Oguzhan Cifdaloz

Panaceas, uncertainty, and the robust control framework in sustainability science.

A critical challenge faced by sustainability science is to develop strategies to cope with highly uncertain social and ecological dynamics. This article explores the use of the robust control framework toward this end. After briefly outlining the robust control framework, we apply it to the traditional Gordon–Schaefer fishery model to explore fundamental performance–robustness and robustness–vulnerability trade-offs in natural resource management. We find that the classic optimal control policy can be very sensitive to parametric uncertainty. By exploring a large class of alternative strategies, we show that there are no panaceas: even mild robustness properties are difficult to achieve, and increasing robustness to some parameters (e.g., biological parameters) results in decreased robustness with respect to others (e.g., economic parameters). On the basis of this example, we extract some broader themes for better management of resources under uncertainty and for sustainability science in general. Specifically, we focus attention on the importance of a continual learning process and the use of robust control to inform this process.

Modeling and Control of Scramjet-Powered Hypersonic Vehicles: Challenges, Trends, & Tradeoffs

In this paper, we provide an overview of scramjet-powered hypersonic vehicle modeling and control challenges. Such vehicles are characterized by unstable non-minimum phase dynamics with significant coupling and low thrust or FER (normalized fuel equivalency ratio) margins. Recent trends in hypersonic vehicle research is summarized. To illustrate control system design issues and tradeoffs, a generic nonlinear 3DOF longitudinal dynamics model capturing aero-elastic-propulsive interactions for wedge-shaped vehicle is used. The model is analyzed over a broad range of hypersonic flight conditions (i.e. operating points). The paper highlights how vehicle level-flight static (trim) and dynamic properties change over the trimmable air-breathing corridor (∼ Mach 4.75-12.6, 70-115 kft). Particular attention is paid to thermal choking constraints imposed on control system design as a direct consequence of having a finite FER margin. The dependence of FER margin on altitude, Mach, and the bow flow turning angle is discussed. The latter depends on Mach, altitude, angle-of-attack (AOA), and forebody flexing. It is (briefly) discussed how FER margin can be estimated on the basis of Mach, altitude, and AOA if a flexing upper bound is assumed. The implication of this state-dependent nonlinear FER margin constraint as well as that of the right half plane (RHP) zero, associated with the elevator-flight path angle (FPA) map, on control system bandwidth (BW) and FPA tracking are discussed. It is argued that while the non-minimum phase zero limits the achievable closed loop FPA BW, FER coupling into FPA can be used to address this. This, however, is limited by FER margin limits and may impose constraints on the size of the FPA (and velocity) commands that can be followed. This is particularly important because the vehicle is inherently unstable which implies a closed loop system (with a finite downward gain margin) that can become destabilized if driven sufficiently deep into control saturation. A consequence of this is that designers must take note of the fact that FPA commands which are sufficiently large and/or rapid may be impossible to follow with the desired level of fidelity. This is quantified within the paper. Speed command following issues are also discussed.

Robustness, vulnerability, and adaptive capacity in small-scale social- ecological systems: The Pumpa Irrigation System in Nepal

Change in freshwater availability is arguably one of the most pressing issues associated with global change. Agriculture, which uses roughly 70% of the total global freshwater supply, figures prominently among sectors that may be adversely affected by global change. Of specific concern are small- scale agricultural systems that make up nearly 90% of all farming systems and generate 40% of agricultural output worldwide. These systems are experiencing a range of novel shocks, including increased variability in precipitation and competing demands for water and labor that challenge their capacity to maintain agricultural output. This paper employs a robustness-vulnerability trade-off framework to explore the capacity of these small-scale systems to cope with novel shocks and directed change. Motivated by the Pumpa Irrigation System in Nepal, we develop and analyze a simple model of rice-paddy irrigation and use it to demonstrate how institutional arrangements may, in becoming very well tuned to cope with specific shocks and manage particular human interactions associated with irrigated agriculture, generate vulnerabilities to novel shocks. This characterization of robustness-vulnerability trade-off relationships is then used to inform policy options to improve the capacity of small-scale irrigation systems to adapt to changes in freshwater availability.

Constraint enforcement for scramjet-powered hypersonic vehicles with significant aero-elastic-propulsion interactions

In this paper, we examine the control of a scramjet-powered hypersonic vehicle with significant aero-elastic-propulsion interactions. Such vehicles are characterized by open loop unstable non-minimum phase dynamics, low frequency aero-elastic modes, significant coupling, and hard constraints (e.g. control surface deflection limits, thrust margin). Within this paper, attention is placed on maintaining acceptable closed loop performance (i.e. tracking of speed and flight path angle commands) while satisfying hard control surface deflection constraints as well as stoichiometrically normalized fuel-equivalency-ratio (FER) margin constraints. Control surface constraints are a consequence of maximum permissible aerodynamic loading. FER margin constraints are a consequence of thermal choking (i.e. unity combustor exit Mach number) and the fact that thrust loss may not be captured for FER greater than unity. Such limits are particularly important since the vehicle is open loop unstable and “saturation” can result in instability. To address these issues, one can design conservative (i.e. less aggressive or lower bandwidth) controllers that maintain operation below saturation levels for anticipated reference commands (and disturbances). Doing so, however, unnecessarily sacrifices performance - particularly when small reference commands are issued. Within this paper, the above issues are addressed using generalized predictive control (GPC). A 3DOF longitudinal model for a generic hypersonic vehicle, which includes aero-elastic-propulsion interactions, is used to illustrate the ideas.

