Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value

Identification and control of dynamical systems

Practical methods, based upon linear systems theory, are explored for applications to nonlinear phenomena and are extended to a larger class of problems. An algorithm for stabilizing, characterizing, and tracking unstable steady states and periodic orbits in multidimensional dynamical systems is developed and applied to stabilize and characterize an unstable four-cell flame front of the Kuramoto-Sivashinsky equation with six unstable degrees of freedom. A new method is presented for probing chemical reaction mechanisms experimentally with perturbations and measurements of the response. Time series analysis and the methods of linear control theory are used to determine the Jacobian matrix of a reaction at a stable stationary state subjected to random perturbations. The method is demonstrated with time series of a model system, and its performance in the presence of noise is examined. A new theory based on the construction of a multitude of linear models, each serving to represent one small region of the phase space, is presented together. Details of its implementation are presented in predicting chaotic Kuramoto-Sivashinsky wave fronts, demonstrating how it overcomes some of the problems associated with high dimensionality phase spaces. Motivated by the relationship between nonlinear prediction methods and the capabilities of neural systems, we demonstrate the possible role of nonlinear phenomena in the morphogenesis of neural tracts

Dynamic operability assessment : a mathematical programming approach based on Q-parametrization

Bibliography: pages 197-208.The ability of a process plant to guarantee high product quality, in terms of low variability, is emerging as a defining feature when distinguishing between alternative suppliers. The extent to which this can be achieved is termed a plant's dynamic operability and is a function of both the plant design and the control system design. In the limit, however, the closedloop performance is determined by the properties inherent in the plant. This realization of the interrelationship between a plant design and its achievable closed-loop performance has motivated research toward systematic techniques for screening inherently inferior designs. Pioneering research in the early 1980's identified right-half-plane transmission zeros, time delays, input constraints and model uncertainty as factors that limit the achievable closedloop performance of a process. Quantifying the performance-limiting effect of combinations of these factors has proven to be a challenging problem, as reflected in the literature. It is the aim of this thesis to develop a systematic procedure for dynamic operability assessment in the presence of combinations of performance-limiting factors. The approach adopted in this thesis is based on the Q-parametrization of stabilizing linear feedback controllers and involves posing dynamic operability assessment as a mathematical programming problet? In the proposed formulation, a convex objective function, reflecting a measure of closed-loop performance, is optimized over all stable Q, subject. to a set of constraints on the closed-loop behavior, which for many specifications of interest is convex. A discrete-time formulation is chosen so as to allow for the convenient hand.ling of time delays and time-domain constraints. An important feature of the approach is that, due to the convexity, global optimality is guaranteed. Furthermore, the fact that Q parametrizes all stabilizing linear feedback controllers implies that the performance at the optimum represents the best possible performance for any such controller. The results are thus not biased by controller type or tuning, apart from the requirement that the controller be linear

An introduction to positive switched systems and their application to HIV treatment modeling

In the present work an introduction to positive switched systems is provided, along with an interesting application of this kind of systems to the biomededical area. Reflecting this twofold objective, the thesis is divided into two parts: in the first one classical theoretical aspects concerning positive switched systems are addressed by resorting to the Lyapunov function approach, while in the second part an application to the problem of drug treatment scheduling in HIV infection is presente

Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control

The main focus in this thesis is the analysis of alternative approaches for estimation and control of automotive vehicles based on sound theoretical principles. Of particular importance is the problem rollover prevention, which is an important problem plaguing vehicles with a high center of gravity (CG). Vehicle rollover is, statistically, the most dangerous accident type, and it is difficult to prevent it due to the time varying nature of the problem. Therefore, a major objective of the thesis is to develop the necessary theoretical and practical tools for the estimation and control of rollover based on robust and adaptive techniques that are stable with respect to parameter variations. Given this background, we first consider an implementation of the multiple model switching and tuning (MMST) algorithm for estimating the unknown parameters of automotive vehicles relevant to the roll and the lateral dynamics including the position of CG. This results in high performance estimation of the CG as well as other time varying parameters, which can be used in tuning of the active safety controllers in real time. We then look into automotive rollover prevention control based on a robust stable control design methodology. As part of this we introduce a dynamic version of the load transfer ratio (LTR) as a rollover detection criterion and then design robust controllers that take into account uncertainty in the CG position. As the next step we refine the controllers by integrating them with the multiple model switched CG position estimation algorithm. This results in adaptive controllers with higher performance than the robust counterparts. In the second half of the thesis we analyze extensions of certain theoretical results with important implications for switched systems. First we obtain a non-Lyapunov stability result for a certain class of linear discrete time switched systems. Based on this result, we suggest switched controller synthesis procedures for two roll dynamics enhancement control applications. One control design approach is related to modifying the dynamical response characteristics of the automotive vehicle while guaranteeing the switching stability under parametric variations. The other control synthesis method aims to obtain transient free reference tracking of vehicle roll dynamics subject to parametric switching. In a later discussion, we consider a particular decentralized control design procedure based on vector Lyapunov functions for simultaneous, and structurally robust model reference tracking of both the lateral and the roll dynamics of automotive vehicles. We show that this controller design approach guarantees the closed loop stability subject to certain types of structural uncertainty. Finally, assuming a purely theoretical pitch, and motivated by the problems considered during the course of the thesis, we give new stability results on common Lyapunov solution (CLS) existence for two classes of switching linear systems; one is concerned with switching pair of systems in companion form and with interval uncertainty, and the other is concerned with switching pair of companion matrices with general inertia. For both problems we give easily verifiable spectral conditions that are sufficient for the CLS existence. For proving the second result we also obtain a certain generalization of the classical Kalman-Yacubovic-Popov lemma for matrices with general inertia

NASA/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program, 1985

Since 1964, the National Aeronautics and Space Administration (NASA) has supported a program of summer faculty fellowships for engineering and science educators. In a series of collaborations between NASA research and development centers and nearby universities, engineering faculty members spend 10 weeks working with professional peers on research. The Summer Faculty Program Committee of the American Society for Engineering Education supervises the programs. The objectives of this program are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to simulate and exchange ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of participants institutions; and (4) to contribute to the research objectives of the NASA center. College or university faculty members will be appointed as research fellows to spend 10 weeks in cooperative research and study at the NASA Langley Research Center. The fellows will devote approximately 90 percent of the time to a research problem and the remaining time to a study program. The study program will consist of lectures and seminars on topics of general interest or that are directly relevant to the fellows' research project. The lecturers and seminar leaders will be distinguished scientists and engineers from NASA, the educational community, or industry

The 1982 NASA/ASEE Summer Faculty Fellowship Program

A NASA/ASEE Summer Faculty Fellowship Research Program was conducted to further the professional knowledge of qualified engineering and science faculty members, to stimulate an exchange of ideas between participants and NASA, to enrich and refresh the research and teaching activities of participants' institutions, and to contribute to the research objectives of the NASA Centers

Feasibility study of an Integrated Program for Aerospace vehicle Design (IPAD). Volume 2: The design process

The extent to which IPAD is to support the design process is identified. Case studies of representative aerospace products were developed as models to characterize the design process and to provide design requirements for the IPAD computing system

De-Centralized and Centralized Control for Realistic EMS Maglev Systems

A comparative study of de-centralized and centralized controllers when used with real EMS Maglev Systems is introduced. This comparison is divided into two parts. Part I is concerned with numerical simulation and experimental testing on a two ton six-magnet EMS Maglev vehicle. Levitation and lateral control with these controllers individually and when including flux feedback control in combination with these controllers to enhance stability are introduced. The centralized controller is better than the de-centralized one when the system is exposed to a lateral disturbing force such as wind gusts. The flux feedback control when combined with de-centralized or centralized controllers does improve the stability and is more resistant and robust with respect to the air gap variations. Part II is concerned with the study of Maglev vehicle-girder dynamic interaction system and the comparison between these two controllers on this typical system based on performance and ride quality achieved. Numerical simulations of the ODU EMS Maglev vehicle interacting with girder are conducted with these two different controllers. The de-centralized and centralized control for EMS Maglev systems that interact with a flexible girder provides similar ride quality

Aeronautical Engineering: A special bibliography, supplement 60

This bibliography lists 284 reports, articles, and other documents introduced into the NASA scientific and technical information system in July 1975