Engineering topics

Fischl, Robert

Publications and source records attributed to Fischl, Robert.

10 records

NASA NTRS1993

Parametric uncertainty modeling for application to robust control

Viewgraphs and a paper on parametric uncertainty modeling for application to robust control are included. Advanced robust control system analysis and design is based on the availability of an uncertainty description which separates the uncertain system elements from the nominal system. Although this modeling structure is relatively straightforward to obtain for multiple unstructured uncertainties modeled throughout the system, it is difficult to formulate for many problems involving real parameter variations. Furthermore, it is difficult to ensure that the uncertainty model is formulated such that the dimension of the resulting model is minimal. A procedure for obtaining an uncertainty model for real uncertain parameter problems in which the uncertain parameters can be represented in a multilinear form is presented. Furthermore, the procedure is formulated such that the resulting uncertainty model is minimal (or near minimal) relative to a given state space realization of the system. The approach is demonstrated for a multivariable third-order example problem having four uncertain parameters.

Belcastro, Christine M.↗

NASA NTRS1992

A monitor for the laboratory evaluation of control integrity in digital control systems operating in harsh electromagnetic environments

This paper presents a strategy for dynamically monitoring digital controllers in the laboratory for susceptibility to electromagnetic disturbances that compromise control integrity. The integrity of digital control systems operating in harsh electromagnetic environments can be compromised by upsets caused by induced transient electrical signals. Digital system upset is a functional error mode that involves no component damage, can occur simultaneously in all channels of a redundant control computer, and is software dependent. The motivation for this work is the need to develop tools and techniques that can be used in the laboratory to validate and/or certify critical aircraft controllers operating in electromagnetically adverse environments that result from lightning, high-intensity radiated fields (HIRF), and nuclear electromagnetic pulses (NEMP). The detection strategy presented in this paper provides dynamic monitoring of a given control computer for degraded functional integrity resulting from redundancy management errors, control calculation errors, and control correctness/effectiveness errors. In particular, this paper discusses the use of Kalman filtering, data fusion, and statistical decision theory in monitoring a given digital controller for control calculation errors.

Belcastro, Celeste M.↗

NASA NTRS1992

A problem formulation for glideslope tracking in wind shear using advanced robust control techniques

A formulation of the longitudinal glideslope tracking of a transport-class aircraft in severe wind shear and turbulence for application to robust control system design is presented. Mathematical wind shear models are incorporated into the vehicle mathematical model, and wind turbulence is modeled as an input disturbance signal. For this problem formulation, the horizontal and vertical wind shear gradients are treated as real uncertain parameters that vary over an entire wind shear profile. The primary objective is to examine the formulation of this problem into an appropriate design format for use in m-synthesis control system design.

Belcastro, Christine M.↗

NASA NTRS1991

Formulation of a strategy for monitoring control integrity in critical digital control systems

Advanced aircraft will require flight critical computer systems for stability augmentation as well as guidance and control that must perform reliably in adverse, as well as nominal, operating environments. Digital system upset is a functional error mode that can occur in electromagnetically harsh environments, involves no component damage, can occur simultaneously in all channels of a redundant control computer, and is software dependent. A strategy is presented for dynamic upset detection to be used in the evaluation of critical digital controllers during the design and/or validation phases of development. Critical controllers must be able to be used in adverse environments that result from disturbances caused by an electromagnetic source such as lightning, high intensity radiated field (HIRF), and nuclear electromagnetic pulses (NEMP). The upset detection strategy presented provides dynamic monitoring of a given control computer for degraded functional integrity that can result from redundancy management errors and control command calculation error that could occur in an electromagnetically harsh operating environment. The use is discussed of Kalman filtering, data fusion, and decision theory in monitoring a given digital controller for control calculation errors, redundancy management errors, and control effectiveness.

Belcastro, Celeste M.↗

NASA NTRS1991

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.

Chang, Bor-Chin↗

NASA NTRS1991

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Belcastro, Christine M.↗

NASA NTRS1991

H-infinity control with bandwidth and H2 constraints

A discussion is presented of practical issues associated with H-infinity controller design based on the results presented by Doyle et al. (1989). First, the optimal H-infinity controller based on these results is discussed from a practical application point of view. Then, tradeoffs between the H-infinity norm and other performance characteristics, specifically bandwidth and the H2 norm, are considered. It is shown that when the optimal H-infinity norm is relaxed by only 10-20 percent and the central controller from Doyle et al. is used, significant benefits in both the controller bandwidth and the H2 norm of the closed-loop system can be achieved.

Belcastro, Christine M.↗

NASA NTRS1991

Fusion techniques using distributed Kalman filtering for detecting changes in systems

A comparison is made of the performances of two detection strategies that are based on different data fusion techniques. The strategies detect changes in a linear system. One detection strategy involves combining the estimates and error covariance matrices of distributed Kalman filters, generating a residual from the used estimates, comparing this residual to a threshold, and making a decision. The other detection strategy involves a distributed decision process in which estimates from distributed Kalman filters are used to generate distributed residuals which are compared locally to a threshold. Local decisions are made and these decisions are then fused into a global decision. The performances of each of these detection schemes are compared, and it is concluded that better performance is achieved when local decisions are made and then fused into a global decision.

Belcastro, Celeste M.↗

NASA NTRS1990

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.

Chang, Bor-Chin↗

NASA NTRS1989

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Belcastro, Christine M.↗