bluuebunny/crossref_metadata_2025 huggingface dataset:
Stable control of nonlinear systems using neural networks
Authors: Tzirkel‐Hancock E. , Fallside F.
Published: July 2007

A neural‐network‐based direct control architecture is presented that achieves output tracking for a class of continuous‐time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,1 sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance.

A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.
Coprime factorization over a class of nonlinear systems
Authors: Moore J. B. , Irlicht L.
Published: July 2007

In this paper, we consider the problem of generalizing elements of linear coprime factorization theory to a nonlinear context. The idea is to work with a suitably wide class of nonlinear systems to cover many practical situations, yet not cope with so broad a class as to disallow useful generalizations to the linear results. In particular, we work with nonlinear systems characterized in terms of (possibly time‐varying) state‐dependent matricesA(x),B(x),C(x),D(x) and an initial statex0. (This class clearly does contain the class of finite‐dimensional linear (time‐varying) systems.) We achieve first right coprime factorizations for idealized situations. To achieve stable left factorizations we specialize to the case where the matrices are output‐dependent. Alternatively, we work with systems, perhaps augmented by a direct feedthrough term, where the input is reconstructible from the output. For nonlinear feedback control systems, with plant and controller having stable left factorizations, then under appropriate regularity‐conditions earlier results have allowed the generation of the class of stabilizing controllers for a system in terms of an arbitrary stable system (parameter). Plant uncertainties, including unknown initial conditions are modelled by means of a Yula–Kucera‐type parametrization approach developed for nonlinear systems. Certain robust stabilization results are also shown, and simulations demonstrate the regulation of nonlinear plants using the techniques developed. All the results are presented in such a way that specialization for the case of linear systems is immediate.
Multi‐input/single‐output computer‐aided control design using the quantitative feedback theory
Authors: Chait Yossi , Yaniv Oded
Published: July 2007

The quantitative feedback theory is an engineering design technique of uncertain feedback systems having robust stability and robust performance specifications. The crux of the quantitative feedback theory is a transformation of robust stability and robust performance specifications into domains in the complex plane, referred to as bounds, where a nominal loop transmission should lie within. To date, a quantitative feedback theory design is being carried out using manual (i.e. graphical) procedures or search algorithms. This paper shows that there exists a formal map from the uncertain plant and each closed‐loop specification to these bounds. In particular, it is shown that each map has a closed form consisting of a quadratic inequality. These maps greatly simplify the computational aspects of the quantitative feedback theory in design of single‐loop feedback systems. Based on this new development, a simple‐to‐implement, efficient computer algorithm is outlined.
A weak kharitonov theorem holds if and only if the stability region and its reciprocal are convex
Authors: Rantzer Anders
Published: July 2007

We give necessary and sufficient conditions on the stability region for the validity of a weak version of Kharitonov's theorem, stating that stability of an ‘interval family’ of complex polynomials is implied by stability of the corner polynomials. Furthermore, we define a class of stability regions which do not satisfy the conditions, but for which the implication still holds in the case of real polynomials.
Asymptotic linearization of uncertain nonlinear systems by means of continuous control
Authors: Bartolini G. , Pydynowski P.
Published: July 2007

In this paper a new method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented. The main feature of this approach consists of a continuous first‐order estimator and control laws with piecewise continuous derivatives. As an important by‐product of this theory we can deal easily with the case of some uncertain systems which do not satisfy the matching condition, and with systems presenting first order unmodelled dynamics.
Robust stabilization of singularly perturbed nonlinear systems
Authors: Corless M. , Garofalo F. , Glielmo L.
Published: July 2007

Consider a singularly perturbed nonlinear system endowed with a control input and suppose a static nonlinear feedback law is designed. We show that the operations ‘compute the reduced order system’ (i.e., let the singular perturbation parameter μ = 0) and ‘close the feedback loop’ commute, i.e. the closed loop reduced‐order system is unambiguously determined. We then show that, if the reduced order system associated with the original system is stabilizable or has uncertainties matched with the input (a condition frequently used in the design of robust controllers), then the closed loop reduced‐order system enjoys the same property. As shown by an example, this result can be used to simplify the structure of a composite controller.
Adaptive control of aircraft in windshear
Authors: Leitmann George , Pandey Sandeep , Ryan Eugene
Published: July 2007

The control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value. An adaptive strategy is developed which uses only climb rate information. Robustness vis à vis windshear structure and intensity is illustrated via simulations employing four different windshear models.
Adaptive stabilization of multi‐input nonlinear systems
Authors: Ryan E. P.
Published: July 2007

