Control theory. Volume 1 - Elements of modern control theory
Control theory, Volume 1, covering linear, nonlinear, stochastic, optimal, adaptive and learning systems, sensitivity analysis, etc
Greensite, A. L.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Analysis of the feedback system in a nonintrusive dynamic flowmeter for measuring Pogo oscillations
Equations were developed which describe the closed loop feedback system operation of a proposed ultrasonic, dynamic, nonintrusive flowmeter whose design is based on a constant phase, voltage controlled frequency feedback concept. These equations are based on linear feedback system theory. The time constant of a low pass filter is taken into account. The equations show that the larger the open loop gain, the smaller the error due to fluctuations in the speed of sound and the smaller the effective time constant.
Chapin, W. G.↗
ORACLS - A modern control theory design package
A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
Armstrong, E. S.↗
Nonlinear state estimation and feedback control of nonlinear and bilinear distributed parameter systems
This paper presents a theory of nonlinear state observers for nonlinear and bilinear distributed parameter systems. Convergence results are proved for these observers. Linear feedback control derived from such state observers is applied to the distributed parameter system and conditions are presented for closed-loop stability. The emphasis is on finite dimensional state observers and controllers (which can be implemented with on-line computers) and conditions for their successful operation with infinite dimensional distributed parameter systems.
Balas, M. J.↗
Models of failure in linear systems
The concept of reliability in systems theory is discussed. Emphasis is placed on identifying failed or degraded systems and constructing a strategy to control the system in the failed mode. Systems are assumed to be linear and transformations into the failed mode occur smoothly. The family into which a nominal system is embedded is examined along with the relations within the family. The class of systems into which a given system can be algebraically transformed is investigated.
Martin, C. F.↗
Development of a digital adaptive optimal linear regulator flight controller
Digital adaptive controllers have been proposed as a means for retaining uniform handling qualities over the flight envelope of a high-performance aircraft. Towards such an implementation, an explicit adaptive controller, which makes direct use of online parameter identification, has been developed and applied to the linearized lateral equations of motion for a typical fighter aircraft. The system is composed of an online weighted least-squares parameter identifier, a Kalman state filter, and a model following control law designed using optimal linear regulator theory. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for onboard implementation.
Berry, P.↗
Controlling Flexible Manipulators, an Experimental Investigation
Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.
Hastings, Gordon Greene↗
Analytical design of a high performance stability and control augmentation system for a hingeless rotor helicopter
A stability and control augmentation system (SCAS) was designed based on a set of comprehensive performance criteria. Linear optimal control theory was applied to determine appropriate feedback gains for the stability augmentation system (SAS). The helicopter was represented by six-degree-of-freedom rigid body equations of motion and constant factors were used as weightings for state and control variables. The ratio of these factors was employed as a parameter for SAS analysis and values of the feedback gains were selected on this basis to satisfy three of the performance criteria for full and partial state feedback systems. A least squares design method was then applied to determine control augmentation system (CAS) cross feed gains to satisfy the remaining seven performance criteria. The SCAS gains were then evaluated by nine degree-of-freedom equations which include flapping motion and conclusions drawn concerning the necessity of including the pitch/regressing and roll/regressing modes in SCAS analyses.
Miyajima, K.↗
A linear quadratic regulator approach to the stabilization of uncertain linear systems
This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.
Shieh, L. S.↗
Robust Kalman filter design for active flutter suppression systems
Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.
Garrard, W. L.↗
Differential geometric methods in system theory.
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
Brockett, R. W.↗
Unsymmetric Lanczos model reduction and linear state function observer for flexible structures
This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures.
Su, Tzu-Jeng↗
Active control of panel vibrations induced by boundary-layer flow
Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.
Chow, Pao-Liu↗
Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method
Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.
Kaufman, H.↗
Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method
Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.
Kaufman, H.↗
Minimum fuel attitude control of a non-linear satellite system
Nonlinear satellite system attitude control for minimum fuel consumption, deriving linear programming algorithm based on optimal control theory
Wolske, G. D.↗
Modern digital flight control system design for VTOL aircraft
Methods for and results from the design and evaluation of a digital flight control system (DFCS) for a CH-47B helicopter are presented. The DFCS employed proportional-integral control logic to provide rapid, precise response to automatic or manual guidance commands while following conventional or spiral-descent approach paths. It contained altitude- and velocity-command modes, and it adapted to varying flight conditions through gain scheduling. Extensive use was made of linear systems analysis techniques. The DFCS was designed, using linear-optimal estimation and control theory, and the effects of gain scheduling are assessed by examination of closed-loop eigenvalues and time responses.
Broussard, J. R.↗
Applications to aeronautics of the theory of transformations of nonlinear systems
The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented.
Meyer, G.↗