THE ABSOLUTE STABILIZATION OF THE SHIPS COURSE IN THE CASE OF ROLLING OSCILATIONS

Abstract

In the first part of this paper it is presented the automatic regulation methods for the absolute stability (a.r.a.s) of the nonlinear dynamical systems that have applications on the stabilization of the rolling oscillations curse for aircraft or rackets. Two methods for the absolute stability are specified: a) the A.I. Lurie method with the effective determination of the Liapunov function; b) the frequency method of the Romanian researcher V.M. Popov who has used the transfer function in the critical cases. The authors develop a new sufficient criterion for (a.r.a.s.), with efficient technique of calculus. In the second part - there are obtained the analytic - numerical solutions and the conditions for the regulator parameters for the realization of the absolute stability for the airplane autopilot route in the case of rolling oscillations. At the end authors prove practically the theorem Kalman - Yakubovich - Popov for the equivalence of these methods. (Th. K-Y-P). In the last section of the paper it is presented the optimal control for the flight system in the case of rolling oscillations. The optimization is made using the maximum principle of Pontreaguine; the authors solve the problem of minimum time. It is determined the command function and the optimal trajectory for this system