Universal stabilizers are presented for two classes of nonlinear systems, linear in their multiple control inputs: (I) a class of pth order controlled differential inclusions on R″ with full state available for feedback, and (II) a class of nonlinearly perturbed linear systems with restricted state availability. The stabilizers are of a discontinuous feedback form (embedded in a set‐valued map), and incorporate adaptive matrix‐valued gain functions which exploit the existence of finite spectrum‐unmixing sets associated with the systems under consideration. The analysis draws on an extension, to differential inclusions, of LaSalle's invariance principle for ordinary differential equations.
Robust absolute stability of continuous systems
Authors: Tsypkin Ya. Z. , Polyak B. T.
Published: July 2007

The problem of stability of continuous‐time nonlinear systems with nonparametric uncertainty of a linear part and sector uncertainty of its nonlinear part is considered. The proposed robust stability criterion is a natural extension of the circle criterion for absolute stability. The situation with the Popov criterion is also discussed; it is demonstrated to be nonrobust for perturbations of a linear part, bounded in H∞ norm.
Nonlinear uncertain systems and robustness optimization
Authors: Ryan E. P. , Townley S.
Published: July 2007

An approach to (adaptive) stabilization is developed for a class of uncertain nonlinearly perturbed linear dynamical systems modelled by a controlled differential inclusion on Rn. The essential features are nonlinear feedback and optimization of robustness with respect to unmatched uncertainty. The approach is geometric: (i) a family 𝒱 of proper subspaces V ⊂ Rn is introduced with the property that {0} ⊂ V is an asymptotically stable equilibrium for the projection, onto V, of the unperturbed linear flow; (ii) for the perturbed system, it is then shown that each V ϵ 𝒱 can be rendered attractive and (almost) invariant by some choice of feedback determined by the nature of the perturbation and other a priori system information; specifically, under differing hypotheses, we can render V ϵ 𝒱 almost invariant and attractive, or invariant and finite‐time attractive, or adaptively attractive via, respectively, linear high‐gain feedback or discontinuous feedback, or adaptive feedback. Associated with each V ϵ 𝒱 is a measure of robustness with respect to unmatched uncertainty (a stability radius), quantified by a real parameter η. The problem of optimizing this measure is formulated as an optimization problem over 𝒱, solvable (in a supremal sense of η‐maximizing sequences (Vj) 𝒱) via solutions of particular algebraic Riccati equations of order k ≤ (n ‐ m), where m ≤ n is the control dimension; typically k = n ‐ m..
Stability of quantitative feedback designs and the existence of robust QFT controllers
Authors: Jayasuriya Suhada , Zhao Yongdong
Published: July 2007

Quantitative feedback theory (QFT) has received much criticism for a lack of clearly stated mathematical results to support its claims. Considered in this paper are two important fundamental questions: (i) whether or not a QFT design is robustly stable, and (ii) does a robust stabilizer exist. Both these are precursors for synthesizing controllers for performance robustness. Necessary and sufficient conditions are given to resolve unambiguously the question of robust stability in SISO systems, which in fact confirms that a properly executed QFT design is automatically robustly stable. This Nyquist‐type stability result is based on the so‐called zero exclusion condition and is applicable to a large class of problems under some simple continuity assumptions. In particular, the class of uncertain plants include those in which there are no right‐half plane pole‐zero cancellations over all plant uncertainties. A sufficiency condition for a robust stabilizer to exist is derived from the well‐known Nevanlinna‐Pick theory in classical analysis. Essentially the same condition may be used to answer the question of existence of a QFT controller for the general robust performance problem. These existence results are based on an upper bound on the nominal sensitivity function. Also considered is QFT design for a special class of interval plants in which only the poles and the DC gain are assumed uncertain. The latter problem lends itself to certain explicit computations that considerably simplify the QFT design problem.
Quantitative design of a class of nonlinear systems with parameter uncertainty
Authors: Oldak S. , Baril C. , Gutman P. O.
Published: July 2007

This paper considers the case in which a linear time‐invariant (LTI) but uncertain plant suffers from nonlinearities y=n(x) which can be expressed as y=Kn+η(x), |η(x)|≤M, with K, a possibly uncertain scalar. This covers a large and very important class of nonlinearities encountered in practice such as friction, backlash, dead zone and quantization.

