Showing papers in "Journal of Guidance Control and Dynamics in 1991"

Sensor placement for on-orbit modal identification and correlation of large space structures

Abstract: A method is presented for the selection of a set of sensor locations from a larger candidate set for the purpose of on-orbit identification and correlation of Large Space Structures. The method ranks the candidate sensor locations according to their contribution to the linear independence of the target modal partitions. In an iterative maner, the locations which do not contribute significantly are removed. The final sensor configuration tends to maximize determinant of the corresponding Fisher Information Matrix.

Fractional order state equations for the control of viscoelasticallydamped structures

Abstract: Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures. The mechanical properties of damping materials are modeled using fractional order time derivatives of stress and strain. These models accurately describe the broadband effects of material damping in the structure's equations of motion. The resulting structural equations of motion are used to derive the fractional order state equations. Substantial differences between the structural and state equations are seen to exist. The mathematical form of the state equations suggests the feedback of fractional order time derivatives of structural displacements to improve control system performance. Several other advantages of the fractional order state formulation are discussed. Nomenclature

Beyond singular values and loop shapes

Abstract: The status of singular value loop-shaping as a design paradigm for multivariable feedback systems is reviewed. It shows that this paradigm is an effective design tool whenever the problem specifications are spacially round. The tool can be arbitrarily conservative, however, when they are not. This happens because singular value conditions for robust performance are not tight (necessary and sufficient) and can severely overstate actual requirements. An alternate paradign is discussed which overcomes these limitations. The alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The state of the art currently permits analysis of feedback systems within this new paradigm. Synthesis remains a subject of research.

Unified formulation of dynamics for serial rigid multibody systems

Abstract: There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.

Reduced-dynamic technique for precise orbit determination of low earth satellites

Abstract: A reduced-dynamic technique for precise orbit determination of low earth satellites is described. This technique optimally combines the conventional dynamic technique with the nondynamic technique which uses differential GPS continuous carrier phase to define the state transition. A Kalman filter formulation for this reduced-dynamic technique is given. A covariance analysis shows that when neither the dynamic nor the nondynamic technique is clearly superior, the reduced-dynamic technique appreciably improves the orbit accuracy. Guidelines for selecting a near-optimum weighting for the combination are given. Sensitivity to suboptimal weighting is assessed.

Model reduction and control of flexible structures using Krylov vectors

Abstract: Krylov vectors and the concept of parameter matching are combined together to develop a model reduction algorithm for a damped structural dynamics system. The obtained reduced-order model matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, three types of control energy spillover generally exist: control, observation, and dynamic. The formulation based on Krylov vectors can eliminate both the control and observation spillovers while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method. I. Introduction A MAJOR difficulty in the control of flexible structures or any other large-scale system is, in the words of Bellman, the "curse of dimensionality." A flexible structure is, by nature, a distributed-pa rameter system, and, hence, it has infinitely many degrees of freedom. Even approximate structural models obtained by some discretization approach are generally still too large for use in control design applications. Therefore, model order reduction plays an indispensable role in the control of flexible structures. Usually, model reduction of a structural dynamics system is performed by the RayleighRitz method, which transforms the system equation to a smaller scale by using a projection subspace. It is indisputable that the choice of projection subspace is important to the accuracy of the reduced model. The eigensubspace, or the normal mode subspace, is frequently used for projection because it has a clear physical meaning and can preserve the system natural frequencies. However, with regard to the accuracy of system response, numerical experience has shown that preservation of the natural frequencies is usually not the only • concern. Other than normal modes, there are other static modes, e.g., constraint modes, attachment modes, and inertiarelief modes, which are frequently used in component mode synthesis.1 In this paper, Krylov vectors, which can be considered as static modes, are used for model reduction. There has been quite a bit of research concerning the convergence and efficiency of Krylov vectors in application to eigenvalue analysis and to the structural dynamics model reduction problem.2'5 Krylov vectors are also efficient when employed in general linear system and controller reduction problems.6'7 The major purpose of this paper is to discuss the possible application of Krylov vectors to controller design for flexible structures. The structural dynamics system studied here is described by a second-order matrix differential equation together with an output measurement equation. To perform model reduction to a structural dynamics system in this input-output configuration, the concept of parameter matching for general linear system model reduction is adopted. Parameter matching constitutes a class of efficient methods for model order reduction

Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates

Abstract: This paper is concerned with the general motion of a flexible body in space. Using the extended Hamilton’s principle for distributed systems, standard Lagrange’s equations for hybrid systems are first derived. Then, the equations for the rigid-body motions are transformed into a symbolic vector form of Lagrange’s equations in terms of general quasi-coordinates. The hybrid Lagrange’s equations of motion in terms of general quasi-coordinates are subsequently expressed in terms of quasi-coordinates representing rigid-body motions. Finally, the second-order Lagrange’s equations for hybrid systems are transformed into a set of state equations suitable for control. An illustrative example is presented.

Near-minimum-time control of distributed parameter-systems - analytical and experimental results

Abstract: We present a method for generating globally stable feedback control laws for maneuvers of distributed parameter structural systems. The method can accommodate system nonlinearity, and our proof of Lyapunov stability does not rely upon spatially discretizing distributed parameter systems. The approach applies directly to controllable distributed parameter systems that are open-loop conservative or dissipative. The most fundamental version of the formulation leads to controls that drive the system to a fixed point in the state space, but more generally, we develop tracking-type control laws to null the departure of the system state from a smooth target trajectory. Both analytical developments and experimental results are presented. The analytical results provide a theoretical foundation for the approach, whereas the experimental results provide conclusive evidence that the approach can be efficiently realized in actual hardware.

Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming

Abstract: A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and controls and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory that can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.

Experimental investigation into passive damping enhancement for space structures

Abstract: This work presents experiments conducted to verify kineticand strain-energy damping enhancement schemes for large/precision space structures. Two types of damping mechanisms were applied to a 5-m-long, 10-bay aluminum cubic box truss with a quasi-free-free suspension. Tunable proof-mass dampers were implemented with space-realizable linear electromechanical drivers. Tunable piezoelectric truss members were designed and constructed for the demonstration of resonant shunted piezoelectric damping concepts. The truss damping was measured and compared with analytical predictions. The proof-mass damper implementation was found to increase the first mode damping ratio from 0.6% of critical to 6.4% of critical with a 2.7% system mass increase. The resonant shunted piezoelectric implementation increased the first mode damping ratio to 6.0%, with a 1.9% increase in system mass.

Angle-only tracking filter in modified spherical coordinates

Abstract: References Gregory, C. Z., Jr., "Reduction of Large Flexible Spacecraft Models Using Internal Balancing Theory,'* Journal of Guidance, Control, and Dynamics, Vol. 7, 1984, pp. 725-732. Moore, B. C., "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Transactions on Automatic Control, Vol. AC-26, 1981, pp. 17-32. Gawronski, W., and Williams, T., "Model Reduction for Flexible Space Structures," Proceedings of the AIAA/ASME/ASCE/AHS/ ASC30th Structures, Structural Dynamics and Materials Conference, AIAA, Washington, DC, 1989, pp. 1555-1565. Gawronski, W., and Juang, J.-N., "Near-Optimal Model Reduction in Balanced and Modal Coordinates," Proceedings of 26th Annual A llerton Conference on Communication, Control and Computing, Sept. 1988, pp. 209-219. Skelton, R. E., "Cost Decomposition of Linear Systems with Application to Model Reduction," International Journal of Control, Vol. 32, No. 6, 1980, pp. 1031-1055. Skelton, R. E., and Yousuff, A., "Component Cost Analysis of Large Scale Systems," International Journal of Control, Vol. 37, No. 2, 1983, pp. 285-304. Clough, R. W., and Penzien, J., Dynamics of Structures, McGraw-Hill, New York, 1975. Angle-Only Tracking Filter in Modified Spherical Coordinates

