Accession Number : AD0822619

Title :   ON THE ABSOLUTE STABILITY OF A DYNAMIC SYSTEM HAVING PRODUCT OF TWO NONLINEARITIES.

Descriptive Note : Technical rept.,

Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Nahi, N. E. ; Partovi, S.

Report Date : JUN 1967

Pagination or Media Count : 25

Abstract : Fluid power systems in many cases fulfill the accuracy and dynamic capability required in space vehicle applications such as on-board tracking systems. The increased stringency of specifications have made design of such systems critical and complicated. The valve control hydraulic systems which are suitable for space vehicle applications are nonlinear systems. The equations describing such a system contain the product of two nonlinear functions. In order to understand the behavior of the system under different conditions and make a proper and economical design, a nonlinear analysis is required. An economical and accurate analysis is feasible by use of the Second Method of Lyapunov and recent criterion of Popov. In this report Popov's theorem is extended to a system with a broader class of nonlinearities. Sufficient conditions for absolute stability of a dynamic system containing a nonlinearity function of two state variables are derived. These conditions are applied to a simplified set of equations describing a hydraulic tracking system with valve control. The sufficient conditions are used to find the range of feedback parameter values, and the absolute stability of the system is examined. The absolute stability of other examples are shown also by the results of the theorems. The results developed for proofs of the main theorems are of a very general nature and it is expected that they will be used to derive additional stability conditions and design procedures. (Author)

Descriptors :   (*NONLINEAR SYSTEMS, STABILITY), (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*FLIGHT CONTROL SYSTEMS, HYDRAULIC EQUIPMENT), FEEDBACK, TRACKING, NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMS.

Subject Categories : Aircraft
      Numerical Mathematics
      Unmanned Spacecraft

Distribution Statement : APPROVED FOR PUBLIC RELEASE