Minimum time control of a nonlinear system
Time-optimal control problem studied for system representing second-order nonlinear differential equation
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Time-optimal control problem studied for system representing second-order nonlinear differential equation
General boundary conditions for second-order ordinary differential operators
Correction of magnetic measurements made by Mariner II, noting use of second-order approximation for interplanetary magnetic field
Stimulated Brillouin scattering in ferroelectric triglycine sulphate crystals and Rochelle salt exhibiting second-order phase transition, measuring scattering threshold as temperature function
Nonlinear behavior of second-order phase locked loop in presence of noise, discussing probability distribution of phase error, statistical properties of loop behavior, etc
Convergence proof and procedure for third-order and fourth-order iteration process for nonlinear equations - Newton-Raphson second-order iteration
Local variation of dynamic programming algorithm and computer simulation of optimal second-order self-pace control systems
Continued fraction rational approximations to solution of second-order nonlinear equation, including Ricatti equations treated by Merkes, Scott and Fair
General formula for homogeneous second-order differential equation by Lie series, noting computer application
Time optimal control study of second-order linear system with delay
Basic active RC networks constructed from stages that realize second-order transfer functions using two integrators offer excellent stability. Modifications of the basic network produce a highly stable bandpass filter having separate controls that independently adjust center frequency, Q, and center frequency gain.
Coupled second-order differential equations solved to determine attitude stability of gyro controlled satellite
An investigation was conducted in the NACA Lewis icing research tunnel to determine the characteristics and requirements of cyclic deicing of a 65,2-216 airfoil by use of an external electric heater. The present investigation was limited to an airspeed of 175 miles per hour. Data are presented to show the effects of variations in heat-on and heat-off periods, ambient air temperature, liquid-water content, angle of attack, and. heating distribution on the requirements for cyclic deicing. The external heat flow at various icing and heating conditions is also presented. A continuously heated parting strip at the airfoil leading edge was found necessary for quick, complete, and consistent ice removal. The cyclic power requirements were found to be primarily a function of the datum temperature and heat-on time, with the other operating and meteorological variables having a second-order effect. Short heat-on periods and high power densities resulted in the most efficient ice removal, the minimum energy input, and the minimum runback ice formations. The optimum chordwise heating distribution pattern was found to consist of a uniform distribution of cycled power density in the impingement region. Downstream of the impingement region the power density decreased to the limits of heating which, for the conditions investigated, extended from 5.7 percent chord on the upper surface of the airfoil to 8.9 percent chord on the lower surface. Ice removal did not take place at a heater surface temperature of 32 F; surface temperatures of approximately 50 to 100 F were required to effect removal. Better de-icing performance and greater energy savings would be possible with a heater having a higher thermal efficiency.
Afterbody pressure distributions and wave drag were calculated using a second-order theory for a variety of conical boattails at zero angle of attack. Results are presented for Mach numbers from 1.5 to 4.5, area ratios from 0.200 to 0.800, and boattail angle from 3 degrees to 11 degrees. The results indicate that for a given boattail angle, the wave drag decreases with increasing Mach number and area ratio. The wave drag, for a constant area ratio, increases with increasing boattail angle. For a specific Mach number, area ratio, and fineness ratio, a comparison of the wave-drag coefficients for conical, tangent-parabolic, and secant-parabolic boattails showed the conical boattail to have the smallest wave drag.
Pressure distributions and forces for a series of four bodies of revolution having nose-fineness ratios varying from 4 to 10 have been obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2x10(sup)6 to 14x10(sup)6, and angles of attack from zero to 9 degrees. In general, a comparison of the experimental data with a second-order theory showed good agreement for the range of variables investigated.
Pressure distributions for a series of four boattailed bodies of revolution were obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2 x 10 to 6th power to 14 x 10 to the 6th power, and angles of attack from zero to 9 degrees. Second-order theory adequately predicted the pressure distribution for regions free of the effects of cross-flow separation.
Shock position was assumed to be controlled by air bleed through a diffuser-exit bypass door operated by a second-order servomotor. Pressure disturbance resulting from changes in bypass-door position had whereas a disturbance in engine speed had a large effect on diffuser pressure and could impose severe requirements on diffuser control response. The controlled diffuser response improved with faster servomotor response and smaller diffuser dead time and lag. The effect of diffuser dead time on diffuser response was greater than the effect of diffuser lag.
A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.