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This paper is concerned with the problem of designing a controller for a complex dynamical system using output feedback. The system selected for the study is the Boeing-Vertol CH-46 tandem rotor helicopter. Feedback gains are obtained by a least square solution of the nonlinear equations derived from pole-placement theory.
A general approach for distributed parameter modeling of complex dynamical systems is described. The method consists of dividing the system in parts which can be modeled by simple partial differential equations and coupling the equations thus obtained by applying Hamilton's variational formalism to the entire system. The modeling of a large, offset-fed, wrap-rib antenna is presented to illustrate the approach. Although such models are perhaps not as precise as finite element models, they can be useful for initial physical insight and parametric design.
All human-machine systems models represent context. This paper proposes a theory of context through which models may be usefully related and integrated for design. The paper presents examples of context representation in various models, describes an application to developing models for the Crew Activity Tracking System (CATS), and advances context as a foundation for integrated design of complex dynamic systems.
This paper reports on an on-going Project to investigate techniques to diagnose complex dynamical systems that are modeled as hybrid systems. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. We cast the diagnosis problem as a model selection problem. To reduce the space of potential models under consideration, we exploit techniques from qualitative reasoning to conjecture an initial set of qualitative candidate diagnoses, which induce a smaller set of models. We refine these diagnoses using parameter estimation and model fitting techniques. As a motivating case study, we have examined the problem of diagnosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.
In this paper we examine the problem of monitoring and diagnosing noisy complex dynamical systems that are modeled as hybrid systems-models of continuous behavior, interleaved by discrete transitions. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. Building on our previous work in this area (MBCG99;MBCG00), our specific focus in this paper ins on the mathematical formulation of the hybrid monitoring and diagnosis task as a Bayesian model tracking algorithm. The nonlinear dynamics of many hybrid systems present challenges to probabilistic tracking. Further, probabilistic tracking of a system for the purposes of diagnosis is problematic because the models of the system corresponding to failure modes are numerous and generally very unlikely. To focus tracking on these unlikely models and to reduce the number of potential models under consideration, we exploit logic-based techniques for qualitative model-based diagnosis to conjecture a limited initial set of consistent candidate models. In this paper we discuss alternative tracking techniques that are relevant to different classes of hybrid systems, focusing specifically on a method for tracking multiple models of nonlinear behavior simultaneously using factored sampling and conditional density propagation. To illustrate and motivate the approach described in this paper we examine the problem of monitoring and diganosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.
Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.
A portion of the Operator Function Model Expert System (OFMspert) research project is described. OFMspert is an architecture for an intelligent operator's associate or assistant that can aid the human operator of a complex, dynamic system. Intelligent aiding requires both understanding and control. The understanding (i.e., intent inferencing) ability of the operator's associate is discussed. Understanding or intent inferencing requires a model of the human operator; the usefulness of an intelligent aid depends directly on the fidelity and completeness of its underlying model. The model chosen for this research is the operator function model (OFM). The OFM represents operator functions, subfunctions, tasks, and actions as a heterarchic-hierarchic network of finite state automata, where the arcs in the network are system triggering events. The OFM provides the structure for intent inferencing in that operator functions and subfunctions correspond to likely operator goals and plans. A blackboard system similar to that of Human Associative Processor (HASP) is proposed as the implementation of intent inferencing function. This system postulates operator intentions based on current system state and attempts to interpret observed operator actions in light of these hypothesized intentions.
The computationally difficult problem of the optimal placement of excitations and sensors to maximize the observed measurements is studied within the framework of combinatorial optimization, and is solved numerically using a variation of the simulated annealing heuristic algorithm. Results of numerical experiments including a square plate and a 960 degrees-of-freedom Control of Flexible Structure (COFS) truss structure, are presented. Though the algorithm produces suboptimal solutions, its generality and simplicity allow the treatment of complex dynamical systems which would otherwise be difficult to handle.
The increasing reliance of state-of-the art, high performance aircraft on high authority stability and command augmentation systems, in order to obtain satisfactory performance and handling qualities, has made critical the achievement of a better understanding of human capabilities, limitations, and preferences during interactions with complex dynamic systems that involve task allocation between man and machine. An analytical and experimental study has been undertaken to investigate human interaction with a simple, multiloop dynamic system in which human activity was systematically varied by changing the levels of automation. Task definition has led to a control loop structure which parallels that for any multiloop manual control system, and may therefore be considered a stereotype.
A method is proposed for designing multivariable systems based on an alternate derivation of Davison's theorem on pole placement and the solution of the nonlinear equations for the feedback gains by the least square error method. Output feedback is used to control a complex dynamical system. The freedom in design, after allocating poles, is used to place zeros and/or satisfy other design objectives. This method results in algorithms which are computationally attractive. However, this is done at a considerable sacrifice in terms of the design freedom available. For a system with m inputs and p outputs only m + p variables are available instead of mp variables.
The inverted pendulum system, a canonical example of an unstable mechanical system, is often used to model the control problems encountered in the flight of rockets in the initial stages of launch, when the airspeed is too small for aerodynamic stability. A system with a flexible pendulum is a variant that more accurately simulates rocket flight nonlinearities (particularly, the flex modes of the rocket). To increase NASA capability of modeling dynamical systems for which closed form solutions are not clear or easily developed, this project aims to provide a machine learning approach that produces a learned dynamical model of the PENNY robot (a rover with a flexible inverted pendulum) from operational data. The developed approach can then be generalized to other complex dynamical systems, including but not limited to rockets and other robotic systems.
