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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Robust Parameter Design on Dual Stochastic Response Models With Constrained Bayesian Optimization

In engineering system design, minimizing the variations of the quality measurements while guaranteeing their overall quality up to certain levels, namely the robust parameter design (RPD), is crucial. Recent works have dealt with the design of a system whose response-control variables relationship is a deterministic function with a complex shape and function evaluation is expensive. In this work, we propose a Bayesian optimization method for the RPD of stochastic functions. Dual stochastic response models are carefully designed for stochastic functions. The heterogeneous variance of the sample mean is addressed by the predictive mean of the log variance surrogate model in a two-step approach. We establish an acquisition function that favors exploration across the feasible and optimality-improvable regions to effectively and efficiently solve the stochastic constrained optimization problem. Further, the performance of our proposed method is demonstrated by the extensive numerical and case studies. Note to Practitioners-Many manufacturing processes involve undesirable variations, which create variations in the final products. For example, many emerging manufacturing processes, such as nanomanufacturing, involve complex physical and chemical dynamics and transformation, creating variations in the manufacturing output. In such processes, it is crucial to design the manufacturing processes or products so that they have minimum variations in their quality. Meanwhile, it is also important to maintain the overall quality of the designed processes or products. Furthermore, acquiring data from many advanced manufacturing processes is often very costly, especially in the designing stage. In this work, we propose a data-driven method that automatically finds the best setting of manufacturing processes or products with the minimum variations of quality and a given constraint on the average quality satisfied. Our proposed method is used before conducting every experiment; It analyzes the historical data from previous experiments and provides a setting to be used in the next experiment. Our proposed method efficiently utilizes the historical data, and thus finds the best robust setting by conducting only a small number of experiments.

42 ENGINEERING↗
NASA NTRS1987

A parameter robust LQG design synthesis with applications to control of flexible structures

An asymptotic LQG design synthesis technique is described which explicitly includes a class of structured plant uncertainties by viewing plant parameter variations as an internal feedback loop. A direct structural relationship between this class of parameter uncertainties and the weighting matrices in the design of the LQG compensator is exploited by an asymptotic procedure in which either the regulator or the filter become insensitive to parameter variations. This asymptotic approach represents a generalization of the LQG/LTR technique. Controllers designed by this new LQG method and LQG/LTR are compared by application to a mass-spring-damper system which approximates the dynamics of flexible structures. For both colocated and noncolocated sensors and actuators configurations, the LQG/LTR design is extremely sensitive to parameter variations whereas the new LQG design allows considerably improved parameter robustness.

Tahk, Minjea↗
NASA NTRS1993

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.

How, Jonathan P.↗
NASA NTRS1997

On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments

Perhaps the most prevalent use of statistics in engineering design is through Taguchi's parameter and robust design -- using orthogonal arrays to compute signal-to-noise ratios in a process of design improvement. In our view, however, there is an equally exciting use of statistics in design that could become just as prevalent: it is the concept of metamodeling whereby statistical models are built to approximate detailed computer analysis codes. Although computers continue to get faster, analysis codes always seem to keep pace so that their computational time remains non-trivial. Through metamodeling, approximations of these codes are built that are orders of magnitude cheaper to run. These metamodels can then be linked to optimization routines for fast analysis, or they can serve as a bridge for integrating analysis codes across different domains. In this paper we first review metamodeling techniques that encompass design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We discuss their existing applications in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of metamodeling techniques in given situations and how common pitfalls can be avoided.

Simpson, Timothy W.↗
NASA NTRS1990

Robust H(infinity) control design for the Space Station with structured parameter uncertainty

A robust H(infinity) control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multiparameter variations in the state-space formulation of H(infinity) control theory. An application of this robust control synthesis technique tothe Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73 percent in one of the structured uncertainty directions. The performance and stability of this new robust H(infinity) controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Byun, Kuk-Whan↗
NASA NTRS1992

Robust H infinity control design for the space station with structured parameter uncertainty

A robust H-infinity control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H-infinity controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Byun, Kuk-Whan↗
NASA NTRS1992

Robust linear quadratic designs with respect to parameter uncertainty

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel↗
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 NTRS1990

Robust integrated autopilot/autothrottle design using constrained parameter optimization

A multivariable control design method based on constrained parameter optimization was applied to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the following: (1) direct synthesis of a multivariable 'inner-loop' feedback control system based on total energy control principles; (2) synthesis of speed/altitude-hold designs as 'outer-loop' feedback/feedforward control systems around the above inner loop; and (3) direct synthesis of a combined 'inner-loop' and 'outer-loop' multivariable control system. The design procedure offers a direct and structured approach for the determination of a set of controller gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The presented approach may be applied to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by this method following careful problem formulation of the design objectives and constraints. Performance characteristics of the optimization design were improved over the current autopilot design on the B737-100 Transport Research Vehicle (TSRV) at the landing approach and cruise flight conditions; particularly in the areas of closed-loop damping, command responses, and control activity in the presence of turbulence.

Ly, Uy-Loi↗
NASA NTRS1996

NASA battery testbed: A designed experiment for the optimization of LEO battery operational parameters

Simulation of spacecraft battery operation is implemented. Robust design experiment to obtain optimum battery operational parameters is performed. It is found that short term tests using robust design of experiments can provide guidelines for optimum battery operation. It is decided to use robust design approach to provide guidelines for battery operation on current spacecraft in orbit as batteries age (GRO, UARS, EUVE, TOPEX).

Deligiannis, F.↗
NASA NTRS1991

Designing for cost

Parametric cost analysis is presently defined as the generation and application of equations to cost analysis; equations defining cost as a function of system-design parameters, performance parameters, or engineering process parameters, constitute a valuable tool for design-to-cost efforts. Cost sensitivity is expressed through the partial derivatives of these functions, furnishing insight into the magnitude and direction of cost change for given parameter changes. The robust design method thus obtained is a systematic and efficient approach for determining the near-optimum set of design parameters for cost, which highlights important factors affecting operation and performance as well as cost.

Dean, Edwin B.↗
NASA NTRS1994

Designing robust control laws using genetic algorithms

The purpose of this research is to create a method of finding practical, robust control laws. The robustness of a controller is judged by Stochastic Robustness metrics and the level of robustness is optimized by searching for design parameters that minimize a robustness cost function.

Marrison, Chris↗
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 NTRS2004

Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

Turso, James A.↗
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↗