On the asymptotic stability of feedback control systems containing a single time- varying element
Asymptotic stability of feedback control systems containing single time varying element
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Asymptotic stability of feedback control systems containing single time varying element
In the last experimental campaign (OP1.2b) of the stellarator Wendelstein 7-X (W7-X), boronisation as a mean for first wall conditioning was applied for the first time which led to strongly reduced impurity fluxes from plasma-facing components. Thermal detachment at the uncooled target plates of the test divertor unit (TDU) was reached at higher plasma densities and was accompanied by high recycling of neutrals at the target plate. A feedback control system was established in W7-X to actively control the gas injection (actuator) for plasma fuelling and impurity seeding [3] through the divertors. It allowed very successful stabilisation of the detached plasma condition state as well as mitigation of thermal overloads to some baffle tiles. Different routinely available diagnostic signals were used as input parameters (sensors). We describe the setup of the feedback control system, its performance and provide some example results with the main focus on the development of the control scheme which led to the detachment stabilisation over the entire longest (30 s) high-power discharge at W7-X so far. In view of the achieved very successful detachment stabilisation and the necessity to include simultaneous optimisation of the core performance in the future, the feedback control system is being upgraded for the upcoming campaign (OP2.1) in which the water cooled and hereby inherently steady-state capable divertor has been currently installed. The prospects and some experiment ideas for active detachment control are discussed.
Electrohydrodynamic equilibrium showing continuum feedback control of Rayleigh-Taylor type instability
A summary is presented of the main results obtained during the course of research on output feedback control. The term output feedback is used to denote a controller design approach which does not rely on an observer to estimate the states of the system. Thus, the order of the controller is fixed, and can even be zero order, which amounts to constant gain ouput feedback. The emphasis has been on optimal output feedback. That is, a fixed order controller is designed based on minimizing a suitably chosen quadratic performance index. A number of problem areas that arise in this context have been addressed. These include developing suitable methods for selecting an index of performance, both time domain and frequency domain methods for achieving robustness of the closed loop system, developing canonical forms to achieve a minimal parameterization for the controller, two time scale design formulations for ill-conditioned systems, and the development of convergent numerical algorithms for solving the output feedback problem.
Feedback logic is given that produces satisfactory penetration of an aircraft through a severe downburst. The logic has two parts: (1) A switch that calls for full throttle and tight climb-rate-hold feedback logic when the magnitude of headwind-rate exceeds a threshold level; this switch stays on until re-set by the pilot after penetration of the downburst. (2) A tight climb-rate-hold autopilot, using feedback of pitch-angle to angle-of-attack. After penetration, recovery to steady climbing flight is aided by using feedback of airspeed deviation to throttle. Insights on control strategy are gained from an analysis of energy changes during flight through a downburst. Closed-loop simulations are given for a 727 aircraft penetrating severe downbursts on take-off. Boeing's recommendation of constant pitch angle was confirmed as an excellent feedback control strategy.
Optimal nonlinear feedback control derived from quartic and higher order performance criteria
Deadbeat control theory gives a feedback solution to the time optimal control of discrete time systems. Experience has shown the results to be impractical because they ignore bounds on the actuator strength. This paper develops two algorithms for generating time optimal control in feedback form for discrete systems with bounded controls. The results are also applicable for generating recovery regions and the set of reachable states. For multiple control problems a method of generating sublayers is developed which decreases off-line and on-line computational effort. Two algorithms are presented with somewhat different computational and storage requirements. The algorithms are practical within certain dimension constraints, and are natural for implementation with parallel processing.
Matrix method for optimal feedback control of linear systems
An improved feedback control system to govern the cyclic operation of the power switch of a non-dissipative power conditioning equipment. The apparatus includes two or three control loops working in unison. The first causes the output DC level to be compared with a reference, and the error amplified for control purposes. The second utilizes the AC component of the voltage across the output filter inductor or the current through the output filter capacitor, and the third loop senses the output transients.
