bluuebunny/crossref_metadata_2025_split huggingface dataset:
Computation of infimalH∞norm over a finite horizon
Authors: Subrahmanyam M. B. 
Published: July 2007

AbstractIn this paper we develop necessary conditions for a minimax problem involving control and exogenous inputs. The problem can be regarded as a finite horizon version of theH∞optimal control problem. We consider problems involving generalized cost functional and non‐zero initial conditions. A criterion for the evaluation of the performance index is given in these cases. Our computational experience shows that the finite horizon performance is useful in computing the infimalH∞norm in the infinite horizon case, as the final time becomes large. Also, expressions are derived for the variation in performance in terms of system parameter variations. These linear expressions are useful in the evaluation of the robustness of the proposed control strategy.
H∞ estimation for uncertain systems
Authors: Fu Minyue , de Souza Carlos E. , Xie Lihua 
Published: July 2007

AbstractThis paper deals with the problem of H∞ estimation for linear systems with a certain type of time‐varying norm‐bounded parameter uncertainty in both the state and output matrices. We address the problem of designing an asymptotically stable estimator that guarantees a prescribed level of H∞ noise attenuation for all admissible parameter uncertainties. Both an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages. The first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic Riccati equations and a parameterization of a class of suitable H∞ estimators. The Riccati equation approach also pinpoints the ‘worst‐case’ uncertainty.
Modelling and decentralized control of a multizone crystal growth furnace
Authors: Abraham R. , Lunze J. 
Published: July 2007

AbstractThe controller of a crystal growth furnace with 15 heating zones must have a decentralized structure. It is shown that each control station must necessarily satisfy a certain robustness property and that the design of the whole decentralized controller can be replaced by the problem of designing the control stations separately from each other as robust centralized controllers. As a basis for this, it is shown that the model can be considerably reduced. Although the zones are strongly coupled it will be seen here that, owing to structural properties of the plant, the furnace can be described by a model which has regard to only three zones. Experimental results with furnace illustrate the modelling and design methods used.
Robust control design of power system stabilizers using multivariable frequency domain techniques
Authors: Chow J. H. , Harris L. P. , Kale M. A. , Othman H. , Sanchez‐Gasca J. J. , Terwilliger G. E. 
Published: July 2007

AbstractH∞ and structured singular value optimization techniques are used to design robust power system stabilizers (PSS) for a single‐machine and a two‐machine system with varying operating conditions. Realistic uncertainty models to represent the possible operating conditions as perturbations from a nominal operating condition are developed. System experience is used to select weighting functions to provide adequate damping and shape the controller frequency response. Computer simulations show that the PSS designed using the proposed technique provides improved damping compared to a conventional PSS.
Zero cancelling compensators for singular control problems and their application to the inner–outer factorization problem
Authors: Copeland B. R. , Safonov M. G. 
Published: July 2007

AbstractMany control problems fall into the category of what we call singular control problems, i.e., problems for which known solutions fail owing to the fact that the relevant transfer functions have zeros on the extended imaginary axis, 𝒞0e. An example of this is the inner–outer factorization (IOF) problem for such transfer functions.In this paper, we show how to design compensators which would allow for a direct solution to these problems through cancellation of the offending 𝒞0e zeros. This is demonstrated for the IOF problem mentioned above. Our interest lies primarily with infinite zeros but we develop formulae for finite 𝒞0e compensators as well. The paper also presents some discussions on the infinite zero structure of linear time‐invariant systems.
Feedback control of nonlinear systems
Authors: Isidori Alberto 
Published: July 2007

AbstractThis paper deals with the design of (memoryless) state‐feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed‐loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standardH∞control problemof linear system theory. In the second one, the penalty variable is required to converge to 0 ast∞; this setup generalizes the so‐calledservomechanism problemof linear system theory.
State‐space solutions to the ℋ︁∞/LTR design problem
Authors: Stoustrup Jakob , Niemann Hans Henrik 
Published: July 2007