Robust LPV H Gain-Scheduled Hover-to-Cruise Conversion for a Tilt-Wing Rotorcraft in the Presence of CG Variations

This paper describes the development and analysis of gain-scheduled, multi-variable Hinfin control law for the conversion of a linear parameter varying (LPV) model of a high-speed autonomous rotorcraft vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing aircraft combine the high-speed cruise capabilities of a conventional airplane with the vertical takeoff and station keeping abilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An Hinfin design methodology was used to develop linear controllers along various operating points of a conversion trajectory. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. Performance robustness with respect to variation in the location of the center of gravity (eg) has been studied.

Robust LPV H ∞ gain-scheduled hover-to-cruise conversion for a tilt-wing rotorcraft in the presence of CG variations

This paper describes the development and analysis of gain-scheduled, multi-variable Hinfin control law for the conversion of a linear parameter varying (LPV) model of a high-speed autonomous rotorcraft vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing aircraft combine the high-speed cruise capabilities of a conventional airplane with the vertical takeoff and station keeping abilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An Hinfin design methodology was used to develop linear controllers along various operating points of a conversion trajectory. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. Performance robustness with respect to variation in the location of the center of gravity (eg) has been studied.

Control of distributed parameter systems subject to convex constraints: Applications to irrigation systems and Hypersonic Vehicles

This paper addresses designing finite dimensional linear time invariant (LTI) controllers for infinite dimensional LTI plants subject to H¿ mixed-sensitivity performance objectives and convex constraints. Specifically, we focus on designing control systems for two classes of systems which are generally described by hyperbolic partial differential equations: (1) irrigation systems and (2) hypersonic vehicles with flexible dynamics. The distributed parameter plant is first approximated by a finite dimensional approximant. The Youla parameterization is then used to parameterize the set of all stabilizing LTI controllers and a weighted mixed-sensitivity H¿ optimization is formulated. After transforming the infinite dimensional problem to a finite-dimensional optimization problem, convex is optimization is used to obtain the solution. Subgradient concepts are used to directly accommodate time domain specifications. Illustrative examples for irrigation systems and hypersonic vehicles are provided.

A Sampled-Data Approach to DC-DC Buck Converter Design

This paper examines the design of digital compensators for high frequency switching dc-dc buck converters. While a high sampling frequency is desirable for digital controllers to minimize intersample effects and recover the performance of the analog compensator (e.g. regulation, robustness with respect input voltage and load fluctuations), finite wordlength effects (i.e. binary approximation/truncation) become more pronounced when faster sampling rates are used. High sampling rates are also accompanied by larger power consumption. When low sampling rates are used, (appropriate truncation algorithms) permit the use of fewer bits to represent compensator coefficients. This reduces final chip area, power consumption, and cost - all very important for application-specific integrated circuit (ASIC) applications. This, however, comes at the expense of performance degradation because of zero-order-hold (ZOH) phase lag and intersample effects. This is a fundamental limitation associated with the traditional two-step design procedure - analog-design followed by conversion-to-digital. While one can compensate for the effects of the ZOH/intersample behavior, direct discrete-time design approach is more systematic. It must be noted, however, that even a direct discrete-time design approach has fundamental limitations. This is because such an approach does not directly take into account intersample behavior. Because of this, the direct design approach may result in unnecessarily (conservatively) high sampling rates.

Constrained H ∞ Mixed-Sensitivity Optimization for Infinite-Dimensional Plants: Applications to Thermal, Structural, and Aircraft Systems

This paper shows how H∞ near-optimal finite-dimensional compensators may be designed for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. The infinite-dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H∞ optimization that is convex in the Youla Q-parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite-dimensional optimization problem to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity H∞ control system design problems, subgradient concepts are used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. Illustrative examples for thermal, structural, and aircraft systems are provided

Constrained H~~ Mixed-Sensitivity Optimization for Stable Infinite-Dimensional Plants: Application to Thermal Diffusion Process

This paper shows how Hinfin near-optimal finite-dimensional compensators may be designed for stable linear time invariant (LTI) infinite dimensional plants subject to convex constraints. The infinite dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity Hinfin optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite dimensional optimization problem from to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed sensitivity Hinfin control system design problems, subgradient concepts are used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. An illustrative example for a thermal diffusion process is also provided