Weak Hamiltonian finite element method for optimal control problems

Abstract: A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Generalized technique for inverse simulation applied to aircraft maneuvers

Abstract: Inverse simulation techniques are computational methods that determine the control inputs to a dynamic system that produce desired system outputs. Such techniques can be powerful tools for the analysis of problems associated with maneuvering flight. An algorithm is developed that serves as an efficient inverse simulation tool for analyzing maneuvering flight. As opposed to current inverse simulation methods, which require numerical time differentiation in their implementation, the generalized technique offered is essentially an integration algorithm. Examples of inverse solutions for a large-amplitude aircraft maneuver and a nap-of-the-Earth helicopter maneuver are presented.

Design of restructurable flight control systems using feedback linearization

Abstract: In this paper, a design method is presented for restructurable flight control systems based on the feedback linearization method. Failures are identified indirectly by estimating parameters of the nonlinear aircraft model using the recursive least square algorithm. The aircraft is assumed to have many control surfaces that can be driven independently. In the design, actuator dynamics are taken into account and the Control distributor, which reduces real inputs to generic inputs, is used. The imaginary actuators for generic inputs are introduced to generate input signals used in parameter identification. Pitch and roll angles are controlled indirectly by controlling pitch and roll rates, respectively, which is an approximate way but makes the control system simpler than applying the feedback linearization method straight to the control of the angles. To evaluate the performance of the restructurable flight control system, two failure cases are simulated on the six-degree-of-freedom nonlinear aircraft model.

Design and evaluation of an air traffic control Final Approach Spacing Tool

Abstract: This paper describes the design and simulator evaluation of an automation tool for assisting terminal radar approach controllers in sequencing and spacing traffic onto the final approach course. The automation tool, referred to as the Final Approach Spacing Tool (FAST), displays speed and heading advisories for arriving aircraft as well as sequencing information on the controller's radar display. The main functional elements of FAST are a scheduler that schedules and sequences the traffic, a four-dimensional trajectory synthesizer that generates the advisories, and a graphical interface that displays the information to the controller. FAST has been implemented on a high-performance workstation. It can be operated as a stand-alone in the terminal radar approach control facility or as an element of a system integrated with automation tools in the air route traffic control center. FAST was evaluated by experienced air traffic controllers in a real-time air traffic control simulation. simulation results summarized in the paper show that the automation tools significantly reduced controller work load and demonstrated a potential for an increase in landing rate.

Model reduction for flexible space structures

Abstract: This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Rapid near-optimal aerospace plane trajectory generation and guidance

Abstract: Effort was directed toward the problems of the real time trajectory optimization and guidance law development for the National Aerospace Plane (NASP) applications. In particular, singular perturbation methods were used to develop guidance algorithms suitable for onboard, real time implementation. The progress made in this research effort is reported.

Selection of component modes for flexible multibody simulation

Abstract: The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates, respectively. This paper focuses on the choice of component modes used to model articulating and nonarticulating flexible multibody systems. Attention is directed toward three classical component mode synthesis methods whereby component normal modes are generated by treating the component interface as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free interface normal modes are augmented by static shape functions termed constraint and residual modes, respectively. In this paper, a mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed interface plus constraint), MacNeal-Rubin (free interface plus residual), or Benfield-Hruda (loaded interface) mode sets in accordance with a modal ordering scheme derived from balanced realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced-order system with that of the full-order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method.

Trajectory optimization on a parallel processor

Abstract: The design of a trajectory for an aerospace vehicle involves choosing a set of variables to optimally shape the path of the vehicle. Typically the trajectory is simulated by numerically solving the differential equations describing the dynamics of the vehicle. The optimal trajectory is usually determined by using a nonlinear programming (parameter optimization) algorithm to select the variables. Problems that require choosing control functions are usually reduced to choosing a finite set of parameters. The computational expense of a trajectory optimization is dominated by two factors: the cost of simulating a trajectory and the cost of computing gradient information for the optimization algorithm. This paper presents a technique for using a parallel processor to reduce the cost of these calculations. The trajectory is broken into phases, which can be simulated in parallel, thereby reducing the cost of an individual trajectory. This multiple shooting technique has been suggested by a number of authors. The nonlinear optimization problem that results from this formulation produces a Jacobian matrix that is sparse. The Jacobian is computed using sparse finite differencing, which is also performed in parallel, thereby reducing the cost of obtaining gradient information for the optimization algorithm. This paper describes the application of sparse finite differencing to a multiple shooting formulation of the two-point boundary-value problem, in a manner suitable for implementation on a parallel processor. Computational experience with the algorithm as implemented on the BBN GPIOOO (Butterfly) parallel processing computer is described.

Control of uncertain structures using an H(infinity) power flow approach

Abstract: A technique is described for generating guaranteed stable control laws for uncertain, modally dense structures with collocated sensors and actuators. By ignoring the reverberant response created by reflections from other parts of the structure, a dereverberated mobility model can be developed that accurately models the local dynamics of the structure. This is similar in many respects to a wave-based model, but can treat more general structures, not only those that can be represented as a collection of waveguides. This model can be determined directly from transfer function data using an analysis technique based on the complex cepstrum. In order to minimize the effect of disturbances propagating through the structure, the power dissipated by the controller is maximized in an //<» sense. This guarantees that the controller is positive real and, thus, that the system will remain stable for any uncertainty, provided that the power flow is correctly modeled. The approach is demonstrated for two examples. The resulting controllers are much more effective than simple collocated rate feedback.

Measure of controllability for actuator placement

Abstract: A new measure of controllability for linear time invariant dynamical systems is introduced. The controllability measure is designed especially to guide the placement of actuators to control vibrating structures. An example is presented, and the design of optimal feedback control laws for each of several actuator configurations supports the practical value of the new controllability measure.

Dynamic interpolation and application to flight control

Abstract: To simplify the specification of a desired trajectory for some subset of the variables of a dynamic control system, it may be advantageous to designate a set of intercept points that the trajectory is required to pass through. The system controls can then be computed in terms of a spline function to meet these requirements for dynamic interpolation. Optimization of a cost function under continuity constraints can be embedded in the determination of spline coefficients to obtain certain desirable geometric properties of the resulting trajectory.

Optimal trajectory synthesis for terrain-following flight

Abstract: A methodology for optimal trajectory planning useful for the nap-of-the-Earth guidance of helicopters is presented. This approach employs an adjoint-control transformatio n together with a one-dimensional search scheme for generating the time-terrain masking optimal trajectories. The trajectory planning problem bears a striking resemblance to the classical Zermelo's problem in the calculus of variations. In addition to being useful for helicopter nap-of-the-Earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and threat envelopes are incorporated into the vehicle equations of motion. Second-order necessary conditions for this problem are examined.

Time-to-go prediction for homing missiles based on minimum-time intercepts

Abstract: Two minimum-time trajectories are developed for use as a time-to-go algorithm for a missile controlled by a linear-quadratic guidance law. The first algorithm is based on the minimum normal-acceleration-weighted final time trajectory for a constant speed missile, and the second algorithm is based on the minimum final time trajectory of an accelerating missile with bounded normal acceleration. Because the initial off-boresight angle is fixed, these algorithms are expected to work well for intercepts where large off-boresight angles occur. Both time-to-go algorithms are tested in a six-degree-of-freedom simulation of a bank-to-turn missile attacking a smart target, and their miss distances are compared with those obtained by time-to-go algorithms known as range over closing speed and accelerated range over closing speed. Both algorithms give low miss distances for a wide range of intercept geometries including those with large off-boresight angles. These results are substantially improved relative to those obtained with range over closing speed. However, the accelerated range over closing speed algorithm matches the minimum-time results and is the preferred algorithm because of its simplicity.