AbstractThe LTR design problem using an ℋ︁∞ optimality criterion is presented for two types of recovery errors, the sensitivity recovery error and the input‐output recovery error. For both errors two different approaches are presented. First, following the classical LTR design philosophy, a Luenberger observer based approach is proposed, where the ℋ︁∞ part of the controller is appended to a standard full‐order observer. Second, allowing for general controllers, an ℋ︁∞ state‐space problem is formulated directly from the recovery errors. Both approaches lead to controller orders of at most 2n. In the minimum phase case, though, the order of the controllers can be reduced to n in all cases. The control problems corresponding to the various controller types are given as four different singular ℋ︁∞ state‐space problems, and the solutions are given in terms of the relevant equations and inequalities.
Robust exponential stability of time‐varying linear systems
Authors: Hinrichsen D. , Pritchard A. J. 
Published: July 2007

AbstractThis paper investigates the robustness of time‐varying linear systems under a large class of complex time‐varying perturbations. Previous results8 which were restricted to bounded linear perturbations of output feedback type are generalized to unbounded and nonlinear perturbations of multi‐output feedback type. We establish a lower bound for the stability radius of these systems and show how it may be possible to improve the bound using time‐varying scalar transformations of the state, input and output variables. The results are applied to derive Gershgorin type stability criteria for time‐varying linear systems.
Stabilization of uncertain boundary control systems
Authors: Rebiai S. E. , Zinober A. S. I. 
Published: July 2007

AbstractWe consider a class of linear infinite‐dimensional systems subject to boundary uncertainties, which are linear and time‐invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.
Nonquadratic cost and nonlinear feedback control
Authors: Bernstein Dennis S. 
Published: July 2007

AbstractNonlinear controllers offer significant advantages over linear controllers in a variety of circumstances. Hence there has been significant interest in extending linear‐quadratic synthesis to nonlinear‐nonquadratic problems. The purpose of this paper is to review the current status of such efforts and to present, in a simplified and tutorial manner, some of the basic ideas underlying these results. Our approach focuses on the role of the Lyapunov function in guaranteeing stability for autonomous systems on an infinite horizon. Sufficient conditions for optimality are given in a form that corresponds to a steady‐state version of the Hamilton‐Jacobi‐Bellman equation. These results are used to provide a simplified derivation of the nonlinear feedback controller obtained by Bass and Webber (1966)38and to obtain a deterministic variation of the stochastic nonlinear feedback controller developed by Speyer (1976).45.
A simplified approach for the design of basically non‐interacting multiple‐input‐multiple‐output systems using qft
Authors: Oldak S. , Horowitz I. 
Published: July 2007

AbstractQuantitative feedback theory (QFT) has presented techniques for the design of multiple‐input‐multiple‐output (MIMO) linear time invariant (LTI) systems with structured parameter uncertainty in the plant P for the satisfaction of specifications on the closed loop transfer function matrix T = [Tij]. In many practical applications the specifications are of the basically non‐interacting (BNIA) type, i.e. aii(ω) < | Tii(jω) | < bii(ω), | Tij(jω) | < bij(ω), (i ≠ j) and bij(ω) < aii(ω) in a significant range of frequencies. In one QFT technique the design is based on expressing magnified image when the matrix of compensators G = diag(Gii(s)), Li = GiiQii, P−1 = [1/Qij], Dij a disturbance due to plant interaction between the different system channels. It is shown in this paper that when the specifications are BNIA and F = diag(Fii(s)), the effect of the disturbance acting on the main diagonal terms (i.e. Dii) can be neglected. This observation saves some computational burden because satisfaction of specifications on the Tiis becomes a single‐input‐single‐output (SISO) design problem instead of the more elaborated multiple‐input‐single‐output (MISO) design problem which had to be designed originally.A detailed 2‐input‐2‐output design example is presented illustrating the simpler approach, stressing the importance of considering the correlation between specifications in the design procedure.
Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. Part I: Continuous‐time theory
Authors: Haddad Wassim M. , Bernstein Dennis S. 
Published: July 2007

