Optimum controllers for linear closed-loop systems
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Boksenbom, Aaron S↗
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Results for “linear systems”
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On the analysis of linear and nonlinear dynamical systems from transient-response data
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Shinbrot, Marvin↗
A genetic technique for planning a control sequence to navigate the state space with a quasi-minimum-cost output trajectory for a non-linear multi-dimnensional system
There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.
Hein, C.↗
A General Method for Solving Systems of Non-Linear Equations
The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.
Nachtsheim, Philip R.↗
Control Reconfigurability of Linear Time-Invariant Systems
For any fault-tolerant control method to take effect, sufficient redundancy must exist in the plant (process) to be controlled. This paper is intended to establish a means of measuring the level of redundancy in connection with feedback control by borrowing the notion of the second-order modes. In particular, it is assumed that foreseeable faults of a process are parameterized in the model of the process. The smallest second-order mode is used as a measure of the potentiality of the process to maintain a certain performance through control reconfiguration at the occurrence of the worst faults over a prescribed set in the fault parameter space. This measure is called by the authors a control reconfigurability. The control reconfigurability is calculated for two process models to show its relevance to redundant actuating capabilities in the models.
Wu, N. Eva↗
Anomaly Detection in Test Equipment via Sliding Mode Observers
Nonlinear observers were originally developed based on the ideas of variable structure control, and for the purpose of detecting disturbances in complex systems. In this anomaly detection application, these observers were designed for estimating the distributed state of fluid flow in a pipe described by a class of advection equations. The observer algorithm uses collected data in a piping system to estimate the distributed system state (pressure and velocity along a pipe containing liquid gas propellant flow) using only boundary measurements. These estimates are then used to further estimate and localize possible anomalies such as leaks or foreign objects, and instrumentation metering problems such as incorrect flow meter orifice plate size. The observer algorithm has the following parts: a mathematical model of the fluid flow, observer control algorithm, and an anomaly identification algorithm. The main functional operation of the algorithm is in creating the sliding mode in the observer system implemented as software. Once the sliding mode starts in the system, the equivalent value of the discontinuous function in sliding mode can be obtained by filtering out the high-frequency chattering component. In control theory, "observers" are dynamic algorithms for the online estimation of the current state of a dynamic system by measurements of an output of the system. Classical linear observers can provide optimal estimates of a system state in case of uncertainty modeled by white noise. For nonlinear cases, the theory of nonlinear observers has been developed and its success is mainly due to the sliding mode approach. Using the mathematical theory of variable structure systems with sliding modes, the observer algorithm is designed in such a way that it steers the output of the model to the output of the system obtained via a variety of sensors, in spite of possible mismatches between the assumed model and actual system. The unique properties of sliding mode control allow not only control of the model internal states to the states of the real-life system, but also identification of the disturbance or anomaly that may occur.
Solano, Wanda M.↗
Adaptive control for linear parameter-varying systems with application to a VTOL aircraft
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Steven Snyder↗
Development of a compact linear ZAO NEG pumping system
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43 PARTICLE ACCELERATORS↗
A compact low-level RF control system for advanced concept compact electron linear accelerator
A compact low-level RF (LLRF) control system based on RF system-on-chip (RFSoC) technology has been designed for the Advanced Concept Compact Electron Linear-accelerator (ACCEL) program, which has challenging requirements in both RF performance and size, weight, and power consumption (SWaP). The compact LLRF solution employs the direct RF sampling technique of RFSoC, which samples the RF signals directly without any analog upconversion and downconversion. Compared with the conventional heterodyne based architecture used for the LLRF system of a linear accelerator (LINAC), the elimination of analog mixers can significantly reduce the size and weight of the system, especially with LINAC requiring a larger number of RF channels. Based on the requirements of ACCEL, a prototype LLRF platform has been developed, and the control schemes have been proposed. The prototype LLRF system demonstrated magnitude and phase fluctuation levels below 1% and 1° on the flattop of a 2 μs RF pulse. The LLRF control schemes proposed for ACCEL are implemented with a prototype hardware platform. In conclusion, this paper will introduce the new compact LLRF solution and summarize a selection of experimental test results of the prototype itself and with the accelerating structure cavities designed for ACCEL.
Liu, C. [SLAC National Accelerator Laboratory (SLA↗
Learning thermodynamic master equations for open quantum systems
The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.
