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Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗

A robust rotorcraft flight control system design methodology utilizing quantitative feedback theory

Rotorcraft flight control systems present design challenges which often exceed those associated with fixed-wing aircraft. First, large variations in the response characteristics of the rotorcraft result from the wide range of airspeeds of typical operation (hover to over 100 kts). Second, the assumption of vehicle rigidity often employed in the design of fixed-wing flight control systems is rarely justified in rotorcraft where rotor degrees of freedom can have a significant impact on the system performance and stability. This research was intended to develop a methodology for the design of robust rotorcraft flight control systems. Quantitative Feedback Theory (QFT) was chosen as the basis for the investigation. Quantitative Feedback Theory is a technique which accounts for variability in the dynamic response of the controlled element in the design robust control systems. It was developed to address a Multiple-Input Single-Output (MISO) design problem, and utilizes two degrees of freedom to satisfy the design criteria. Two techniques were examined for extending the QFT MISO technique to the design of a Multiple-Input-Multiple-Output (MIMO) flight control system (FCS) for a UH-60 Black Hawk Helicopter. In the first, a set of MISO systems, mathematically equivalent to the MIMO system, was determined. QFT was applied to each member of the set simultaneously. In the second, the same set of equivalent MISO systems were analyzed sequentially, with closed loop response information from each loop utilized in subsequent MISO designs. The results of each technique were compared, and the advantages of the second, termed Sequential Loop Closure, were clearly evident.

Gorder, Peter James↗

X33 Reusable Launch Vehicle Control on Sliding Modes: Concepts for a Control System Development

Control of the X33 reusable launch vehicle is considered. The launch control problem consists of automatic tracking of the launch trajectory which is assumed to be optimally precalculated. It requires development of a reliable, robust control algorithm that can automatically adjust to some changes in mission specifications (mass of payload, target orbit) and the operating environment (atmospheric perturbations, interconnection perturbations from the other subsystems of the vehicle, thrust deficiencies, failure scenarios). One of the effective control strategies successfully applied in nonlinear systems is the Sliding Mode Control. The main advantage of the Sliding Mode Control is that the system's state response in the sliding surface remains insensitive to certain parameter variations, nonlinearities and disturbances. Employing the time scaling concept, a new two (three)-loop structure of the control system for the X33 launch vehicle was developed. Smoothed sliding mode controllers were designed to robustly enforce the given closed-loop dynamics. Simulations of the 3-DOF model of the X33 launch vehicle with the table-look-up models for Euler angle reference profiles and disturbance torque profiles showed a very accurate, robust tracking performance.

Shtessel, Yuri B.↗

A multiloop, digital flutter suppression control law synthesis case study

A methodology for obtaining a digital low-order, multiloop, robust control law for aeroelastic application from a full-state Linear Quadratic Gaussian design is presented. As part of the design methodology, the multivariable system robustness at the plant input and output is evaluated using singular value properties and improved using constrained optimization procedures. To validate the methodology, a digital flutter suppression system has been designed for the full-span Active Flexible Wing (AFW) wind-tunnel model as part of a collaborative effort between the NASA Langley Research Center and Rockwell International. Preliminary results for a low-order discrete, symmetric flutter suppression system design that significantly improved the AFW model stability are provided and the experiences gained during the design process are discussed.

Mukhopadhyay, Vivek↗

Hypersonic vehicle control law development using H infinity and mu-synthesis

Applicability and effectiveness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectiveness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Gregory, Irene M.↗

Hypersonic vehicle control law development using H infinity and mu-synthesis

Applicability and effectivness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectivness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting an angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Gregory, Irene M.↗

Absolute Stability And Hyperstability In Hilbert Space

Theorems on stabilities of feedback control systems proved. Paper presents recent developments regarding theorems of absolute stability and hyperstability of feedforward-and-feedback control system. Theorems applied in analysis of nonlinear, adaptive, and robust control. Extended to provide sufficient conditions for stability in system including nonlinear feedback subsystem and linear time-invariant (LTI) feedforward subsystem, state space of which is Hilbert space, and input and output spaces having finite numbers of dimensions. (In case of absolute stability, feedback subsystem memoryless and possibly time varying. For hyperstability, feedback system dynamical system.)