Quantitative design techniques are presented for this class for the satisfaction of specifications. Special attention is paid to the avoidance of limit cycles using describing function theory, although the design method is also amenable of application using other stability criteria such as the circle criteria. Numerical examples are developed illustrating the design procedure.
Multi‐input, multi‐output flight control system design for the YF‐16 using nonlinear QFT and pilot compensation
Authors: Miller Russel B. , Horowitz Isaac M. , Houpis Constantine H. , Finley Barfield A.
Published: July 2007

Nonlinear quantitative feedback theory (QFT) and pilot compensation techniques are used to design a 2 × 2 flight control system for the YF‐16 aircraft over a large range of plant uncertainty. The design is based on numerical input‐output time histories generated with a FORTRAN implemented nonlinear simulation of the YF‐16. The first step of the design process is the generation of a set of equivalent linear time‐invariant (LTI) plant models to represent the actual nonlinear plant. It has been proven that the solution to the equivalent plant problem is guaranteed to solve the original nonlinear problem. Standard QFT techniques are then used in the design synthesis based on the equivalent plant models. A detailed mathematical development of the method used to develop these equivalent LTI plant models is provided. After this inner‐loop design, pilot compensation is developed to reduce the pilot's workload. This outer‐loop design is also based on a set of equivalent LTI plant models. This is accomplished by modelling the pilot with parameters that result in good handling qualities ratings, and developing the necessary compensation to force the desired system responses.
Neural networks for nonlinear state estimation
Authors: Parisini T. , Zoppoli R.
Published: July 2007

Estimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non‐recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.
Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete‐time theory
Authors: Haddad Wassim M. , Bernstein Dennis S.
Published: July 2007

In a companion paper (‘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’), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete‐time case. As in the continuous‐time case, each result is based upon a suitable Riccati‐like matrix equation that 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. Multivariable versions of the discrete‐time circle and Popov criteria are obtained as extensions of known results. Each result is specialized to the linear uncertainty case and connections with robust stability for state‐space systems is explored.
Admissible controls and attainable states for a class of nonlinear systems with general constraints
Authors: Achhab M. E. , Callier F. M. , Wertz V.
Published: July 2007

We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example.
Quantification of model uncertainty from data
Authors: de Vries Douwe K. , Van Hof Paul M. J. Den
Published: July 2007

Identification of linear models in view of robust control design requires the identification of a control‐relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency‐dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.
Polynomial solutions toH∞problems
Authors: Meinsma Gjerrit
Published: July 2007

The paper presents a polynomial solution to the standardH∞‐optimal control problem. Based on two polynomialJ‐spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomialJ‐spectral factorization problems.
Construction of value set for robustness analysis via circular arithmetic
Authors: Polyak B. T. , Scherbakov P. S. , Shmulyian S. B.
Published: July 2007

Circular arithmetic technique is developed for constructing value set of a characteristic polynomial. It provides necessary and sufficient conditions for robust stability of disk polynomials and their simple combinations. In more complicated cases sufficient conditions can be obtained. Various examples including multilinear (real or complex) parameter perturbations are considered.
Regulator problem for uncertain linear discrete‐time systems with constrained control
Authors: Benzaouia Abdellah , Mesquine Fouad
Published: July 2007

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.
The discrete‐timeH∞control problem with measurement feedback
Authors: Stoorvogel Anton A. , Saberi Ali , Chen Ben M.
Published: July 2007

This paper is concerned with the discrete‐timeH∞control problem with measurement feedback. We extend previous results by having weaker assumptions on the system parameters. We also show explicitly the structure ofH∞controllers. Finally, we show that it is in certain cases possible, without loss of performance, to reduce the dynamical order of the controllers.
Frequency‐restricted norm bounds for interval systems
Authors: Kimura Tetsuya , Hara Shinji
Published: July 2007

We investigate bounds of frequency‐restricted norms (FRN), a generalization ofH∞‐norm, for SISO LTI interval systems, where the numerator and the denominator are interval polynomials. Though theH∞‐norm of interval systems can be determined by 16 Kharitonov‐type systems, we can show that this fact is not true in general by a counterexample. A special class of systems for which the FRN is bounded by fixed extremal systems is derived. On the basis of this result, an example of PI‐type controller design considering both parametric and unstructured perturbations is illustrated by a parameter space design method.
Equivalence of stability concepts for discrete time‐varying systems
Authors: Bhaya Amit , Das Francisco , Mota Chagas
Published: July 2007

