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The author's studies in astroelasticity are reviewed, covering the dynamics of coupled systems of dynamic solids, the vibrations of a paraboloidal antenna, the thermal flutter of spacecraft boom and the effect of large structural deflection on control stability. A method proposed by Popov in nonlinear automatic control theory (1961) is used as the basis of the studies.
The paper presents an unsteady aerodynamic influence coefficient method based on the low-frequency approximation. The influence coefficients are of a type which have been used to compute steady flow about wing-body combinations; therefore, the new method may be extended readily to low-frequency unsteady flow about wing-body combinations. The validity of the method is demonstrated by comparisons with numerical results from conventional, unsteady lifting surface methods. The method is valid for arbitrary wings in supersonic flow and for wings of finite span in subsonic flow. The method, when extended to include wing-body-tail interactions, will have important applications for predicting stability, control, and gust response characteristics of large airplanes. Dynamic stability derivatives and pressure distributions are given for several planforms. The comparison with either analytical or other well established numerical methods shows good agreement.-
The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.
A description is given of the application of a multivariable control design method (SANDY) based on constrained parameter optimization to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the direct synthesis of a multiloop AFCS inner-loop feedback control system based on total energy control system (TECS) principles. The design procedure offers a structured approach for the determination of a set of stabilizing controller design gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The approach can be extended to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by proper formulation of the design objectives and constraints. Satisfactory designs are usually obtained in few iterations. Performance characteristics of the optimized TECS design have been improved, particularly in the areas of closed-loop damping and control activity in the presence of turbulence.
Over the last five decades, extensive research has been performed to design and develop adaptive control systems for aerospace systems and other applications where the capability to change controller behavior at different operating conditions is highly desirable. Although adaptive flight control has been partially implemented through the use of gain-scheduled control, truly adaptive control systems using learning algorithms and on-line system identification methods have not seen commercial deployment. The reason is that the certification process for adaptive flight control software for use in national air space has not yet been decided. The purpose of this paper is to examine the gaps between the state-of-the-art methodologies used to certify conventional (i.e., non-adaptive) flight control system software and what will likely to be needed to satisfy FAA airworthiness requirements. These gaps include the lack of a certification plan or process guide, the need to develop verification and validation tools and methodologies to analyze adaptive controller stability and convergence, as well as the development of metrics to evaluate adaptive controller performance at off-nominal flight conditions. This paper presents the major certification gap areas, a description of the current state of the verification methodologies, and what further research efforts will likely be needed to close the gaps remaining in current certification practices. It is envisioned that closing the gap will require certain advances in simulation methods, comprehensive methods to determine learning algorithm stability and convergence rates, the development of performance metrics for adaptive controllers, the application of formal software assurance methods, the application of on-line software monitoring tools for adaptive controller health assessment, and the development of a certification case for adaptive system safety of flight.
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.
Asymptotic stability of feedback control systems containing single time varying element
High-contrast imaging systems using active control with adaptive optics (AO) are often limited by non-common path (NCP) aberrations that are seen only at the final science image. AO systems employing focal-plane wavefront sensors (FP-WFSs) are able to simultaneously correct NCP aberrations and measure science images, but they typically require a second stage of control that adds system cost and complexity. We present control algorithms to augment AO systems with FP-WFSs within their existing control setup. We demonstrate inter-arm NCP aberration transfer can be mitigated through temporal filtering, present frequency- and time-domain validation of controller stability and performance, and discuss the optimality of the chosen controllers. This work will enable the development, testing, and installation of FP-WFS technologies for direct imaging of exoplanets.
The hypersonic stability, control, and performance characteristics of two configurations have been determined. Each configuration had a 50 deg swept delta wing, a vertical tail, and a body flap. One model represented a control configured vehicle with a reduced level of longitudinal static stability; the other model was designed for a conventional level of stability. Data were obtained over an angle of attack range of 0 deg to 50 deg and included effects of component buildup. In addition, the effects of the vertical tail on the lateral directional characteristics were obtained.
The convergence of finite dimensional controllers for infinite dimensional systems designed using approximations is examined. Stable coprime factorization theory is used to show that under the standard assumptions of uniform stabilizability/detectability, the controllers stabilize the original system for large enough model order. The controllers converge uniformly to an infinite dimensional controller, as does the closed loop response.
