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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Stochastic Robustness: Towards a Comprehensive Robustness Tool

Stochastic robustness is a simple technique to determine the robustness of linear, time-invariant systems by Monte Carlo methods. Stochastic stability robustness has been described previously. Those results are extended here to provide insight into control system design for performance. Together, stochastic stability and performance robustness concepts constitute a comprehensive tool that can be used to analyze control system robustness properties. As well, they offer control system design insight that can set the stage for stochastic robustness synthesis. The concept of stochastic stability robustness is reviewed, stochastic performance robustness is introduced, and stochastic robustness synthesis is described qualitatively. Confidence intervals necessary for comparing control laws statistically are presented.

Ray, Laurie Ryan↗
NASA NTRS2001

Robust Fault Detection Using Robust Z1 Estimation and Fuzzy Logic

This research considers the application of robust Z(sub 1), estimation in conjunction with fuzzy logic to robust fault detection for an aircraft fight control system. It begins with the development of robust Z(sub 1) estimators based on multiplier theory and then develops a fixed threshold approach to fault detection (FD). It then considers the use of fuzzy logic for robust residual evaluation and FD. Due to modeling errors and unmeasurable disturbances, it is difficult to distinguish between the effects of an actual fault and those caused by uncertainty and disturbance. Hence, it is the aim of a robust FD system to be sensitive to faults while remaining insensitive to uncertainty and disturbances. While fixed thresholds only allow a decision on whether a fault has or has not occurred, it is more valuable to have the residual evaluation lead to a conclusion related to the degree of, or probability of, a fault. Fuzzy logic is a viable means of determining the degree of a fault and allows the introduction of human observations that may not be incorporated in the rigorous threshold theory. Hence, fuzzy logic can provide a more reliable and informative fault detection process. Using an aircraft flight control system, the results of FD using robust Z(sub 1) estimation with a fixed threshold are demonstrated. FD that combines robust Z(sub 1) estimation and fuzzy logic is also demonstrated. It is seen that combining the robust estimator with fuzzy logic proves to be advantageous in increasing the sensitivity to smaller faults while remaining insensitive to uncertainty and disturbances.

Curry, Tramone↗
NASA NTRS2012

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Dorobantu, Andrei↗
NASA NTRS1992

Robust stabilization, robust performance, and disturbance attenuation for uncertain linear systems

This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both the robust stability with optimal performance and the disturbance attenuation with H-infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance-attenuation robust-stabilizing controllers.

Wang, Yeih J.↗
NASA NTRS2001

A Robust Design Methodology for Optimal Microscale Secondary Flow Control in Compact Inlet Diffusers

It is the purpose of this study to develop an economical Robust design methodology for microscale secondary flow control in compact inlet diffusers. To illustrate the potential of economical Robust Design methodology, two different mission strategies were considered for the subject inlet, namely Maximum Performance and Maximum HCF Life Expectancy. The Maximum Performance mission maximized total pressure recovery while the Maximum HCF Life Expectancy mission minimized the mean of the first five Fourier harmonic amplitudes, i.e., 'collectively' reduced all the harmonic 1/2 amplitudes of engine face distortion. Each of the mission strategies was subject to a low engine face distortion constraint, i.e., DC60<0.10, which is a level acceptable for commercial engines. For each of these missions strategies, an 'Optimal Robust' (open loop control) and an 'Optimal Adaptive' (closed loop control) installation was designed over a twenty degree angle-of-incidence range. The Optimal Robust installation used economical Robust Design methodology to arrive at a single design which operated over the entire angle-of-incident range (open loop control). The Optimal Adaptive installation optimized all the design parameters at each angle-of-incidence. Thus, the Optimal Adaptive installation would require a closed loop control system to sense a proper signal for each effector and modify that effector device, whether mechanical or fluidic, for optimal inlet performance. In general, the performance differences between the Optimal Adaptive and Optimal Robust installation designs were found to be marginal. This suggests, however, that Optimal Robust open loop installation designs can be very competitive with Optimal Adaptive close loop designs. Secondary flow control in inlets is inherently robust, provided it is optimally designed. Therefore, the new methodology presented in this paper, combined array 'Lower Order' approach to Robust DOE, offers the aerodynamicist a very viable and economical way of exploring the concept of Robust inlet design, where the mission variables are brought directly into the inlet design process and insensitivity or robustness to the mission variables becomes a design objective.

Anderson, Bernhard H.↗
NASA NTRS1990

Stochastic Satbility and Performance Robustness of Linear Multivariable Systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.

Ryan, Laurie E.↗
NASA NTRS1990

Stochastic stability and performance robustness of linear multivariable systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters is discussed. The application of stochastic performance robustness and the relationship between performance objectives and design parameters are demonstrated by means of the example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.

Stengel, Robert F.↗
NASA NTRS2005

Robust Control Design for Systems With Probabilistic Uncertainty

This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.

Crespo, Luis G.↗
NASA NTRS1989

Application of stochastic robustness to aircraft control systems

Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.