Stability concepts arising in the literature on absolute stability, difference inclusions and interval matrices are all shown to be equivalent to simultaneous asymptotic stability of a class of linear time‐varying discrete systems and, in turn, to exponential stability. This enables the classification of an interval matrix stability test due to Baueret al., a Lyapunov indicator test due to Barabanov and a constructive Lyapunov function test due to Brayton and Tong into a hierarchy of stability tests. Some applications of these tests are given and it is observed that they are not, in general, polynomial‐time tests.
Loop shaping and a zero‐placement technique as applied to the benchmark problem
Authors: Schmidt David K. , Benson Dwayne
Published: July 2007

A classical and a ‘quasi‐modern’ approach are taken to develop robust control laws for the 1992 ACC benchmark problem of Wie and Bernstein. In both approaches, copious use of loop‐shaping à la Bode design is employed. The quasi‐modern approach reported herein is a zero‐placement technique, which is a variant on LQG/LTR. This approach allows for the direct selection of the zeros of the loop transfer function, leading to the desired loop shape. Therefore, undesirable pole‐zero cancellations may be avoided. The modern and quasi‐modern approaches are closely related, and can lead to similar control laws. Though the problem addressed here is SISO, the zero‐placement approach can be used on MIMO systems. However, in the case discussed herein, the classically designed controller has superior performance and stability robustness.
Robust controller design for a non‐colocated spring‐mass system via mixed 𝓁/∞ optimization
Authors: Sznaier Mario , Rotstein Héctor
Published: July 2007

A successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addressed using the ℋ︁∞robust control framework. However, this framework cannot accommodate the realistic case where in addition to robustness considerations, the system is subject to time‐domain specifications. We recently proposed design procedures to explicitly incorporate time‐domain specifications into the ℋ︁∞framework. In this paper we apply these design procedures to the simple mass‐spring system used as a benchmark in the 1990–1992 ACC, with the goal of minimizing the peak control effort while satisfying disturbance rejection, settling time, tracking and robustness specifications. The results show that there exist a severe trade‐off between peak control action and robustness to unstructured model uncertainty.
A zero compensation approach to singular H2 and H∞ problems
Authors: Copeland B. R. , Safonov M. G.
Published: July 2007

In this work we analyse singular H2 and H∞ problems for which the usual Riccati equations become ill‐posed owing to the existence of plant zeros at infinity.

We adopt a two‐step approach to the analysis. First we replace the usual Riccati equations with two generalized eigenproblems; these problems are always well‐posed. Next we extract those structural elements which pertain to the troublesome plant zeros. We do this by introducing pre‐compensators which cancel the offending zeros. In so doing, we temporarily relax the controller properness constraint that is traditionally imposed in H2 and H∞ problems by allowing pole‐zero cancellations between the plant and controller at infinity. Since no significant added complexity of analysis results, we also treat the case of singularity due to finite jω‐axis plant zeros by relaxing the internal stability requirement and allowing finite jω‐axis pole‐zero cancellations.

The resultant theory allows us to specify necessary and sufficient conditions for the existence of solutions to singular H2 and H∞ problems. The existence conditions and the resultant control laws are expressed directly in terms of the eigenvalues and eigenvectors of two Hamiltonian matrices associated with the problem. The theory also gives some insight into the character of the subset of all proper, internally stabilizing solutions, including whether this set is nonempty. An example is included.
A design procedure for the exact H∞ siso‐robust performance problem
Authors: Nordgren R. E. , Franchek M. A. , Nwokah O. D. I.
Published: July 2007

Presented in this paper is a loop‐shaping solution to the H∞ robust performance problem for a class of SISO systems. The key feature of this work is the explicit incorporation of phase information into the controller synthesis to facilitate loop‐shaping over all frequencies. Consequently, a significant reduction in the required controller gain/bandwidth is achieved. It is also shown that the optimal solution, in the sense of controller gain/bandwidth minimization, to the robust performance problem is that which makes μ = 1 over all frequencies. This is different from the usual definition of optimality in the H∞/μ literature. An example is included for completeness.
Minimax optimal control of uncertain systems with structured uncertainty
Authors: Savkin Andrey V. , Petersen Ian R.
Published: July 2007

This paper considers a minimax control problem for an uncertain system containing structured uncertainties. The uncertainties in this system are assumed to satisfy a certain integral quadratic constraint. For a given initial condition, the minimax optimal controller is constructed by solving a parameter‐dependent Riccati equation of the game type. This controller leads to a closed‐loop uncertain system which is absolutely stable.
Input to state stabilizability for parametrized families of systems
Authors: Lin Yuandan , Sontag Eduardo D. , Wang Yuan
Published: July 2007

This paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov‐theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state‐space stability to ‘input to state’ (bounded‐input bounded‐state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analysed.
Joint‐space orthogonalization and passivity for physical interpretations of dextrous robot motions under geometric constraints
Authors: Arimoto Suguru
Published: July 2007

A principle of ‘joint‐space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real‐time from a Jacobian matrix of the constraint equation in joint coordinates.