Stability analysis algorithm for estimating equilibrium state of OAO control system
Large space structures are characterized by the following features: they are in general infinite-dimensional systems, and have large numbers of undamped or lightly damped poles. Any attempt to apply linear control theory to large space structures must therefore take into account these features. Phase I consisted of an attempt to apply the recently developed Stable Factorization (SF) design philosophy to problems of large space structures, with particular attention to the aspects of robustness and fault tolerance. The final report on the Phase I effort consists of four sections, each devoted to one task. The first three sections report theoretical results, while the last consists of a design example. Significant results were obtained in all four tasks of the project. More specifically, an innovative approach to order reduction was obtained, stabilizing controller structures for plants with an infinite number of unstable poles were determined under some conditions, conditions for simultaneous stabilizability of an infinite number of plants were explored, and a fault tolerance controller design that stabilizes a flexible structure model was obtained which is robust against one failure condition.
A game theoretic controller is developed for a linear time-invariant system with parameter uncertainties in system and input matrices. The input-output decomposition modeling for the plant uncertainty is adopted. The uncertain dynamic system is represented as an internal feedback loop in which the system is assumed forced by fictitious disturbance caused by the parameter uncertainty. By considering the input and the fictitious disturbance as two noncooperative players, a differential game problem is constructed. It is shown that the resulting time invariant controller stabilizes the uncertain system for a prescribed uncertainty bound. This game theoretic controller is applied to the momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Inclusion of the external disturbance torque to the design procedure results in a dynamical feedback controller which consists of conventional PID control and cyclic disturbance rejection filter. It is shown that the game theoretic design, comparing to the LQR design or pole placement design, improves the stability robustness with respect to inertia variations.
An iterative numerical algorithm for simultaneously improving multiple performance and stability robustness criteria for multivariable feedback systems is developed. The unsatisfied design criteria are improved by updating the free parameters of an initial, stabilizing controller's state-space matrices. Analytical expressions for the gradients of the design criteria are employed to determine a parameter correction that improves all of the feasible, unsatisfied design criteria at each iteration. A controller design is performed using the algorithm with experimentally derived data from a large space structure test facility. Experimental results of the controller's performance at the facility are presented.
Abstract Operation-induced surface reconstruction of photoelectrodes is underexplored as a path to control stability and performance. We show how adaptive junctions form via surface reconstruction of BiVO4 during glycerol photooxidation and how these surfaces affect electrolyte-dependent kinetics and durability. Preferential V dissolution in both acidic and alkaline media forms a Bi-rich layer. In situ measurements through a dual-working-electrode platform quantify the changes in photovoltage and charge-transfer resistance derived from adaptive junction formation, while enabling quantitative separation of the driving forces for charge separation and interfacial catalysis. The reconstructed surface in acidic media improves hole-transfer kinetics, functions as a glycerol-oxidation catalyst, and imparts photostability. Surface reconstruction in alkaline media exhibits the opposite behavior, impeding hole injection. This instability is mitigated by trace Ni2+ ions, which drive in situ surface activation without cocatalyst pre-deposition. This study shows the significance of surface reconstruction in the design of durable photoelectrodes for applications targeting organic electro-oxidation.
Transfer function models for basic structural elements with boundary control reveal certain inherent properties relevant to questions of control system realization, design, and analysis of robustness. The transfer functions involved are not strictly proper, may be nonminimum phase (except for the special case of colocated actuation and sensing), and often have large number of poles on the imaginary axis. In this paper these basic questions are considered in terms of modeling and control system design for robustness. The application of algebraic methods for computing stabilizing control, based on certain exact, irrational transfer functions is investigated. Boundary control of the wave equation is considered and extension of the method to more general problems is suggested. Special attention is given to implementation issues associated with a class of infinite dimensional control laws.
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
An orientation control system prototype has been developed for hoisted payloads. This system will allow payloads to be lifted off inclined surfaces while maintaining orientation control, allowing removal of tightly packed payloads without colliding with adjacent objects. For this concept, the payload is hoisted with a crane using a rigging system composed of a cable routed through two capstans and three or four attachment points on the payload. Motors rotate the capstans to adjust the cable lengths to the payload, and thereby control the orientation of the payload. Initial testing of the prototype was completed using manual control, however the algorithms necessary to fully automate the system are presented in this paper.