Four different sample positioners are discussed. The four systems share a common operating principle in that the sample positioning is achieved by feedback controlled forces which can be electrostatic, dielectrophoretic, or electromagnetic. The first system is the electrostatic liquid drop positioner which operates at the near ambient position. The second system is the tetrahedral electrostatic positioner which is being developed for the high temperature materials processing in vacuum. The third system is essentially the the same tetrahedral system above except that the position control is achieved by dielectrophoretic forces in the pressurized gas environment. Finally, the feasibility of a feedback controlled electromagnetic positioner is discussed.
The results of a study of the application of H infinity and mu synthesis techniques to the design of feedback control laws for the longitudinal dynamics of the High Angle of Attack Research Vehicle (HARV) are presented. The objective of this study is to develop methods for the design of feedback control laws which cause the closed loop longitudinal dynamics of the HARV to meet handling quality specifications over the entire flight envelope. Control law designs are based on models of the HARV linearized at various flight conditions. The control laws are evaluated by both linear and nonlinear simulations of typical maneuvers. The fixed gain control laws resulting from both the H infinity and mu synthesis techniques result in excellent performance even when the aircraft performs maneuvers in which the system states vary significantly from their equilibrium design values. Both the H infinity and mu synthesis control laws result in performance which compares favorably with an existing baseline longitudinal control law.
Lateral stability augmentation of supersonic aircraft using linear multichannel state-vector optimal feedback control
The automated restoration of power systems with variable energy resources is a timely problem to tackle. Automated restoration advice can support operators in deciding on strategic actions to restore power grids from a blackout with a mix of conventional and renewable generation resources. To this end, this paper frames the restoration process of power grids with solar resources as a nonlinear dynamic model with algebraic constraints in discrete time which is steered by feedback control loops. We discuss two feedback-control strategies based on greedy and reinforcement learning algorithms, and contrast their performance with restoration plans generated by a mixed-integer linear program. We found that the reinforcement learning algorithm infers restoration actions faster than the greedy one. However, the tuning process of the reinforcement learning parameters is slower than for the greedy one.
Stochastic extensions of techniques for using Liapunov second method in design and analysis of feedback controls, using differential equations
The aim of this initial study is to incorporate an acoustic metric into the flight control system of an unmanned aerial vehicle. This could be used to mitigate the noise impact of unmanned aerial systems operating near residential communities. To incorporate an acoustic metric into a pre-existing flight control system, two things are required: a source noise model, and an acoustic controller. An acoustic model was developed based on Gutin's work to estimate propeller noise. The flight control system was augmented with a controller to reduce propeller noise using feedback control of the commanded flight speed until an acoustic target was met. This control approach focuses on modifying flight speed only, with no perturbation to the trajectory. Multiple flight simulations were performed and the results showed that integrating an acoustic metric into the flight control system of an unmanned aerial system is possible.
The calculation and implementation of the neighboring optimal feedback control law for multiinput, nonlinear dynamical systems, using discontinuous control, is discussed. An initialization procedure is described which removes the requirement that the neighboring initial state be in the neighborhood of the nominal initial state. This procedure is a bootstrap technique for determining the most appropriate control-law gain for the neighboring initial state. The mechanization of the neighboring control law described is closed loop in that the concept of time-to-go is utilized in the determination of the control-law gains appropriate for each neighboring state. The gains are chosen such that the time-to-go until the next predicted switch time or predicted final time is the same for both the neighboring and nominal trajectories. The procedure described is utilized to solve the minimum-time satellite attitude-acquisition problem.
The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
The development and characteristics of electrical feedback controlled heat pipes (FCHP) are discussed. An analytical model was produced to describe the performance of the FCHP under steady state and transient conditions. An advanced thermal control flight experiment was designed to demonstrate the performance of the thermal control component in a space environment. The thermal control equipment was evaluated on the ATS-F satellite to provide performance data for the components and to act as a thermal control system which can be used to provide temperature stability of spacecraft components in future applications.