To show the important role of the principle in control of robot manipulators, two basic set‐point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi‐natural potential and the joint‐space orthogonalization. Various stability problems of PID‐type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper‐stability theory.
Control of constrained robots including effects of joint flexibility and actuator dynamics
Authors: Krishnan Hariharan
Published: July 2007

We consider mathematical representations of constrained robot systems in which the effects of joint flexibility and actuator dynamics are significant. The objective is to design a feedback control law so that the position output variables and the force output variables of the robot follows the desired position and the desired force trajectories respectively despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. The development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility. Thus using the force/position control law developed in this paper one can achieve better tracking performance in cases where such effects are significant.
NonlinearH∞disturbance attenuation for robots with flexible joints
Authors: Tomei Patrizio
Published: July 2007

The tracking problem is considered for robots having flexible joints. We propose a state feedback control algorithm which guarantees arbitrary attenuation on the outputs of the effects of time‐varying disturbances as well as of parameter uncertainties. Only a lower bound on the values of the elastic constants is required to be known.
A semi‐global low‐and‐high gain design technique for linear systems with input saturation—stabilization and disturbance rejection
Authors: Lin Zongli , Saberi Ali
Published: July 2007

In this paper we propose a linear low‐and‐high gain design technique to solve the semi‐global stabilization problem for a class of linear systems subject to input saturation. The central idea behind this new technique is to increase the utilization of the available control capability of the system. The power of this new semi‐global design technique is shown by solving the problem of semi‐global stabilization with input‐additive disturbance rejection which is formulated as a semi‐global practical stabilization problem.
Linear systems with input nonlinearities: Global stabilization by scheduling a family ofH∞‐type controllers
Authors: Teel Andrew R.
Published: July 2007

A new global stabilization algorithm is presented for linear systems that have (A,B) stabilizable, the eigenvalues ofAin the closed left‐half plane, but where the controls pass through nonlinearities of a general type. This algorithm is based on a semi‐global stabilization solution for the same class of systems. The global solution is constructed by dynamically scheduling the adjustable parameter of the semi‐global solution according to the size of the state. The semi‐global solution is a family of linear control laws generated by a family ofH∞‐type algebraic Riccati equations. We show that the closed‐loop state feedback system has the property that additive disturbances which converge exponentially to zero cannot produce unbounded states. This fact is used to show that, under a linear detectability assumption, the state feedback results are recovered when the solution is implemented via a standard linear‐based observer.
Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities
Authors: Michel Anthony N. , Liu Derong , Wang Kaining
Published: July 2007

For linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback.

Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities).

We demonstrate the applicability of the present results by means of several specific examples.
Anti‐windup compensator synthesis for systems with saturation actuators
Authors: Tyan Feng , Bernstein Dennis S.
Published: July 2007

In this paper we synthesize linear and nonlinear output feedback dynamic compensators for plants with saturating actuators. Our approach is direct in the sense that it accounts for the saturation nonlinearity throughout the design procedure as distinct from traditional design techniques that first obtain a linear controller for the ‘unsaturated’ plant and then employ controller modification. We utilize fixed‐structure techniques for output feedback compensation while specifying the structure and order of the controller. In the full‐order case the controller gains are given by LQG‐type Riccati equations that account for the saturation nonlinearity.
A practical approach for robust control of flexible structures
Authors: Coville Arnaud , Abou‐Kandil Hisham
Published: July 2007

This paper deals with the robust control of linear single‐input, single‐output (SISO) systems. First, general concepts of the frequency‐domain approach are presented. We then focus on the particular problem of flexible structure and control. A new method is proposed which combines the advantages of hyperstability and small gain approaches. Finally, an application of an industrial sight system prototype is detailed.
Asymptotic output tracking through singular points for nonlinear systems: Stability, disturbance rejection and robustness
Authors: Retchkiman Zvi , Alvarez Jaime , Castro Rafael
Published: July 2007

