Engineering topics
Publications and source records attributed to Colburn, B. K..
A power regulation system incorporating n-parallel power supplies employing PWM switching regulators is studied. Analysis of individual unit operation and coupled-system parameter sensitivity is considered from an operations viewpoint. A detailed example is included to illustrate parallel system operation for 18 such units powered by solar-cell banks.
Discretization of a popular continuous-time control algorithm is effected and an equivalent discrete-time identification law developed and compared to a published discrete identification algorithm developed from Lyapunov Theory. Results are compared as regards asymptotic stability as insured using Lyapunov theory. Some analysis and design guidelines are proposed as regards implementation and practical utility.
A general simulation program (GSP) for state estimation of a nonlinear space vehicle flight navigation system is developed and used as a basis for evaluating the performance of a Space Tug navigation system. An explanation of the iterative guidance mode (IGM) guidance law, derivation of the dynamics, coordinate frames and state estimation routines are given in order to clarify the assumptions and approximations made. A number of simulation and analytical studies are used to demonstrate the operation of the Tug system. Included in the simulation studies are (1) initial offset vector parameter study; (2) propagation time vs accuracy; (3) measurement noise parametric study and (4) reduction in computational burden of an on-board implementable scheme. From the results of these studies, conclusions and recommendations concerning future areas of practical and theoretical work are presented.
A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.
An empirically obtained reaction control jet relay control law with deadband is used as the basis for determining an equivalent weighted time-fuel optimal switching curve according to a least-squares criterion. The derived transformation from the empirical to the optimal law is found to be reversible and to yield a unique transformed control law. The proposed method provides a basis for determining the behavior of an easily implemented relay control law using well-known optimal control results, as well as determining the equivalent relay law corresponding to an analytically determined optimal control law. A numerical example illustrates the transformation technique and simulation results are presented to compare the two control laws.
The steady-state matrix Ricatti equation is studied with respect to sensitivity and computational burden for a linear regulator controller in spacecraft. The class of systems studied use control moment gyros (CMGs) as the torque driver, assuming that the CMGs are free of gimbal stops. Different solution techniques are evaluated relative to computation time and accuracy to determine which solution method is most acceptable with respect to the prescribed requirements. It is shown that it is not feasible to eliminate off-diagonal Ricatti equation terms in the relevent updata equation due to their high sensitivity, that Potter's algebraic technique requires the least computation time of the methods studied, and that the simple Euler method yields the best results when accuracy and computation time are equally weighted. If an optimal linear regulator formulation is employed, a full Ricatti equation solution of n(n + 1)2 elements of the symmetric positive definite gain matrix which is the solution to the matrix Ricatti equation must be computed at each update cycle.
Design characteristics of thruster configurations for spacecraft attitude control systems investigated. A standard six engine approach is developed and used as the basis for comparison of different thruster configurations. These methods include cases of both skewed and non-skewed configurations. Simulation results are used as a basis for comparison, critical thruster design factors being given based on an analysis of the data.
Conventional and adaptive attitude control of spacecraft which use control moment gyros (CMG's) as torque sources are discussed. Control laws predicated on the assumption of a linear system are used since the spacecraft equations of motion are formulated in an 'eigenaxis system' so that they are essentially linear during 'slow' maneuvers even if large angles are involved. The overall control schemes are 'optimal' in several senses. Eigenaxis rotations and a weighted pseudo-inverse CMG steering law are used and, in the adaptive case, a Model Reference Adaptive System (MRAS) controller based on Liapunov's Second Method is adopted. To substantiate the theory, digital simulation results obtained using physical parameters of a Large Space Telescope type spacecraft are presented. These results indicate that an adaptive control law is often desirable.
A second order approximation is derived from a linearized error characteristic equation for Lyapunov designed model-reference adaptive systems and is used to estimate the maximum error between the model and plant states, and the time to reach this peak following a plant perturbation. The results are applicable in the analysis of plants containing magnitude-dependent nonlinearities.
Use is made of linearized error characteristic equation for model-reference adaptive systems to determine a parameter adjustment rule for obtaining time-invariant error dynamics. Theoretical justification of error stability is given and an illustrative example included to demonstrate the utility of the proposed technique.