A survey of methods of feasible directions for the solution of optimal control problems.
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An examination of two aircraft controller structures applicable to on-line implementation was conducted. The two controllers, a linear regulator model follower and an inner-product model follower, were applied to the lateral dynamics of the F8-C aircraft. For the purposes of this research effort, the lateral dynamics of the F8-C aircraft were considered. The controller designs were evaluated for four flight conditions. Additionally, effects of pilot input, rapid variation of flight condition and control surface rate and magnitude deflection limits were considered.
A bibliography is presented of publications and reports resulting from the research project.
A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.
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Digital program has been written to solve the LSOCE problem by using a time-domain formulation. LSOCE problem is defined as that of designing controls for linear time-invariant system which is disturbed by white noise in such a way as to minimize quadratic performance index.
Problem is defined as that of designing controls for linear time invariant system, which is disturbed by white noise, in such a way as to minimize quadratic performance index.
This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.
The effects of gravity gradient torques during boom deployment maneuvers of a spinning spacecraft are examined. Configurations where the booms extended only along the hub principal axes and where one or two booms are offset from the principal axes were considered. For the special case of symmetric deployment (principal axes booms) the stability boundaries are determined, and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified. In the second configuration an expression for gravity torque about the hub center of mass was developed. The nonlinear equations of motion are solved numerically, and the substantial influence of the gravity torque during asymmetric deployment maneuvers is indicated.
The dynamics of a spinning symmetrical spacecraft system during the deployment (or retraction) of flexible boom-type appendages were investigated. The effect of flexibility during boom deployment is treated by modelling the deployable members as compound spherical pendula of varying length (according to a control law). The orientation of the flexible booms with respect to the hub, is described by a sequence of two Euler angles. The boom members contain a flexural stiffness which can be related to an assumed effective restoring linear spring constant, and structural damping which effects the entire system. Linearized equations of motion for this system, when the boom length is constant, involve periodic coefficients with the frequency of the hub spin. A bounded transformation is found which converts this system into a kinematically equivalent one involving only constant coefficients.
The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom end mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using nonoptimal control logic. For the general case results are obtained numerically.
The underlying motivation and concepts are presented, along with a review of the development and application of the model. The structure of the model is described and results validating the model are presented.
The paper considers the design of fault-tolerant controllers that may endow systems with dynamic reliability. Results for jump linear quadratic Gaussian control problems are extended to include random jump costs, trajectory discontinuities, and a simple case of non-Markovian mode transitions.
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Alternate control laws based on an application of the linear regulator problem are developed for possible use in the operation of the Shuttle-Tethered-Subsatellite system. Control is assumed to be provided only by modulating the tension level in the tether as a function of the difference between actual and commanded tether line length, length rate, in (orbital) plane swing angle and swing angle rate. Necessary and sufficient conditions for stability of the (linear) system motion in the vicinity of its nominal local vertical orientation are developed. By proper selection of the state and control penalty matrices it is possible to obtain faster responses with no increase in maximum power levels for use in station keeping when compared with alternate control strategies. The weighting matrices are adjusted in a piecewise adaptive manner to provide control law gains in order to achieve a smooth deployment history. Successful retrieval is dependent mainly on the initial conditions and the rate at which the commanded length is reduced.
The design of a control system using the linear-quadratic regulator (LQR) control law theory for time invariant systems in conjunction with an incremental gradient procedure is presented. The incremental gradient technique reduces the full-state feedback controller design, generated by the LQR algorithm, to a realizable design. With a realizable controller, the feedback gains are based only on the available system outputs instead of being based on the full-state outputs. The design is for a remotely piloted research vehicle (RPRV) stability augmentation system. The design includes methods for accounting for noisy measurements, discrete controls with zero-order-hold outputs, and computational delay errors. Results from simulation studies of the response of the RPRV to a step in the elevator and frequency analysis techniques are included to illustrate these abnormalities and their influence on the controller design.