The problem of output tracking in the presence of singularities started by Hirschorn and Davis (1987)2is reexamined. A transformation which allows us to make a study of the closed‐loop stability of the nonlinear system is proposed. An error feedback control law relaxes the initial conditions imposed on the system and the function to be followed, obtaining asymptotic output tracking. A study of the singular tracking problem, when there exist disturbances or uncertainties in the dynamics, is also made. Again a stability analysis is carried out. Finally, the results obtained for the SISO case, to the MIMO case are extended.
Computing bounds for the mixed μ problem
Authors: Young Peter M. , Newlin Matthew P. , Doyle John C.
Published: July 2007

Robustness problems involving real parametric uncertainty can be reformulated as mixed μ problems, where the block‐structured uncertainty description is allowed to contain both real and complex blocks. Upper and lower bounds for the mixed μ problem have recently been developed, and this paper examines the computational aspects of these bounds. In particular a practical algorithm is developed to compute the bounds. This has been implemented as a Matlab function (m‐file), which is currently available in conjunction with the μ‐Tools toolbox. Some results from our extensive numerical experience with the algorithm are presented. The algorithm performance is very encouraging, in terms both of accuracy of the resulting bounds, and of growth rate in required computation with problem size. In particular it appears that one can handle medium‐size problems (fewer than 100 perturbations) with reasonable computational requirements.
Robust and quadratic stability via polytopic set covering
Authors: Amato F. , Garofalo F. , Glielmo L. , Pironti A.
Published: July 2007

In this paper we consider the problem of covering the image of a given function by a polytope. This problem arises in both the robust and quadratic stability context. We present two main algorithms: the first one performs such a covering and works under quite general assumptions on the nature of the function; the second one is iterative and allows us to improve at will the goodness of the covering. The convergence properties of this algorithm are also discussed. Finally two examples of application of our techniques are presented.
Molekülstrahlepitaxie
Authors: Sitter Helmut , Herman Marian A.
Published: July 2007

“Molecular beam epitaxy is a very flexible method for the preparation of thin epilayers of semiconductors, metals or insulators. In this contribution we deal with the questions how such an epitaxy system can be realized, why it is used in high technology of the future and what are the main advantages”.
Gefriertrocknung in Labor‐ und Industrieanwendungen
Authors: Barfuss Heinz
Published: July 2007

For preservation and extension of shelf life time for food, pharmaceutical and biotechnical products, Freeze Drying has been proven to be the most effective and economical technology. The freeze dried products remain unchanged in structure, keep their colour, aroma, nutrition and their biological consistence, In the following the author would like to present an overview of the definition, technology with its restrictions and the process with the use of vacuum.
Prozesse mit hoher Plasmastromdichte und unterschiedlichen Verdampfungsquellen
Authors: Bergmann Erich
Published: July 2007

The hot filament supported high current discharge can be used with various process steps. During the heating cycle, intense electron bombardment provides a soft and efficient energy source. In triode etching the high plasma density improves the throwing power and reduces the arcing problem on oxide inclusions from preceding grinding steps.

For the coating cycle the high current density can be fitted into different deposition processes. Activated reactive ion plating is done with a high voltage electron beam gun. But one can also combine the high current density plasma with a magnetron to produce a high plasma density on the substrate and solve the problems of reactivity of this vapor source. Alternatively the high current density plasma can also be used to drive a CVD‐reaction. Several of these processes can be combined to hybrid deposition technologies. A few examples of coating realisations and performance in the different processes will be given.
COSY, eine neue Forschungsanlage mit Ultra‐Hochvakuum‐Technologie
Authors: Schröder G. , Jaegers H. , Pauly F. , Stechemesser H.
Published: July 2007

The report shows that the development, construction and later successful operation of UHV facilities in the pressure range of ≤10−10mbar is not possible without a highly sensitive nondestructive testing technique. The example of the large technical research facility COSY is used to demonstrate that the leakage rates (≤10−10mbar · I · s−1) and surface purities required can only be achieved by strict compliance with fundamental UHV production conditions and by the rigorous application of helium leak detection techniques and mass‐spectrometric residual gas analysis.
Verbesserung des Vakuums in Isoliergefäßen aus Glas
Authors: Lochner Karl Heinz , Fahrenkrog Hans‐Hermann , Ballweg Thomas
Published: July 2007

Durch eine Verbesserung des Vakuums auf Drücke unterhalb von 10−4 mbar ließe sich die Isolierfähigkeit handelsüblicher Isolierglasbehälter etwa verdoppeln. Um dieses Ziel zu erreichen, wurden verschiedene Wege beschritten.

Als Alternative zum bisher üblichen Abschmelzen werden drei Möglichkeiten vorgestellt, die eine den Leitwert reduzierende Verengung des Pumpstutzens überflüssig machen. Außerdem werden, je nach Verfahren, die beim Abschmelzen auftretenden Ausgasungen entweder ganz vermieden oder durch die Möglichkeit genauer Temperaturkontrolle bzw. durch eine niedrigere Abtrenntemperatur reduziert.

Ein ganz anderer Weg wird mit dem Einsatz eines Getters, einem Metallhydrid auf TiVMn‐Basis aufgezeigt. Seine Aktivierung erfolgt durch Wärme und läßt sich ohne Schwierigkeit in den herkömmlichen Produktionsablauf integrieren. Neben einer Verkürzung der Pumpzeit tritt hier als weiterer Vorteil die Bindung der beim Abschmelzen auftretenden sowie der langfristigen Ausgasungen hinzu.
Kalibrierung, Abnahme und Zertifizierung
Authors: Jitschin E.
Published: July 2007

Zuverlässige Aussagen über die Genauigkeit eines Meßgerätes oder über die Einhaltung von Produktspezifikationen lassen sich nur durch eine Prüfung gewinnen. Um sicherzustellen, daß Ergebnisse verschiedener Prüflaboratorien unter gleichartigen Bedingungen erhalten wurden und somit allgemein gültig sind, müssen genormte Prüfvorschriften angewendet und kalibrierte Bezugsgeräte verwendet werden. Weiterhin ist Fachkenntnis und Erfahrung notwendig. Erfahrene Prüflaboratorien können sich ihre Kompetenz durch eine Akkreditierung bestätigen lassen, z.B. durch den Deutschen Kalibrierdienst DKD. Der vorliegende Artikel gibt zunächst eine Übersicht über die wichtigsten Begriffe der Kalibrierung und Abnahmen und beschreibt dann das Prüflabor für Meßgrößen der Vakuumtechnik an der Fachhochschule in Gießen.
Die Entwicklung der Totaldruckmessung im Ultrahochvakuum‐ und Extremvakuumbereich
Authors: Edelmann Christian
Published: July 2007

Obwohl man Ultrahochvakuum bereits vor fast 60 Jahren erzeugen konnte, war eine kontinuierliche Messung erst durch die Entwicklung eines speziellen Glühkatoden‐Ionisationsmanometers durch Bayard und Alpert möglich. Ursachen für die untere Druckmeßgrenze sind vor allem der durch Röntgenstrahlung erzeugte Photoelektronenstrom und der Desorbationenstrom. Manometerkonstruktionen, die diese Effekte reduzieren, um sogar extremes Hochvakuum (XHV) messen zu können, werden vorgestellt. Die im XHV‐Bereich zu erwartenden kleinsten Ionenströme werden mit kontinuierlichen Sekundärelektronenvervielfachern gemessen. Auch besondere Bauformen von Kaltkatoden‐Ionisationsmanometern sind für den UHV‐Bereich geeignet.
Anwendung der Hohlkatodenplasmaquelle in der Vakuumtechnik
Authors: Leonhardt Gunter , Wilberg Rüdiger
Published: July 2007

Various effective and simple constructed plasma sources can be developed by using the hollow cathode effect. The improve of the plasma efficiency is caused by the penetration of two or more glow regions of different parts of the cathode. The equatation p × d ∽ 1 mbar cm is a rule of thumb for the appearance of the hollow cathode effect. The hollow cathode arc discharge is caused by an additional thermal electron emission besides the effectes of the hollow cathode glow discharge. All this effects are the reason for the higher degree of ionization for a hollow cathode source in comparison with the most other plasma sources.

Application of the hollow cathode glow discharge for surface finish are technics like plasmacleaning, electron beam ablation or gas flow sputtering. Latters are new technics which allow the development of new sources for the coating technology.