Wen, John Ting-Yung↗

CSI technology validation on an LSS ground experiment facility

The test bed developed at JPL for experimental evaluation of new technologies for the control of large flexible space structures is described. The experiment consists of a flexible spacecraft dynamic simulator, sensors, actuators, a microcomputer, and an advanced programming environment. The test bed has been operational for over a year, and thus far nine experiments were completed or are currently in progress. Several of these experiments were reported at the 1987 CSI conference, and several recent ones are documented in this paper, including high order adaptive control, non-parametric system identification, and mu-synthesis robust control. An aggressive program of experiments is planned for the forseeable future.

Wang, S. J.↗

Uncertainty Modeling for Robustness Analysis of Control Upset Prevention and Recovery Systems

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. Such systems (developed for failure detection, identification, and reconfiguration, as well as upset recovery) need to be evaluated over broad regions of the flight envelope and under extreme flight conditions, and should include various sources of uncertainty. However, formulation of linear fractional transformation (LFT) models for representing system uncertainty can be very difficult for complex parameter-dependent systems. This paper describes a preliminary LFT modeling software tool which uses a matrix-based computational approach that can be directly applied to parametric uncertainty problems involving multivariate matrix polynomial dependencies. Several examples are presented (including an F-16 at an extreme flight condition, a missile model, and a generic example with numerous crossproduct terms), and comparisons are given with other LFT modeling tools that are currently available. The LFT modeling method and preliminary software tool presented in this paper are shown to compare favorably with these methods.

Belcastro, Christine M.↗

Robust Decentralized Secondary Control Scheme for Inverter-based Power Networks

Inverter-dominated microgrids are quickly becoming a key building block of future power systems. They rely on centralized controllers that can provide reliability and resiliency in extreme events. Nonetheless, communication failures due to cyber-physical attacks or natural disasters can make autonomous operation of islanded microgrids challenging. This paper examines a unified decentralized secondary control scheme that is robust to inverter clock synchronization errors and can be seamlessly applied to grid-following or grid-forming control architectures. The proposed scheme overcomes the well-known stability problem that arises from parallel operation of local integral controllers. Theoretical guarantees for stability are provided along with criteria to appropriately tune the secondary control gains to achieve good frequency regulation performance while ensuring fair power sharing. The efficacy of our approach is demonstrated through simulations on a 5-bus microgrid with four grid-forming inverters.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Controller design for microgravity vibration isolation systems

Control aspects of the vibration isolation problem of manned orbiters are investigated, and a viable robust control is proposed. The application of modern control theory to this problem, incorporating frequency-weighting and disturbance accommodation techniques, is investigated. The resulting controller achieves excellent performance for plants within a reasonable range of variations from the nominal. Robust stability and performance guarantees are measured by singular value and structured singular value checks, yielding guarantees on allowable real plant parameter uncertainties and on acceptable controller and sensor phase and gain variations. The problem of unmodeled HG modes is eliminated by using frequency weighting to reduce controller bandwidth. The method is applied successfully to the single-degree-of-freedom isolation problem.

Hampton, R. D.↗

Methodologies for Root Locus and Loop Shaping Control Design with Comparisons

This paper describes some basics for the root locus controls design method as well as for loop shaping, and establishes approaches to expedite the application of these two design methodologies to easily obtain control designs that meet requirements with superior performance. The two design approaches are compared for their ability to meet control design specifications and for ease of application using control design examples. These approaches are also compared with traditional Proportional Integral Derivative (PID) control in order to demonstrate the limitations of PID control. Robustness of these designs is covered as it pertains to these control methodologies and for the example problems.

