Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties

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

Aircraft Loss-of-Control Accident Prevention: Switching Control of the GTM Aircraft with Elevator Jam Failures

Switching control, servomechanism, and H2 control theory are used to provide a practical and easy-to-implement solution for the actuator jam problem. A jammed actuator not only causes a reduction of control authority, but also creates a persistent disturbance with uncertain amplitude. The longitudinal dynamics model of the NASA GTM UAV is employed to demonstrate that a single fixed reconfigured controller design based on the proposed approach is capable of accommodating an elevator jam failure with arbitrary jam position as long as the thrust control has enough control authority. This paper is a first step towards solving a more comprehensive in-flight loss-of-control accident prevention problem that involves multiple actuator failures, structure damages, unanticipated faults, and nonlinear upset regime recovery, etc

Bifurcation analysis of flight control systems

Proceedings International Federation of Automatic Control Triennial World Congress, Prague, July 2005. Retrieved April 2006 from http://www.pages.drexel.edu/~hgk22/OnlinePubs/Thomas%20Kwatny%20Chang%20IFAC%202005.pdfHigh performance systems, like the F-16, when pushed to their limits encounter qualitative changes in control system properties like loss of controllability or observability. This work identifies and characterizes bifurcations occurring in a nonlinear six degree of freedom F-16 in two scenarios - straight and level flight and in a coordinated turn. Phenomena such as stall, tumbling and spin-roll departure were observed around bifurcation points. This work provides a basis for a formal understanding of how aircraft depart from controlled flight, it is a prerequisite for the systematic design of recovery strategies, and it will contribute to the design of reconfigurable control of impaired aircraft

Nonlinear reconfiguration for asymmetric failures in a six degree-of-freedom F-16

Proceedings, American Control Conference, pp 1823-1828. Retrieved April 2006 from http://www.pages.drexel.edu/~hgk22/OnlinePubs/Thomas%20Kwatny%20Chang%20ACC04%200326_WeP15.6.pdf.In this paper we consider an F-16 fighter aircraft subject to asymmetric actuator failures. To address nonsymmetric faults it is not possible to decouple the longitudinal and lateral dynamics. It is necessary to deal with a full six degree of freedom airframe. First, we outline an automated procedure to assemble symbolic and simulation models of complex aircraft. The symbolic model can be manipulated in various ways and used for both linear and nonlinear control system design. In the event of actuator failures, the failed surfaces not only cease to function as viable inputs but also impose persistent disturbances on the system. As previously shown, the problem of designing a reconfigured controller can be formulated as a nonlinear disturbance rejection problem. We apply this method to design a controller for the F-16

Aircraft Accident Prevention: Loss-of-Control Analysis

The majority of fatal aircraft accidents are associated with loss-of-control . Yet the notion of loss-of-control is not well-defined in terms suitable for rigorous control systems analysis. Loss-of-control is generally associated with flight outside of the normal flight envelope, with nonlinear influences, and with an inability of the pilot to control the aircraft. The two primary sources of nonlinearity are the intrinsic nonlinear dynamics of the aircraft and the state and control constraints within which the aircraft must operate. In this paper we examine how these nonlinearities affect the ability to control the aircraft and how they may contribute to loss-of-control. Examples are provided using NASA s Generic Transport Model

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

Indoxyl Sulfate-Induced Oxidative Stress, Mitochondrial Dysfunction, and Impaired Biogenesis Are Partly Protected by Vitamin C and N-Acetylcysteine

Indoxyl sulfate (IS) contributes to oxidative stress and endothelial dysfunction in chronic kidney disease patients. However, the role of mitochondria in IS-induced oxidative stress is not very clear. In this study, we examined whether mitochondria play a pivotal role in modulating the effects of antioxidants during IS treatment. In the context of human umbilical vein endothelial cells, we found that IS had a dose-dependent antiproliferative effect. In addition, we used flow cytometry to demonstrate that the level of reactive oxygen species increased in a dose-dependent manner after treatment with IS. High doses of IS also corresponded to increased mitochondrial depolarization and decreased mitochondrial DNA copy number and mitochondrial mass. However, these effects could be reversed by the addition of antioxidants, namely, vitamin C and N-acetylcysteine. Thus, our results suggest that IS-induced oxidative stress and antiproliferative effect can be attributed to mitochondrial dysfunction and impaired biogenesis and that these processes can be protected by treatment with antioxidants

Effects of HIP Treatment on the Microstructure of Cr50-Si50 Target

Hot Isostatic Pressing (HIP) is a process that uniquely combines higher pressure and temperature to produce materials and parts with substantially better properties than those fabricated by other methods. Commercial as-hp (hot pressing) treated Cr50-Si50 targets are used throughout this study. The aim of this paper is to discuss the methods and to find a suitable HIP treatment for the as-hp treated Cr50-Si50 target. Otherwise, we also to find the effects of microstructure on the mechanical properties of HIP treated Cr50-Si50 target. To evaluate the effects on microstructure and properties of the Cr50-Si50 target by HIP process, SEM, TEM and porosity, density inspections were performed. The experiment results show that HIP treatment at 1373 K under the pressure of 175 MPa and 4 hours for Cr50-Si50 target is the optimum condition. In this study, HIP treatment reduced the porosity of the target about 60%