AbstractThe purpose of this paper is to construct Lyapunov functions to prove the key fundamental results of linear system theory, namely, the small gain (bounded real), positivity (positive real), circle, and Popov theorems. For each result a suitable Riccati‐like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time‐invariant system and a memoryless nonlinearity. Lyapunov functions for the small gain and positivity results are also constructed for the interconnection of two transfer functions. A multivariable version of the circle criterion, which yields the bounded real and positive real results as limiting cases, is also derived. For a multivariable extension of the Popov criterion, a Lure‐Postnikov Lyapunov function involving both a quadratic term and an integral of the nonlinearity, is constructed. Each result is specialized to the case of linear uncertainty for the problem of robust stability. In the case of the Popov criterion, the Lyapunov function is a parameter‐dependent quadratic Lyapunov function.
PD‐control for stablewise tracking with finite reachability time: Linear continuous‐time mimo systems with state‐space description
Authors: Grujić Ljubomir T. , Mounfield William Pratt 
Published: July 2007

AbstractThe key problems addressed and solved in the framework of time‐invariant continuous‐time multiple‐input multiple‐output (MIMO) linear systems are the following: (a) the necessary and sufficient condition on the system under which there exists a control that can force the system to exhibit a requested tracking property without using any information about the mathematical description of the system internal dynamics and external disturbances; (b) the synthesis of an output error algorithm expressing stablewise tracking with finite (pre‐specified) reachability time; (c) the synthesis of a Proportional‐Derivative (PD) control algorithm for stablewise tracking with finite (given) reachability time without utilizing a mathematical model of the system internal dynamics, its state and the unmeasured, unknown time‐varying disturbances. Simulation results illustrate the theory with an unstable MIMO system under different desired stablewise tracking settling times.
A delta transform approach to loop gain‐phase shaping design of robust digital control systems
Authors: Punyko A. J. , Bailey F. N. 
Published: July 2007

AbstractThis paper addresses the existence of loop gain‐phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum‐phase, continuous‐time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete‐time systems using the Δ‐transform, a transform method that applies to both continuous‐time and discrete‐time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.
Quantitative feedback theory with applications in welding
Authors: Bentley Anthony E. 
Published: July 2007

AbstractTwo different control systems were developed using quantitative feedback theory for weld quality improvement. The first application to be discussed was designed for the resistance pinch welding process and uses electrode displacement and force as feedback parameters. A correlation between weld quality and electrode displacement is established for constant electrode force. The system is capable of producing repeatable welds of consistent quality, with wide variations in weld parameters. This is the first time feedback control has been successfully applied to pinch welding. The second example presented in this paper was developed for penetration control of the gas‐tungsten‐arc welding process. The feedback signal is obtained by measuring the amount of light emitted from the back side of the weld. Welds of constant penetration have been demonstrated in tests with travel speeds varying from 1.5 to 6 inches per minute and with 200 per cent changes in part thickness.
A model reference quantitative feedback design theory with application to turbomachinery
Authors: Yau Chin‐Horng , Gallagher Joseph E. , Nwokah Osita D. I. 
Published: July 2007

AbstractA new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity‐based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single‐loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD‐514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.
OptimalH∞general distance problem with degree constraint
Authors: Kavranogtlu Davut , Bettayeb Maamar 
Published: July 2007

AbstractIn this paper the optimalH∞, general distance problem, for continuous‐time systems, with a prescribed degree on the solution is studied. The approach is based on designing the Hankel singular values using an imbedding idea. The problem is first imbedded into another problem with desirable characteristics on the Hankel singular values, then the solution to the original problem is retracted via a compression. The result is applicable to both the one‐block and the four‐block problems. A special case is given for illustration.
Semi‐global stabilization of minimum phase nonlinear systems in special normal form via linear high‐and‐low‐gain state feedback
Authors: Lin Zongli , Saberi Ali 
Published: July 2007

AbstractWe provide an alternative solution to the problem of semi‐global stabilization of a class of minimum phase nonlinear systems which is considered in Reference 17. Our method yields a stabilizinglinearstate feedback law in contrast to anonlinearstate feedback law proposed in Reference 17. We eliminate the peaking phenomenon by inducing a specific time‐scale structure in the linear part of the closed‐loop system. This time‐scale structure consists of a very slow and a very fast time scale. The crucial component in our method is the relation between the slow and the fast time scales. Our proposed linear state feedback control law has asingletunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in somea priorigiven (arbitrarily large) bounded set.
Fixed‐orderH∞compensator design
Authors: Yeh Hsi‐Han , Hsu Chin S. , Banda Siva S. 
Published: July 2007

