Robust Dynamic Positioning of offshore vessels using mixed-μ synthesis modeling, design, and practice
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Hassani, Vahid↗
Engineering topics
Athans, Michael
Publications and source records attributed to Athans, Michael.
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↗
Robust control for uncertain structures
Viewgraphs on robust control for uncertain structures are presented. Topics covered include: robust linear quadratic regulator (RLQR) formulas; mismatched LQR design; RLQR design; interpretations of RLQR design; disturbance rejection; and performance comparisons: RLQR vs. mismatched LQR.
Douglas, Joel↗
Guaranteed properties of gain scheduled control for linear parameter-varying plants
Gain scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain scheduled design. This paper presents such an analysis for one type of gain scheduled system, namely, a linear parameter-varying plant scheduling on its exogenous parameters. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain scheduled design. These conditions confirm and formalize popular notions regarding gain scheduled design, such as the scheduling variable should 'vary slowly'.
Shamma, Jeff S.↗
A frequency-domain estimator for use in adaptive control systems
This paper presents a frequency-domain estimator that can identify both a parametrized nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
Lamaire, Richard O.↗
Gain scheduling - Potential hazards and possible remedies
A common gain scheduling rule-of-thumb is to schedule on a slow variable. In this work, it is shown how current gain scheduling practice is necessarily limited to slow variations in the scheduling variable. These limitations are revealed to be consequences of fundamental control concepts. Furthermore, it is shown how a formulation of the gain scheduling procedure can lead toward ultimately removing these restrictions.
Shamma, Jeff S.↗
Robust LQR control for the benchmark problem
An examination is made of the performance of a linear quadratic regulator which is robust to parametric uncertainty. The controller, which feeds back all states, is based upon Petersen's approach. Simulations show, using the benchmark problem, that remarkable performance robustness can be achieved.
Douglas, Joel↗
Analysis of gain scheduled control for nonlinear plants
Gain scheduling has proven to be a successful design methodology in many engineering applications. In the absence of a sound theoretical analysis, these designs come with no guarantees of the robustness, performance, or even nominal stability of the overall gain-scheduled design. An analysis is presented for two types of nonlinear gain-scheduled control systems: (1) scheduling on a reference trajectory and (2) scheduling on the plant output. Conditions which guarantee stability, robustness, and performance properties of the global gain schedule designs are given. These conditions confirm and formalize popular notions regarding gain-scheduled designs, such as that the scheduling variable should vary slowly and capture the plant's nonlinearities.
Shamma, Jeff S.↗
Nonlinear and adaptive control
The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies.
Athans, Michael↗
Design of feedback control systems for unstable plants with saturating actuators
A new control design methodology is introduced for multi-input/multi-output systems with unstable open loop plants and saturating actuators. A control system is designed using well known linear control theory techniques and then a reference prefilter is introduced so that when the references are sufficiently small, the control system operates linearly as designated. For signals large enough to cause saturations, the control law is modified in such a way to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: the modified feedback system never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directionaL properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an approximation of the AFTI-16 (Advanced Fighter Technology Integration) aircraft multivariable longitudinal dynamics.
Kapasouris, Petros↗
A method for designing robust multivariable feedback systems
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Milich, David Albert↗
Design of feedback control systems for stable plants with saturating actuators
A systematic control design methodology is introduced for multi-input/multi-output stable open loop plants with multiple saturations. This new methodology is a substantial improvement over previous heuristic single-input/single-output approaches. The idea is to introduce a supervisor loop so that when the references and/or disturbances are sufficiently small, the control system operates linearly as designed. For signals large enough to cause saturations, the control law is modified in such a way as to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of the methodology are: the modified compensator never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directional properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an academic example and the simulation of the multivariable longitudinal control of a modified model of the F-8 aircraft.
Kapasouris, Petros↗
Design of feedback control systems for stable plants with saturating actuators
A systematic control design methodology is introduced for multi-input/multi-output stable open-loop plants with multiple saturations. This new methodology is a substantial improvement over previous heuristic single-input/single-output approaches. The idea is to introduce a supervisor loop so that when the references and/or disturbances are sufficiently small, the control system operates linearly as designed. For signals large enough to cause saturations, the control law is modified in such a way as to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: the modified compensator never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directional properties of the controls are maintained, and the closed-loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated in the simulation of an academic example and the simulation of the multivariable longitudinal control of a modified model of the F-8 aircraft.
Kapasouris, Petros↗
A method for designing robust multivariable feedback systems
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the causality recovery methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Milich, David A.↗
Guaranteed properties for nonlinear gain scheduled control systems
An analysis is presented of two types of nonlinear gain-scheduled control systems: scheduling on a reference trajectory and scheduling on the plant output. Conditions are given which guarantee stability, robustness, and performance properties of the global gain-scheduled designs. These conditions confirm and formalize popular notions regarding gain-scheduled designs; e.g., that the scheduling variable should vary slowly and capture the plant's nonlinearities. These results extend the work of Shamma and Athans (1987), which addressed the case of linear plants whose dynamics depends on exogenous parameters.
Shamma, Jeff S.↗
The LQR/LTR procedure for multivariable feedback control design
This paper provides a tutorial overview of the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) design procedure for linear multivariable feedback systems. LQR/LTR is interpreted as the solution of a specific weighted H-squared tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.
Stein, Gunter↗
A frequency-domain estimator for use in adaptive control systems
The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which is called a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
Lamaire, Richard O.↗
Stability and robustness of slowly time-varying linear systems
A well-known result for finite-dimensional time-varying linear systems is that if each `frozen time' is stable, then the time-varying system is stable for sufficiently slow time-variations. These results are reviewed and extended to a class of Volterra integrodifferential equations, specifically, differential equations with a convolution operator in the right-hand-side. The results are interpreted in the context of robustness of time-varying linear systems with special emphasis on analysis of gain-scheduled control systems.
Shamma, Jeff S.↗