Accession Number:

AD0743090

Title:

Modal Analysis of a Distributed Parameter System for Control at an Unstable Steady State.

Descriptive Note:

Final rept.,

Corporate Author:

NAVAL SHIP ENGINEERING CENTER PHILADELPHIA PA PHILADELPHIA DIV

Personal Author(s):

• Loeb,Alfred M.

Report Date:

1972-05-22

Pagination or Media Count:

229.0

Abstract:

The report describes the results of a detailed investigation of the dynamics of a distributed parameter system exhibiting three steady states, one of which is open loop unstable. The specific model selected for this study was the adiabatic tubular chemical reactor with axial flow mixing. The techniques developed for both analysis and simulation are directly applicable to a variety of problems in propulsion machinery systems control, particularly where the mathematical models involve distributed parameters. In the study described in the report a form of modal analysis is employed to investigate the stability of the steady states and to devise a method for operating the reactor at the unstable state under feedback control. The results of this investigation, which are verified by a thorough digital computer simulation of the nonlinear system, clearly show that, for the conditions investigated, the unstable steady state may be stabilized and that operation at the unstable state is possible. Furthermore, it is shown that the unstable state can be attained from reasonable start-up conditions. Author

Descriptors:

• (*ADAPTIVE CONTROL SYSTEMS
• MATHEMATICAL MODELS)
• (*CHEMICAL ENGINEERING
• ADAPTIVE CONTROL SYSTEMS)
• CHEMICAL REACTIONS
• FEEDBACK
• NONLINEAR SYSTEMS
• NONLINEAR DIFFERENTIAL EQUATIONS
• PARTIAL DIFFERENTIAL EQUATIONS
• PERTURBATION THEORY
• STABILITY
• CURVE FITTING
• GRAPHICS

Subject Categories:

• Industrial Chemistry and Chemical Processing
• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE