Study of numeric Saturation Effects in Linear Digital Compensators

Saturation arithmetic is often used in finite precision digital compensators to circumvent instability due to radix overflow. The saturation limits in the digital structure lead to nonlinear behavior during large state transients. It is shown that if all recursive loops in a compensator are interrupted by at least one saturation limit, then there exists a bounded external scaling rule which assures against overflow at all nodes in the structure. Design methods are proposed based on the generalized second method of Lyapunov, which take the internal saturation limits into account to implement a robust dual-mode suboptimal control for bounded input plants. The saturating digital compensator provides linear regulation for small disturbances, and near-time-optimal control for large disturbances or changes in the operating point. Computer aided design tools are developed to facilitate the analysis and design of this class of digital compensators

Sampled-data control of linear systems subject to input saturation : a hybrid system approach

In this work, a new method for the stability analysis and synthesis of sampled-data control systems subject to variable sampling intervals and input saturation is proposed. From a hybrid systems representation, stability conditions based on quadratic clockdependent Lyapunov functions and the generalized sector condition to handle saturation are developed. These conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction, to estimate the maximum intersampling interval for which a region of stability is ensured, or to produce a stabilizing controller that results in a large implicit region of attraction, through the maximization of an estimate of it.Neste trabalho é proposto um novo método para a análise da estabilidade de sistemas de controle amostrados aperiodicamente e com saturação na entrada, e também para a síntese de controladores estabilizantes. A partir de uma representação por sistemas híbridos, condições de estabilidade baseadas em funções quadráticas de Lyapunov dependentes do clock e na condição de setor generalizada para o tratamento de saturação são desenvolvidas para o sistema amostrado em questão. Essas condições são incorporadas como restrições em problemas de otimização. Os problemas de otimização são baseados em programação semidefinida e em programação sum-of-squares, e têm o objetivo de obter estimativas maximizadas da região de atração do sistema, estimativas do intervalo de amostragem máximo para o qual uma dada região de estados iniciais seja uma região de estabilidade, ou para produzir controladores (dados por ganhos estáticos estabilizantes) que resultem em uma região de atração implicitamente grande, através da maximização da estimativa dessa região de atração

Study of dynamics of X-14B VTOL aircraft

Research was initiated to investigate certain facets of modern control theory and their integration with a digital computer to provide a tractable flight control system for a VTOL aircraft. Since the hover mode is the most demanding phase in the operation of a VTOL aircraft, the research efforts were concentrated in this mode of aircraft operation. Research work on three different aspects of the operation of the X-14B VTOL aircraft is discussed. A general theory for optimal, prespecified, closed-loop control is developed. The ultimate goal was optimal decoupling of the modes of the VTOL aircraft to simplify the pilot's task of handling the aircraft. Modern control theory is used to design deterministic state estimators which provide state variables not measured directly, but which are needed for state variable feedback control. The effect of atmospheric turbulence on the X-14B is investigated. A maximum magnitude gust envelope within which the aircraft could operate stably with the available control power is determined

Méthode itérative linéaire pour le contrôle en boucle fermée des écoulements quasi-périodiques

International audienceThis work proposes a feedback-loop strategy to suppress intrinsic oscillations of resonating flows in the fully nonlinear regime. The frequency response of the flow is obtained from the resolvent operator about the mean flow, extending the framework initially introduced by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to study receptivity mechanisms in turbulent flows. Using this linear time-invariant model of the nonlinear flow, modern control methods such as structured H∞-synthesis can be used to design a controller. The approach is successful in damping self-sustained oscillations associated with specific eigenmodes of the mean-flow spectrum. Despite excellent performance, the linear controller is however unable to completely suppress flow oscillations, and the controlled flow is effectively attracted towards a new dynamical equilibrium. This new attractor is characterized by a different mean flow, which can in turn be used to design a second controller. The method can then be iterated on subsequent mean flows, until the coupled system eventually converges to the base flow. An intuitive parallel can be drawn with Newton’s iteration: at each step, a linearized model of the flow response to a perturbation of the input is sought, and a new linear controller is designed, aiming at further reducing the fluctuations. The method is illustrated on the well-known case of two-dimensional incompressible open-cavity flow at Reynolds number Re=7500, where the fully developed flow is initially quasiperiodic (2-torus state). The base flow is reached after five iterations. The present work demonstrates that nonlinear control problems may be solved without resorting to nonlinear reduced-order models. It also shows that physically relevant linear models can be systematically derived for nonlinear flows, without resorting to black-box identification from input–output data; the key ingredient being frequency-domain models based on the linearized Navier–Stokes equations about the mean flow. Applicability to amplifier flows and turbulent dynamics has, however, yet to be investigated

Cascaded Control for Improved Building HVAC Performance

As of 2011 buildings consumed 41% of all primary energy in the U.S. and can represent more than 70% of peak demand on the electrical grid. Usage by this sector has grown almost 50% since the 1980s and projections foresee an additional growth of 17% by 2035 due to increases in population, new home construction, and commercial development. Three-quarters of building energy is derived from fossil fuels making it a large contributor of the country’s CO2 and NOx output both of which greatly affect the environment and local air quality. Up to half of energy used by the building sector is related to Heating, Ventilation, and Air-Condition systems. Focusing on improving building HVAC control therefore has a large aggregate effect on US energy usage with economic and environmental benefits for end users. This dissertation develops cascaded loop architectures as a solution to common HVAC control issues. These systems display strong load-dependent nonlinearities and coupling behaviors that can lead to actuator hunting (sustained input oscillations) from standard PI controllers that waste energy and cost money. Cascaded loops offer a simple way to eliminate hunting and decouple complex HVAC systems with minimal a priori knowledge of system dynamics. As cascaded loops are easily implementable in building automation systems they can be readily and widely adopted in the field. An examination of the current state of PI control in HVAC and discussion of coordinated, optimal control strategies being developed for reduced energy usage are discussed in Chapter 1. The following two chapters outline the structure and benefits of the cascaded architecture and demonstrate the same using a series of simulation case studies. Implementation approaches and parameterizations of the architecture are explored in Chapter 4 with a derivation showing that the addition of an additional feedback path (i.e., inner loop control) provides more design freedom and ultimately allows for improved control. Finally, Chapter 5 details results from initial cascaded loop implementation at three campus buildings. Results showed improved control performance and an elimination of identified hunting behavior

Study, definition and analysis of pilot/system performance measurements for planetary entry experiments

Definition analysis for experimental prediction of pilot performance during planetary entr

Some Results on Reset Control systems

Hybrid controllers are flexible tools for achieving system stabilization and/or performance improvement tasks. More particularly, hybrid controllers enrich the spectrum of achievable trade-offs. Indeed, the interaction of continuous- and discrete-time dynamics in a hybrid controller leads to rich dynamical behavior and phenomena not encountered in purely continuous-time system. Reset control systems are a class of hybrid controllers whose states are reset depending on an algebraic condition. In this thesis, we propose constructive conditions (Linear Matrix Inequalities) to analyze stability and performance level of a closed-loop system including a reset element. More particularly, we consider a magnitude saturation which could be the source of undesirable effects on these performances, including instability. Proposed results estimate the stability domain and a performance level of such a system, by using Lyapunov-like approaches. Constructive algorithms are obtained by exploiting properties of quadratic - or piecewise quadratic - Lyapunov functions. Beyond analysis results, we propose design methods to obtain a stability domain as large as possible. Design methods are based on both continuous-time approaches (anti-windup compensator) and hybrid-time approaches (design of adapted reset rules)

Variable structure techniques in control system design

During the last twenty years, control theorists belonging almost exclusively to the USSR, have laid down the foundations of variable-structure systems (commonly abbreviated to vsS). As the name implies, such systems are allowed to change their structure through time in accordance with some preassigned algorithm. The theory has demonstrated that some significant advantages could be gained by adopting that approach in the, design of automatic control systems, amongst which are good transient responses and insensitivity to parametric variations and to external disturbances. The VS controller is slightly more complex than a fixed structure design based on standard methods such as state feedback or frequency response techniques, but is a great deal less complex than some adaptive designs. It also lends itself to a straightforward microcomputer implementation. While the theoretical aspect of VSS has been well explored, its general applicability to engineering problems is yet to be established. There are still unanswered questions as to the suitability of the method for practical systems, which invariably contain a certain amount of noise, uncertainties and nonlinearities. The work described in this thesis concentrates on that particular aspect and is, in brief, an investigation of VSS as an engineering design procedure. The theory of VSS is reviewed and the principles are then applied to a number of engineering examples. The performance of the systems are assessed from digital simulation runs, hybrid computation and the microcomputer control of a DC motor

Proceedings of the 4th Annual SCOLE Workshop

This publication is a collection of papers presented at the Fourth Annual Spacecraft Control Laboratory Experiment (SCOLE) Workshop held at the U.S.A.F. Academy, Colorado Springs, Colorado, November 16, 1987. The papers address the modeling, systems identification, and control synthesis for the Spacecraft Control Laboratory Experiment (SCOLE) configuration