can be implemented with on-line configurations. For the state reconstruction scheme, two approaches are considered, one is the full order observer which reconstructs all the state vector of the plant, and the other is the reduced order observer which estimates only the unaccessible state. Special considerations are given for synthesizing the observers with good response characteristics and for improving the closed-loop response of the whole system. Moreover, the problems of sensitivity reduction to the variation of plant parameters are investigated by including the integral feedback terms. Numerical computations are performed for the nontrivial aircraft flight control problem.
The attitude of a rocket is determined by two kinds of angle which are formed between the axis of a rocket and two standard lines. The one is a pitch angle, and the other is a yaw angle. In this paper, the method of the design of a horizon sensor device to determine a pitch angle, the observed results using it and the discussion on them are reported. The output of this device is remarkably affected by the several factors such as the time constant of a sensor, the altitude and the attitude of a rocket and the setting angle of a sensor for a rocket. So that, making these factors as parameters, the method of the design for the optical system and the amplifier of this device were studied. Two horizon sensor devices designed based on these results were boarded on the rocket L-3H7 and the rocket K-10-10 respectively. The observed results by these two devices gave not only the pitch angles of two rockets, but also the temperature distribution of the earth from which the yaw angles were gained.
COLEMAN'S equations for the mechanical instability of a multi-blade rotor are re-examined in relation to the effect of general anisotropy of support stiffness. The characteristic equations for the special cases of support stiffness in which supports are free or fixed in one direction, or isotropic are derived from the one for general anisotropy. The behaviour of the characteristic roots for these special cases is clearly understood in comparison with that for the general anisotropic case. Next, a proof is developed of PRICE's Approximation: the stability boundary for supports fixed in one direction can be approximated by replacing the parameter Λ3 with half that value in the equation for isotropic supports. A check for correspondence of the characteristic roots of the fourth-order equation for isotropic supports with those of sixth-order equation for supports fixed in one direction clarifies the conditions on which the approximation bases.