Optimal Guidance for High-Order and Acceleration Constrained Missile

Abstract: Explicit formulas of optimal guidance for a linear, time-invariant, arbitrary-order, and acceleration constrained missile are derived. These formulas are given in terms of the missile's transfer function and acceleration constraint. Optimal, full-state feedback guidance laws are synthesized and compared to first-order approximation and the proportional navigation for minimum and nonminimum missile dynamics. Simulations on a third-order missile model show the relative gain from using the full-order guidance law vs the acceleration constraint as well as some robustness tests. HE optimal control theory has been used to derive modern/optimal guidance laws which have improved performance. The improved performance of these homing laws is achieved by a consideration of the detailed dynamics of the threat (target) and the interceptor (missile). However, it comes at the expense of increased complexity in realization (cost), sensitivity to knowledge of various parameters, etc. An extensive study of literature on guidance laws in general, and optimal guidance laws in particular, is performed by Pastrick et al.1 In various references,2'6 optimal guidance laws are derived for first- and second-order missiles, respectively. In our previous paper,7 the structure of optimal guidance laws for a linear, arbitrary high-order missile was considered. Mainly, we derived the closed-loop, general structure formulas of the guidance law. Further, we studied the behavior of the gains for minimum and nonminimum phase missiles and compared the performance of some sub-optimal approximations of the guidance laws. The effect of the acceleration constraint, which is imposed by the structural or aerodynamic limitations, on guidance laws and performance for a first-order missile is systematicall y treated by Anderson.8 In this paper we derive an optimal/moder n guidance law, on collision course, for a linear, time-invariant, arbitrary order and acceleration constrained missile. It is shown that, for a minimum phase missile, the optimal guidance law is the guidance law for an unconstrained missile with saturation on the commanded acceleration. However, for a nonminimum phase missile, this is only a suboptimal guidance law, and the optimal controller is more complicated. In the paper comparison of the proportional navigation, first-order approximation, and full-order guidance laws is performed on a third-order minimum and nonminimum phase model of a missile. The comparison is performed on a common basis. Moreover, the robustness of these guidance laws is subject to an analysis, namely, the sensitivity to uncertainty/ variation in parameters, radome refraction slope, and acceleration constraint is checked for minimum and nonminimum phase air frames. The main conclusions are that, for a minimum phase missile, the full-order guidance law does not give improved performance with respect to the first-order approximation,

Closed-loop assessment of flight simulator fidelity

Abstract: An analytical methodology is presented for the preliminary assessment of piloted flight simulator fidelity. The hypothesis that forms the central theme of the methodology is that many major simulator fidelity problems stem from simulator limitations that adversely affect the pilot's innermost feedback control loop, referred to here as the "primary control loop." This loop is the most critical in terms of task performance and the pilot's evaluation of vehicle handling qualities. The proposed methodology, based on a pilot/vehicle analysis of the vehicle and tasks being simulated, has the potential for serving as a tool for the rapid diagnosis of simulator fidelity problems. Selected results from experiments involving both flight test and piloted simulation of a UH-60A rotorcraft in a pair of demanding vertical and lateral hover tasks are used to exercise the methodology and indicate its potential.

New technique for aircraft flight control reconfiguration

Abstract: A particular algorithm is applied to the aircraft flight control reconfiguration problem. The determination of the desired control law, which can adapt in a very short period of time to major damage of a control surface, is obtained by making use of the recent control and response time histories. The estimated model of the damaged aircraft used in this technique is obtained by using a multiple model Kalman filtering approach. The model estimation and the control algorithm have been codified in a computer simulation program for a six degree-of-freedom aircraft model. The simulation results of the reconfiguration are presented.

Mission function control for a slew maneuver experiment

Abstract: A control algorithm named mission function control is experimentally demonstrated and verified on a slew maneuver of a flexible space structure model. The mission function control algorithm employs a Lyapunov-type function that consists of generalized energy functions. The model consists of a rigid body having a cantilevered flexible appendage; it is controlled to slew in a horizontal plane by a torque motor. Analytical study indicates that vibrational motion of the flexible appendage can be sensed by strain gauges as a bending moment and shear force at the root of the appendage. Results of the experiment show that a simple implementation of the algorithm leads to excellent controlled behavior of the slew maneuver as well as excellent control robustness.