Some useful expressions for optimum linear filtering in white noise. II.
Optimum linear separation of random message from additive white noise of given spectral height realized as unity feedback system
RANDOM SIGNAL↗
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Sea surface temperature anomalies, planetary waves, and air-sea feedback in the middle latitudes
Current analytical models for large-scale air-sea interactions in the middle latitudes are reviewed in terms of known sea-surface temperature (SST) anomalies. The scales and strength of different atmospheric forcing mechanisms are discussed, along with the damping and feedback processes controlling the evolution of the SST. Difficulties with effective SST modeling are described in terms of the techniques and results of case studies, numerical simulations of mixed-layer variability and statistical modeling. The relationship between SST and diabatic heating anomalies is considered and a linear model is developed for the response of the stationary atmosphere to the air-sea feedback. The results obtained with linear wave models are compared with the linear model results. Finally, sample data are presented from experiments with general circulation models into which specific SST anomaly data for the middle latitudes were introduced.
Frankignoul, C.↗
Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.
A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.
Reid, G. F.↗
A new approach to active control of rotorcraft vibration
A state-variable feedback approach is utilized for active control of rotorcraft vibration. Fuselage accelerations are passed through undamped second-order filters with resonant frequencies at N/rev. The resulting outputs contain predominantly the N/rev vibration components, phase shifted by 180 deg, and are used to drive the blade pitch to cancel this component of fuselage vibration. The linear-quadratic-gaussian (LQG) method is used to design a feedback control system utilizing these filtered accelerations. The design is based on a nine-degree-of-freedom linear model of the Rotor System Research Aircraft (RSRA) in hover and is evaluated on a nonlinear blade-element simulation of the RSRA for this flight condition. The system is shown to essentially eliminate vibrations at N/rev in all axes. The required blade-pitch amplitude is within the capability of conventional actuators at the N/rev frequency.
Gupta, N. K.↗
Wide power range microwave feedback controller
A substantially constant power level is derived over a predetermined frequency band, in each of a plurality of relatively widely spaced power ranges, from a microwave load having a predetermined amplitude versus frequency response, such as an antenna. A microwave source of substantially constant amplitude drives a forward path connected between the source and the load. A feedback path responsive to the microwave power level in the forward path derives a control voltage for the PIN attenuator. The equalizer attenuator drives a linear, crystal amplitude detector. Attenuating means included in the forward and feedback paths are selectively connected in circuit to maintain the power level of the microwave input to the amplitude detector substantially constant, even though different power ranges are supplied to the load by the forward path.
Titus, L. E.↗
Neighboring optimal guidance theory and computer program
Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.
Powers, W. F.↗
Preliminary demonstration of a robust controller design method
Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.
Anderson, L. R.↗
Design of feedback control systems for unstable plants with saturating actuators
A new control design methodology is introduced for multi-input/multi-output systems with unstable open loop plants and saturating actuators. A control system is designed using well known linear control theory techniques and then a reference prefilter is introduced so that when the references are sufficiently small, the control system operates linearly as designated. For signals large enough to cause saturations, the control law is modified in such a way to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: the modified feedback system never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directionaL properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an approximation of the AFTI-16 (Advanced Fighter Technology Integration) aircraft multivariable longitudinal dynamics.
Kapasouris, Petros↗
LQG and direct rate feedback control with model reduction on a flexible laboratory grid structure
This paper presents experimental and theoretical comparisons of three control laws applied to a complex laboratory structure. A reduced finite element model was generated for designing the control systems and then corrected based on measured mode shapes and frequencies. A standard time-invariant linear quadratic regulator with state estimation was investigated first. Two simple direct rate feedback control laws both guaranteeing stability were also designed using the reduced model. One minimizes the maximum control force and the other minimizes the same quadratic performance index as the linear quadratic regulator. The three control laws have comparable performance indices with the direct rate feedback designs having better spillover properties. Experimental results for all designs were obtained with digital implementation. It was shown that the performance of the control system designed on the basis of the corrected finite element model agreed better with experimental results than the performance of the control system designed on the basis of the uncorrected model.