Classical ControlFeedback ControlsRoot LocusLoop S↗

Imaging X-Ray Polarimetry Explorer Mission Attitude Determination and Control Concept

The goal of the Imaging X-Ray Polarimetry Explorer (IXPE) Mission is to expand understanding of high-energy astrophysical processes and sources, in support of NASA's first science objective in Astrophysics: "Discover how the universe works." X-ray polarimetry is the focus of the IXPE science mission. Polarimetry uniquely probes physical anisotropies-ordered magnetic fields, aspheric matter distributions, or general relativistic coupling to black-hole spin-that are not otherwise measurable. The IXPE Observatory consists of Spacecraft and Payload modules. The Payload includes three polarization sensitive, X-ray detector units (DU), each paired with its corresponding grazing incidence mirror module assemblies (MMA). A deployable boom provides the correct separation (focal length) between the DUs and MMAs. These Payload elements are supported by the IXPE Spacecraft. A star tracker is mounted directly with the deployed Payload to minimize alignment errors between the star tracker line of sight (LoS) and Payload LoS. Stringent pointing requirements coupled with a flexible structure and a non-collocated attitude sensor-actuator configuration requires a thorough analysis of control-structure interactions. A non-minimum phase notch filter supports robust control loop stability margins. This paper summarizes the IXPE mission science objectives and Observatory concepts, and then it describes IXPE attitude determination and control implementation. IXPE LoS pointing accuracy, control loop stability, and angular momentum management are discussed.

Attitude Determination and Contro↗

Robust Output Feedback Control Design for Inertia Emulation by Wind Turbine Generators

Wind generation has gained widespread use as a renewable energy source. Most wind turbines and other renewables connected to the grid through converters result in a reduction in the natural inertial response to grid frequency changes. The doubly-fed induction generator (DFIG) can be controlled to compensate for this reduction and, in fact, provide faster response than traditional synchronous machines. This paper proposes to design observer based output feedback linear quadratic regulator (LQR) and H control laws to realize the inertia emulation function and deliver fast frequency support. Furthermore, the aim is to track the reference speed by a diesel synchronous generator (DSG) in order to reach the desired inertia. The control signal is computed based on a reduced order model using the balanced truncation technique. A comparison with selective modal analysis (SMA) and balanced truncation model reduction techniques is presented. Comprehensive results show the effective emulation of synthetic inertia by implementing the control laws on a nonlinear three- phase diesel-wind system. The proposed technique is analyzed for different short circuit ratio (SCR) scenarios.

17 WIND ENERGY↗

Robust precision pointing control of large space platform payloads

Large space structure (LSS) secondary controllers to enhance inherent damping, and primary controllers for controlling rigid-body modes and structural modes are discussed. It was concluded that LSS control is stable and robust and offers promise. Further investigation is needed on the effects of actuator/sensor bandwidth.

Joshi, S. M.↗

Detection of Transient Instabilities in Multi-Agent Systems and Swarms

In this paper, we introduce the novel concept of transient instabilities in multi-agent systems and swarms, i.e., a small disturbance leads to increasing-amplitude oscillations throughout the swarm, which results in a large number of interagent collisions. This instability is dominant in the transient phase of the system and it does not appear in the steady-state behavior of the system, as each agent uses Lyapunov-stable feedback control laws. We present a rigorous definition of transient instability in swarms, and discuss its key properties. We also present a sufficient condition to check if a swarm will be transient stable. Using both theoretical techniques and numerical results, we show that a simple Proportional-Integral-Derivative (PID) feedback-tracking control law is not suitable for these applications. We also present a robust control law for Euler- Lagrangian systems that maintains transient stability across static swarms or time-varying reconfiguration in swarms. Both theoretical results and numerical simulations are presented to demonstrate the effectiveness of our proposed approach.

Quadrelli, Marco B.↗

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

feed - forward↗

Robust Passification via Optimal Sensor Blending and Control Allocation

Robust passification is considered for uncertain linear, time invariant, systems having redundant actuators and sensors. The approach is to obtain optimal sensor blending and control allocation matrices that maximize the region in the parameter space in which the system remains passive. The approach results in a generalized eigenvalue problem consisting of a number of linear matrix inequalities (LMIs). Reduction of the number of LMIs is investigated, and a numerical example is given for demonstrating the approach.

Joshi, S. M.↗