AbstractA method is presented for the construction of fixed‐order compensators to provideH∞norm constraint for linear control systems with exogenous disturbances. The method is based on the celebrated bounded‐real lemma that predicates theH∞norm constraint via a Riccati inequality. The synthesis of fixed‐order controllers whose dimensions are less than the order of a given plant, is demonstrated by a set of sufficient conditions along with a numerical algorithm.
Approximate output tracking for nonlinear non‐minimum phase systems with an application to flight control
Authors: Benvenuti L. , di Benedetto M. D. , Grizzle J. W. 
Published: July 2007

AbstractAn unstable zero‐dynamics is a known obstruction to inducing exact asymptotic tracking for an open set of output trajectories with internal stability. This paper proposes a procedure for achieving approximate tracking for a nonlinear system whose linearization possesses real right‐half plane zeros. The method is guaranteed to remove the right‐half plane zeros while the other zeros remain in their previous location; moreover, it provides information on the class of signals for which good approximate tracking can be obtained. With other methods, the right‐half plane zeros are eliminated but the final location of the remaining zeros is not known a priori. The design procedure is illustrated on a trajectory control problem of an aircraft in rapid manoeuvres. Simulations illustrate the computations involved and show that precise lateral and longitudinal manoeuvres can be performed, even in the presence of uncertainties.
A linear matrix inequality approach toH∞control
Authors: Gahinet Pascal , Apkarian Pierre 
Published: July 2007

AbstractThe continuous‐ and discrete‐timeH∞control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI‐based parametrization of allH∞‐suboptimal controllers, including reduced‐order controllers.The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set ofH∞controllers and bear important connections with the controller order and the closed‐loop Lyapunov functions.Thanks to such connections, the LMI‐based characterization ofH∞controllers opens new perspectives for the refinement ofH∞design. Applications to cancellation‐free design and controller order reduction are discussed and illustrated by examples.
Optimal solutions to a two‐block ℋ︁∞problem
Authors: Meinsma Gjerrit 
Published: July 2007

AbstractIn this paper a generator of all optimal solutions to two‐block ℋ︁∞problems is derived. The derivation is in frequency domain and hinges on geometrical arguments. The results involve noncanonical Wiener‐Hopf factorization of rational matrices.
Robust control of multi‐robot systems: The generalized energy accumulation approach
Authors: Song Y. D. , Anderson J. N. , Lai H. Y. 
Published: July 2007

AbstractThis paper is concerned with the control problem of a multi‐robot system handling a common payload with unknown mass properties. Force constraints at the grasp points are considered. Robust control schemes are proposed to cope with the model uncertainty and achieve asymptotic path tracking. To deal with the force constraints, a strategy for optimally sharing the task is suggested. This strategy basically consists of two steps. The first is to detect the roots that need help and the second to arrange for help. It is shown that the overall system is robust to uncertain payload parameters, and satisfies the force constraints.
Design of minimax robust LQG controllers under parameter and noise uncertainties
Authors: Chen Wen‐Hua 
Published: July 2007

AbstractThe problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two‐person, zero‐sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least‐favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst‐case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.
New filters for internal model control design
Authors: Campi Marco , Lee Wee Sit , Anderson Brian D. O. 
Published: July 2007

AbstractIn this paper we study the design of a new two‐degree‐of‐freedom filter for the internal model control (IMC) method. The new filter alleviates some disadvantages of the standard IMC filter when the IMC method is applied to unstable plants that do not have non‐minimum‐phase zeros. We show that by employing the new filter, the resulting system has a flatter frequency response, better stability robustness, and little overshoot in the step response. Furthermore, one of its design parameters can be related directly to the closed‐loop bandwidth and the other parameter can be used to control the recovery time after an overshoot has occurred in the step response. These features are important in the application of the IMC method to a new approach of adaptive robust control. Examples are given in the paper to illustrate the new filter design.
Quadratic stabilization and tracking results applied to the benchmark problem
Authors: Dolphus R. M. , Schmitendorf W. E. 
Published: July 2007

AbstractRecent results regarding quadratic stabilization and disturbance attenuation are applied to the benchmark problem. We investigate the minimum achievable levels of disturbance attenuation for different disturbance inputs and controlled outputs. We then develop a feedforward tracking controller design which tracks step inputs while maintaining the disturbance attenuation properties of the regulator.