Developing computed-torque controllers for complex manipulator systems using current techniques and tools is difficult because they address the issues pertinent to simulation, as opposed to control. A new formulation of computed-torque (CT) control that leads to an automated computer-torque robot controller program is presented. This automated tool is used for simulations and experimental demonstrations of endpoint and object control from a free-flying robot. A new computed-torque formulation states the multibody control problem in an elegant, homogeneous, and practical form. A recursive dynamics algorithm is presented that numerically evaluates kinematics and dynamics terms for multibody systems given a topological description. Manipulators may be free-flying, and may have closed-chain constraints. With the exception of object squeeze-force control, the algorithm does not deal with actuator redundancy. The algorithm is used to implement an automated 2D computed-torque dynamics and control package that allows joint, endpoint, orientation, momentum, and object squeeze-force control. This package obviates the need for hand-derivation of kinematics and dynamics, and is used for both simulation and experimental control. Endpoint control experiments are performed on a laboratory robot that has two arms to manipulate payloads, and uses an air bearing to achieve very-low drag characteristics. Simulations and experimental data for endpoint and object controllers are presented for the experimental robot - a complex dynamic system. There is a certain rather wide set of conditions under which CT endpoint controllers can neglect robot base accelerations (but not motions) and achieve comparable performance including base accelerations in the model. The regime over which this simplification holds is explored by simulation and experiment.
The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.
This study investigates the dynamic regulation of the sodium cold trap purification temperature at Argonne National Laboratory’s liquid sodium test facility, employing long short-term memory (LSTM) system identification techniques. The investigation introduces an innovative hybrid approach by integrating model predictive control (MPC) based on first principles dynamic models with a multi-step time–frequency LSTM model in predicting the temperature profiles of a sodium cold trap purification system. The long short-term memory–model predictive controller (LSTM-MPC) model employs a sliding window scheme to gather training samples for multi-step prediction, leveraging historical data to construct predictive models that capture the non-linearities of the complex system dynamics without explicitly modeling the underlying physical processes. The performance of the LSTM-MPC and MPC were evaluated through simulation experiments, where both models were assessed on their capacity to maintain the cold trap temperature within predefined set-points while minimizing deviations and overshoots. Results obtained show how the data-driven LSTM-MPC model demonstrates stability and adaptability. In contrast, the traditional MPC model exhibits irregularities, particularly evident as overshoots around set-point limits, which can potentially compromise its effectiveness over long prediction time intervals. The findings obtained offer valuable insights into integrating data-driven techniques for enhancing real-time monitoring systems.
Adaptive physics-constrained superresolution diffusion is developed for noninvasive virtual diagnostics of the six-dimensional (6D) phase space density of charged particle beams. An adaptive variational autoencoder embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a 32 6 pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent two-dimensional projections. Physics-guided superresolution diffusion transforms low-resolution images of the 6D density to high resolution 256 × 256 pixel images. Unsupervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multiparticle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without retraining. Published by the American Physical Society 2025
The power system is undergoing rapid evolution with increasing penetration of inverter-based resources (IBRs), large loads, microgrids, and power electronic devices. Ensuring reliable and stable operation of the modern power grid is a multi-faceted challenge that requires detailed understanding of this complex system. Dynamic stability is a major concern in maintaining the security of power grids as the generation mixes and large loads transitions to include high shares of power electronic devices. The operation of IBRs in regions with low system strength and higher grid impedances has been found to be the main reason behind many of the power system instabilities that manifest themselves in various types of oscillations and interactions that, if not properly addressed and damped, can jeopardize the reliable operation of the power system. Weak grid conditions compound such stability problems, particularly when many IBRs operate in proximity to and connect to weak power grids. Therefore, it is important to assess grid strength for planning, integration and operation of IBRs for a given power system. In this report, we aim to understand and classify existing methodologies for grid strength assessment, along with their limitations and future needs. Further, we aim to utilize the huge untapped potential in utilizing hydro energy resources in addressing some of the pertinent challenges of grid strength and reliable operation of modern power systems. Hydropower, historically valued for its flexibility and dispatchability, now faces new constraints due to reduced share of synchronous machines in the generation mix and seasonal variability of available water resources. Yet, these same plants present untapped potential beyond energy generation - notably, as providers of critical grid services. This report explores how hydropower plants, particularly through operation as synchronous condensers, can play a pivotal role in strengthening the grid amid evolving system dynamics.
This paper briefly reviews the problems of defining and measuring the 'mental workload' of aircraft pilots and other human operators of complex dynamic systems. Of the alternative approaches the author indicates a clear preference for the use of subjective scaling. Some recent experiments from MIT and elsewhere are described which utilize subjective mental workload scales in conjunction with human decision and control tasks in the laboratory. Finally a new three-dimensional mental workload rating scale, under current development for use by IFR aircraft pilots, is presented.
Control of a slowly responding complex dynamic system such as a large supertanker poses special problems for the human. Experienced ship's crew members maneuvered a simulated ship in real time. The simulation was performed using a graphics display run by a DPD 11/40 minicomputer. The maneuvers consisted of piloting a large ship along a narrow waterway. Preliminary results suggest that the human operates as a feedforward controller utilizing the preview information for 'gross changes' in heading, and as a feedback controller for correcting small deviations. The instruments displayed on the deck do not seem to be helpful in all situations. In fact, evidence seems to indicate that some of the displays might even interfere with the pilot's attempt to form a good internal model.