Schamel, G. C., II↗
Exact-Output Tracking Theory for Systems with Parameter Jumps
In this paper we consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to nonminimum-phase systems and obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exo-system, then we develop an exact-tracking controller in a feedback form. As in standard regulator theory, we obtain a linear map from the states of the exo-system to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.
Devasia, Santosh↗
On the minimum effort regulation of stationary linear systems.
Minimum effort restoration of perturbed system to equilibrium state defined as time varying function of instantaneous state of system
TIME OPTIMAL CONTROL↗
Flux-Feedback Magnetic-Suspension Actuator
Flux-feedback magnetic-suspension actuator provides magnetic suspension and control forces having linear transfer characteristics between force command and force output over large range of gaps. Hall-effect devices used as sensors for electronic feedback circuit controlling currents flowing in electromagnetic windings to maintain flux linking suspended element at substantially constant value independent of changes in length of gap. Technique provides effective method for maintenance of constant flux density in gap and simpler than previous methods. Applications include magnetic actuators for control of shapes and figures of antennas and of precise segmented reflectors, magnetic suspensions in devices for storage of angular momentum and/or kinetic energy, and systems for control, pointing, and isolation of instruments.
Groom, Nelson J.↗
On the Stability of Collocated Controllers in the Presence or Uncertain Nonlinearities and Other Perils
Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.
Joshi, S. M.↗
Robustness properties of collocated controllers for flexible spacecraft
Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0, infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.
Joshi, S. M.↗
Feedback-Based Fault-Tolerant and Health-Adaptive Optimal Charging of Batteries
The key technology barriers that hinder the growth of Electric Vehicles (EVs) are long charging time, the shorter life-time of EV batteries, and battery safety. Specifically, EV charging protocols have significant effects on battery lifetime and safety. If not charged properly, the battery could end up with shorter life, and more importantly, improper charging can cause battery faults leading to catastrophic failures. To overcome these barriers, we propose a closed-loop feedback based approach, that enables real-time optimal fast charging protocol adaptation to battery health and possess active diagnostic capabilities in the sense that, during charging, it detects real-time faults and takes corrective action to mitigate such fault effects. We utilize battery electrical-thermal model, explicit battery capacity and power fade aging models, and thermal fault model to capture battery behavior. In conjunction with the models, we adopt linear quadratic optimal control techniques to realize the feedback-based control algorithm. Simulation studies are presented to illustrate the effectiveness of the proposed scheme.
batteries↗
Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction
Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. Furthermore, a neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.
Gaussian process↗
Impact of impurities on peeling–ballooning modes and turbulence in tokamak plasmas
This study investigates the impact of various impurity species on peeling–ballooning (PB) modes and microturbulence in tokamak plasmas through the extension of traditional two-fluid and gyro-landau-fluid (GLF) models. By incorporating finite Larmor radius (FLR) effects, the analysis provides a comprehensive understanding of impurity-driven impact and its interaction with plasma turbulence. Depending on charge state and local plasma conditions, heavy impurities may exhibit gyro-radii larger than those of main ions, which are captured in the extended GLF model presented. Following the presentation of modified two-fluid equations incorporating impurity effects, we systematically analyze the distinctions between impurity and main ion dynamics and their resultant feedback mechanisms on plasma behavior. Derivation of the linear dispersion relation enables quantification of impurity-mediated modifications to: plasma vorticity, diamagnetic drift and gyroviscous effects, electron Hall physics, and FLR effects. BOUT++ – based linear simulations corroborate this formalism, demonstrating systematic stabilization of PB modes upon impurity seeding. And then operational implications for practical impurity control strategies in tokamak devices are proposed. The results underscore the necessity of impurity management to maintain stability and optimize plasma confinement, with specific focus on how FLR effects contribute to transport dynamics. This work paves the way for enhanced modeling and simulation efforts, supporting the development of strategies to control impurity-induced turbulence and improve overall reactor performance.
BOUT++ simulation↗
The application of linear optimal control to systems containing uncertain parameters.
Linear optimal control in systems with uncertain parameters, noting application to design of compensating network for flexible booster for uncertain value of first bending mode
NETWORK SYNTHESIS↗