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In this paper the problem of synthesizing dual reflector antennas for both amplitude and phase control of the final aperture distribution is discussed. An approximate procedure for the offset synthesis problem is presented and applications of the procedure to the shaping of beam waveguides and reflectors for high-gain antenna systems are illustrated.
We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.
This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-off problem is considered with reference to flight in a vertical plane. First, trajectories for optimum performance in a windshear are determined for different windshear models and different windshear intensities. Use is made of the methods of optimal control theory in conjunction with the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. In this approach, global information on the wind flow field is needed. Then, guidance strategies for near-optimum performance in a windshear are developed, starting from the optimal trajectories. Specifically, three guidance schemes are presented: (1) gamma guidance, based on the relative path inclination; (2) theta guidance, based on the pitch attitude angle; and (3) acceleration guidance, based on the relative acceleration. In this approach, local information on the wind flow field is needed.
An approximate synthesis method is presented for solving the problem of offset dual-shaped reflectors. It is shown that the equations obtained by this method are partial differential equations that can be integrated numerically, except that these equations are generally not total and therefore do not have a 'smooth' solution. However, it is demonstrated that these equations form a nearly total differential that enables one to generate a smooth subreflector by integrating the differential equations and then synthesizing a main reflector which gives an exact solution for the specified aperture phase distribution. Several important illustrative examples are treated, which validate the adequacy of the proposed method.
The cryosphere is a major component of the hydrosphere and interacts significantly with the global climate system, the geosphere, and the biosphere. Measurement of the amount of water stored in the snow pack and forecasting the rate of melt are thus essential for managing water supply and flood control systems. Snow hydrologists are confronted with the dual problems of estimating both the quantity of water held by seasonal snow packs and time of snow melt. Monitoring these snow parameters is essential for one of the objectives of the Earth Science Enterprise-understanding of the global hydrologic cycle. Measuring spatially distributed snow properties, such as snow water equivalence (SWE) and wetness, from space is a key component for improvement of our understanding of coupled atmosphere-surface processes. Through the GWEC project, we have significantly advanced our understandings and improved modeling capabilities of the microwave signatures in response to snow and underground properties.
An approach for modeling dynamic equations of motion of a plate attached with rigid bodies is presented. The equations of motion are developed using the principle of virtual work. Lagrange multipliers are used as interaction forces and/or moments to maintain prescribed constraints which is the basis of the interconnection between the plate and rigid bodies. The overall approach is unique in the sense that a continuous model described by a family of partial differential equations is established. An approximate formulation by using variational method is established yielding a solution compatible with the assumed degree of approximation. The formulation is useful particularly when parametric study of dynamic response for a satellite power system is desired. As an example, an approximate governing equation of algebraic eigenvalue problem is given for a dual microwave power transmission system. Controller design is discussed.
Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.
This paper presents a state-space approach to the multivariable 'type one' servomechanism problem. Necessary and sufficient conditions for the controllability of such systems are derived and applied to the observability of the (dual) state reconstructor problem for a system with an unknown constant input. The paper also presents a simple systematic design algorithm which provides type one servomechanism performance to command inputs, together with pre-specified closed-loop pole locations. Examples are given to illustrate the utility of the design procedure.
Synthesis of dual-shaped offset reflector antennas to control the exit aperture distribution of amplitude and phase has received considerable attention in recent years. For a given feed illumination and desired aperture field distribution, an exact formulation of the problem of simultaneously synthesizing the shapes of the sub and main reflectors was presented recently by Galindo-Israel et al. (1987) in terms of a set of nonlinear first-order differential equations. In this paper, a numerical approach to solving these equations is discussed which circumvents some of the difficulties encountered by Galindo-Israel et al., particularly for small values of theta.
This paper presents some of the technical aspects in the development at the Langley Research Center of an air-cove, dual-wound, single-coil, magnetic-suspension system with one-dimensional control. Overall electrical system design features and techniques are discussed in addition to the problems of control and stability. Special treatment is given to the operation of a dual-wound, high-current support coil which provides the bias fields and superimposed modulated field. Other designs features include a six-phase, solid-state power stage for modulation of the relatively large magnitude control current, and an associated six-phase trigger circuit.
Design problems and the solutions adopted for them in the attitude and articulation control subsystem for the Galileo spacecraft are discussed as an illustration of the application of dual-spin control to an interplanetary spacecraft. Following a review of the baseline design of the Galileo system and mission, consideration is given to problems encountered in the areas of autonomous attitude determination, attitude control, spacecraft dynamics and software margins. Design issues raised by subsequent changes in spacecraft configuration are also indicated. It is pointed out that although difficulties associated with control system complexity in a dual-spin interplanetary spacecraft have been satisfactorily resolved for the Galileo mission, the future application of dual spin in interplanetary flight is in doubt.
A folded optics reflector system could mitigate problems associated with the pointability and controllability of the large UHF antenna for MSAT. Such a system is comprised of a parabolic main reflector and a hyperboloidal subreflector (Cassegrain arrangement) or an ellipsoidal subreflector (Gregorian arrangement), either of which brings the feed closer to the main reflector. By shaping the subreflector and the main reflector, an improved scan capability might be achieved and the size of the required feed aperture-per-beam could be reduced. In such a shaped dual reflector system, the need for overlapping cluster feed arrangement and its concomitant beam forming network could be removed. In this system, a relatively low gain feed element together with the shaped subreflector would be sufficient to produce the required high illumination taper that at the main reflector.
The research is reported on the problems of failure detection and reliable system design for digital aircraft control systems. Failure modes, cross detection probability, wrong time detection, application of performance tools, and the GLR computer package are discussed.
One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.
A simple way of tuning usual proportional-and-derivative (PD) controllers is presented. The tuning is devised so that the closed-loop system has a speed of response near that of time-optimal bang-bang control during a large portion of the transient period. When the system is near the desired equilibrium it behaves linearly, and thus avoids the problem of being overly sensitive to the disturbances and noise. The idea is rather intuitive. Unlike dual-mode control, the plant is controlled throughout by a PD controller. Numerical results are included.
Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.
Viewgraphs on a stochastic approach to robust broadband structural control are presented. Topics covered include: travelling wave model; dereverberated mobility model; computation of dereverberated mobility; power flow; impedance matching; stochastic systems; control problem; control of stochastic systems; using cost functional; Bernoulli-Euler beam example; compensator design; 'power' dual variables; dereverberation of complex structure; and dereverberated transfer function.
The optimal tuning of multiple tuned-mass dampers for the transient vibration damping of large space structures is investigated. A multidisciplinary approach is used. Structural dynamic techniques are applied to gain physical insight into absorber/structure interaction and to optimize specific cases. Modern control theory and parameter optimization techniques are applied to the general optimization problem. A design procedure for multi-absorber multi-DOF vibration damping problems is presented. Classical dynamic models are extended to investigate the effects of absorber placement, existing structural damping, and absorber cross-coupling on the optimal design synthesis. The control design process for the general optimization problem is formulated as a linear output feedback control problem via the development of a feedback control canonical form. The techniques are applied to sample micro-g and pointing problems on the NASA dual keel space station.