Frequency response of linear systems from transient data

Methods are presented that use general correlative time-response input and output data for a linear system to determine the frequency-response function of that system. These methods give an exact description of any linear system for which such transient data are available. Examples are shown of application of a method to both an underdamped and a critically damped exact second-order system, and to an exact first-order system with and without dead time. Experimental data for a turbine-propeller engine showing the response of engine speed to change in propeller-blade angle are presented and analyzed

Automatic control systems satisfying certain general criterions on transient behavior

An analytic method for the design of automatic controls is developed that starts from certain arbitrary criterions on the behavior of the controlled system and gives those physically realizable equations that the control system can follow in order to realize this behavior. The criterions used are developed in the form of certain time integrals. General results are shown for systems of second order and of any number of degrees of freedom. Detailed examples for several cases in the control of a turbojet engine are presented

NACA Technical Reports

"A general algebraic method of attack on the problem of controlling gas-turbine engines having any number of independent variables was utilized employing operational functions to describe the assumed linear characteristics for the engine, the control, and the other units in the system. Matrices were used to describe the various units of the system, to form a combined system showing all effects, and to form a single condensed matrix showing the principal effects. This method directly led to the conditions on the control system for noninteraction so that any setting disturbance would affect only its corresponding controlled variable" (p. 581)

NACA Technical Reports

"An analytic method for the design of automatic controls is developed that starts from certain arbitrary criterions on the behavior of the controlled system and gives those physically realizable equations that the control system can follow in order to realize this behavior. The criterions used are developed in the form of certain time integrals. General results are shown for systems of second order and of any number of degrees of freedom. Detailed examples for several cases in the control of a turbojet engine are presented" (p. 207)