Stengel, Robert F.↗
NASA NTRS1993

A comparative study of multivariable robustness analysis methods as applied to integrated flight and propulsion control

Three multivariable robustness analysis methods are compared and contrasted. The focus of the analysis is on system stability and performance robustness to uncertainty in the coupling dynamics between two interacting subsystems. Of particular interest is interacting airframe and engine subsystems, and an example airframe/engine vehicle configuration is utilized in the demonstration of these approaches. The singular value (SV) and structured singular value (SSV) analysis methods are compared to a method especially well suited for analysis of robustness to uncertainties in subsystem interactions. This approach is referred to here as the interacting subsystem (IS) analysis method. This method has been used previously to analyze airframe/engine systems, emphasizing the study of stability robustness. However, performance robustness is also investigated here, and a new measure of allowable uncertainty for acceptable performance robustness is introduced. The IS methodology does not require plant uncertainty models to measure the robustness of the system, and is shown to yield valuable information regarding the effects of subsystem interactions. In contrast, the SV and SSV methods allow for the evaluation of the robustness of the system to particular models of uncertainty, and do not directly indicate how the airframe (engine) subsystem interacts with the engine (airframe) subsystem.

Schierman, John D.↗
NASA NTRS2006

Towards Robust Designs Via Multiple-Objective Optimization Methods

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Man Mohan, Rai↗
NASA NTRS1981

Practical robustness measures in multivariable control system analysis

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Lehtomaki, N. A.↗
NASA NTRS1981

Robustness tests utilizing the structure of modelling error

The present investigation is essentially concerned with the extension of results presented by Lehtomaki et al. (1981) on the robustness of multivariable linear time invariant feedback control systems. The work reported by Lehtomaki et al. is based on a multivariable version of Nyquist's theorem from which several robustness theorems were derived. In connection with the current investigation a slightly more general approach based on Nyquist's theorem is given in a fundamental robustness theorem from which various robustness tests may be obtained. A fundamental characterization of robustness is considered, and important tools from matrix theory are introduced. Attention is given to robustness tests and unstructured model error, and a robustness analysis for linear systems with structured model error.

Lehtomaki, N. A.↗
NASA NTRS1990

Stochastic performance robustness of aircraft control systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a twin-jet transport aircraft control system. Concepts behind stochastic stability robustness are extended to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications and measures specific to aircraft handling qualities are introduced. Confidence intervals for both individual stochastic robustness measures and for comparing two measures are presented. The application of stochastic performance robustness, the use of confidence intervals, and tradeoffs between performance objectives are demonstrated by means of the twin-jet aircraft example.

Stengel, Robert F.↗
NASA NTRS1990

Design optimization for cost and quality: The robust design approach

Designing reliable, low cost, and operable space systems has become the key to future space operations. Designing high quality space systems at low cost is an economic and technological challenge to the designer. A systematic and efficient way to meet this challenge is a new method of design optimization for performance, quality, and cost, called Robust Design. Robust Design is an approach for design optimization. It consists of: making system performance insensitive to material and subsystem variation, thus allowing the use of less costly materials and components; making designs less sensitive to the variations in the operating environment, thus improving reliability and reducing operating costs; and using a new structured development process so that engineering time is used most productively. The objective in Robust Design is to select the best combination of controllable design parameters so that the system is most robust to uncontrollable noise factors. The robust design methodology uses a mathematical tool called an orthogonal array, from design of experiments theory, to study a large number of decision variables with a significantly small number of experiments. Robust design also uses a statistical measure of performance, called a signal-to-noise ratio, from electrical control theory, to evaluate the level of performance and the effect of noise factors. The purpose is to investigate the Robust Design methodology for improving quality and cost, demonstrate its application by the use of an example, and suggest its use as an integral part of space system design process.

Unal, Resit↗
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 NTRS1993

A Monte Carlo approach to the analysis of control system robustness

Stochastic robustness, a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems, is described. The scalar probability of instability is introduced as a measure of stability robustness. Examples are given of stochastic performance robustness measures based on classical time-domain specifications. The relationship between stochastic robustness measures and control system design parameters is discussed. The technique is demonstrated by analyzing an LQG/LTR system designed for a flexible robot arm. It is concluded that the analysis of stochastic robustness offers a good alternative to existing robustness metrics.

Ray, Laura R.↗
DOE OSTI2026

Robustness of inertial fusion energy relevant implosions to low-mode asymmetries

Inertial confinement fusion implosions for power production need to be robust. Degradation sources need to be understood and considered for an economic power plant. In this work, the impact of low-mode asymmetries on yield is studied using 2D radiation hydrodynamics simulations for inertial fusion energy relevant implosions. First, a high-gain indirectly driven capsule design is developed. This design is subsequently degraded with low-mode drive asymmetries. The results show that yield is constant with increasing amounts of asymmetry until a cliff is reached where the yield quickly drops below ignition. Robustness arises because the degraded hotspot still has enough time to get to ignition before capsule decompression. This robustness occurs even though the asymmetry couples less energy to the hotspot and causes decompression to occur sooner. The robustness is linked to the generalized Lawson parameter, χ⁠. The value of χ steadily decreases with increasing asymmetry. Once χ is close to one, the hotspot is no longer able to ignite before the capsule decompresses. A simple piston model is used to predict where the robustness cliff is for any design. The trade-off between yield and robustness is also demonstrated.

Physics - Plasma physics↗