It is well known that application of feedback optimization technique, a technique for detecting disturbances suffered so far and then optimizing the subsequent control strategy, is most effective to improve the accuracy of the orbit in launching a satellite. In this paper, a radio guidance concept for 3 stage launching rocket with a thrust vector controlled second stage motor and an injection controlled final motor is discussed as an example of real time feedback optimization. As to a guidance method concerning the final motor, its concept and algorithm have been already shown in ref. 1, and the radio guidance program was applied to L4SC-2 launching experiment. Therefore, the discussion is mainly focused on the guidance scheme for controlling the second stage motor to compensate disturbances caused by the uncontrolled first stage motor in an optimum way considering the succeeding correction for the final motor. Though this is a simple example of two step dynamic optimization problem, the precise calculation for the first step of optimization (guidance to the second stage motor) becomes very complex because of the following step of optimization, results of which are necessary to optimize the first step. In this case, a time interval for computation is not long enough to obtain the completely optimum guidance law, for the long time interval between burn out of the first motor and ignition of the second motor cannot be allowed because of the demand for effective use of rocket energy. However, as the disturbance suffered in the first stage flight is not enlarged for the same reason, a linear perturbation method developed at the nominal trajectory is applicable and the criterion function of this step is approximated by a quadratic function in terms of attainable trajectory parameters of the second stage flight. This function approximately represents the performance index for the first step optimization on the condition that the next step optimization is executed. With these approximations, the computation becomes very simple and a nearly optimum solution for this step can be obtained immediately. In addition, all hard-wares or radio guidance systems shown in ref. 1, are also available for this case. The adaptability of the method for practical experiments and the validity of assumptions are assured by the numerical examples applied to some typical flight data. The accuracy of trajectory estimation of the first stage flight that is most significant for the method is investigated, and the results of last few experiments show that the estimation from ten seconds data will give enough accuracy for this object.
電波誘導方式(II)
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