Mathematics and Computing↗
Linear stable unity-feedback system - Necessary and sufficient conditions for stability under nonlinear plant perturbations
The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.
Desoer, C. A.↗
An improved algorithm for learning systems
Algorithm for implementing learning controller based on subgoal concept applicable to linear stationary system
Lindorff, D. P.↗
Parameter uncertainties in control system design
Design method including effects of parameter uncertainties in design of linear control systems
Palsson, T.↗
Antenna feed for linear and circular polarization
Antenna system ransmits linearly-polarized microwave radio signal, yet circularly-polarized incoming signal is received without polarization-mismatch losses. Network uses only hybrid junctions, diplexer, and four-probe antenna; no waveguide switches are required. Other circuit arrangements are possible, using additional transmitters and receivers.
Bathker, D. A.↗
Polynomial approximation of Poincare maps for Hamiltonian system
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Froeschle, Claude↗
Two-Step Multi-Physics Analysis of an Annular Linear Induction Pump for Fission Power Systems
One of the key technologies associated with fission power systems (FPS) is the annular linear induction pump (ALIP). ALIPs are used to circulate liquid-metal fluid for transporting thermal energy from the nuclear reactor to the power conversion device. ALIPs designed and built to date for FPS project applications have not performed up to expectations. A unique, two-step approach was taken toward the multi-physics examination of an ALIP using ANSYS Maxwell 3D and Fluent. This multi-physics approach was developed so that engineers could investigate design variations that might improve pump performance. Of interest was to determine if simple geometric modifications could be made to the ALIP components with the goal of increasing the Lorentz forces acting on the liquid-metal fluid, which in turn would increase pumping capacity. The multi-physics model first calculates the Lorentz forces acting on the liquid metal fluid in the ALIP annulus. These forces are then used in a computational fluid dynamics simulation as (a) internal boundary conditions and (b) source functions in the momentum equations within the Navier-Stokes equations. The end result of the two-step analysis is a predicted pump pressure rise that can be compared with experimental data.
Fission Power Systems↗
Two-Step Multi-Physics Analysis of an Annular Linear Induction Pump for Fission Power Systems
One of the key technologies associated with fission power systems (FPS) is the annular linear induction pump (ALIP). ALIPs are used to circulate liquid-metal fluid for transporting thermal energy from the nuclear reactor to the power conversion device. ALIPs designed and built to date for FPS project applications have not performed up to expectations. A unique, two-step approach was taken toward the multi-physics examination of an ALIP using ANSYS Maxwell 3D and Fluent. This multi-physics approach was developed so that engineers could investigate design variations that might improve pump performance. Of interest was to determine if simple geometric modifications could be made to the ALIP components with the goal of increasing the Lorentz forces acting on the liquid-metal fluid, which in turn would increase pumping capacity. The multi-physics model first calculates the Lorentz forces acting on the liquid metal fluid in the ALIP annulus. These forces are then used in a computational fluid dynamics simulation as (a) internal boundary conditions and (b) source functions in the momentum equations within the Navier-Stokes equations. The end result of the two-step analysis is a predicted pump pressure rise that can be compared with experimental data.
Fission Power Systems↗
Comparison of Approach-to-Critical Results in Current and Pulse Mode for Systems with High Starter Neutron Rates
Reactors and critical assemblies use a variety of detection systems to monitor the neutron population. The count rate is proportional to the neutron flux present at the location of the detector. When such systems are placed external to an assembly, it is often assumed that the relative leakage multiplication will be proportional to the detector count rate (assuming that the source term, system geometry, and detector placement have not changed). Such systems are often used in an approach-to-critical during reactor startup to ensure that the critical configuration is well predicted. Various types of detectors have been used during an approach-to-critical. These include 3 He, BF 3 , ion chambers, fission chambers, and fission foils. Any of these types of systems (or others) should work well when adequate counting statistics are available. These detector systems can be operated in either pulse or current mode. The National Criticality Experiments Research Center (NCERC) has two detection systems that are commonly used in critical assembly operations. The start-up (referred to as "SU" in this work) system is made up of 3 He proportional counters in pulse mode and the linear counter system (referred to as "LC" in this work) consists of compensated ion-chambers in current mode. Typically the SU system is used for approach-to-critical operations and the LC system is only used at/above delayed critical ( k eff = 1). This work investigates the use of the LC system for an approach-to-critical. It has been long hypothesized that such an approach would be feasible for systems with high starter neutron rates.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