The application of the hollow cathode are discharge is possible by using the thermal energy generated by the electron beam (electron beam heating, electron beam melting, and electron beam evaporation) and by using the different possibilities of coating technologies whith the hollow cathode arc source (plasma enhanced evaporation, plasma enhanced reactive PVD and plasma CVD).
Industrielle Dichtheitsprüftechnik ohne Testgas nach dem Massenspektrometerprüfverfahren
Authors: Fuhrmann W.
Published: July 2007

Umweltschutz, Funktionssicherheit und insbesonders qualitätssichernde Systeme wie ISO 9000 stellen höchste Anforderungen an die Dichtheit von Komponenten und Systemen.

Es wird ein Dichtheitsprüfverfahren auf der Basis der Massenspektrometertechnik vorgestellt, das seit etwa 3 Jahren im Produktionsbereich (Prüfung von einigen tausend Einheiten pro Tag) Komponenten vollautomatisch auf Dichtheit prüft im Bereich ⩾ 10−3 cm3/s unter Verwendung von „Normalluft”︁ als Testgas.

Es werden spezifische Anwendungsfälle der Verpackungsindustrie als auch der Kfz‐Zuliefererindustrie vorgestellt.
Standardisierte Steckverbindung für aktive Vakuummeßköpfe
Authors: Jacoby W. , Jitschin W.
Published: July 2007

Bei der Gesellschaft für Schwerionenforschung, Darmstadt, wurde in Zusammenarbeit mit der Industrie eine achtpolige Steckverbindung für aktive Vakuummeßköpfe und ihre Betriebsgeräte standardisiert. Diese ist für auf dem Markt bzw. In Entwicklung befindliche Meßköpfe geeignet, die den gesamten technisch interessanten Druckbereich von 1000 mbar bis 10−12 mbar überdecken. Die achtadrige Kabelverbindung beinhaltet die Spannungsversorgung der Meßröhre, das Meßsignal sowie Steuer‐ und Rückmeldesignale. Es wird nur ein einziger Steckverbindertyp verwendet, so daß die Lagerhaltung und der Anschluß unterschiedlicher Meßköpfe vereinfacht werden. Der gewählte Steckverbinder (bekannt als Modular‐Steckverbinder) läßt sich lötfrei konfektionieren. Ferner dient ein in den Meßkopf eingebauter Kodierwiderstand zur Identifikation des Kopftyps durch das Betriebsgerät. Damit ist zum Betrieb der unterschiedlichen Meßköpfe lediglich ein einziges Betriebsgerät oder eine PC‐Einschubkarte erforderlich.
Three‐Chamber UHV System for Organic Molecular Beam Epitaxy
Authors: Bella L. Dalla , Taliani C. , Zamboni R.
Published: July 2007

Die organische Molekularstrahl‐Epitaxie (OMBE) ist ein Verfahren zum Aufwachsen organischer und halbleitender Stoffe im UHV. Der Artikel beschreibt eine modulare Anlage aus 3 UHV‐ Kammern, die speziell für einzelne Verfahrensschritte ausgelegt sind. Die Anlage ist flexibel und erlaubt vielfältige optische Untersuchungen der Proben ohne diese der Atmosphäre auszusetzen. Eine wichtige Anwendung ist die Herstellung neuer LED‐Bauteile basierend auf Fullerenen.
Vakuum in der Abwasseraufbereitung
Authors: Schneider W.
Published: July 2007

In den industriellen Prozessen fallen unterschiedlichste Abwässer an. Diese müssen vor der Einleitung in den Kanal aufbereitet oder fremdentsorgt werden. Durch den Einsatz der Vakuumtechnik und die konsequente Umsetzung des Wärmepumpenprozesses wurde eine kostengünstige Problemlösung zur Aufbereitung industrieller Abwässer vor Ort entwickelt. Diese werden mit minimalem Energieaufwand eingedampft, so daß nur noch ca. 5–10% des Abfallvolumens mit geringem Restwasseranteil entsorgt werden muß. Das gewonnene Destillat kann abgeleitet oder aufgrund seiner hohen Qualität in den Kreislauf zur Wiederverwendung zurückgegeben werden.
Anlagenkonzept für die Abscheidung dünner Schichten durch Plasmapolymerisation
Authors: Poll Hans‐Ulrich , Schreiter Steffen
Published: July 2007

Dünne Polymerschichten werden durch plasmagestützte CVD direkt aus der Dampfphase eines organischen Ausgangsmaterials abgeschieden (Plasmapolymerisation). Die zugeführte Gasmenge begrenzt die Schichtwachstumsrate. Durch plasmachemische Stoffwandlung im Gasraum und an der Schichtoberfläche kann auf die Schichteigenschaften Einfluß genommen werden. Die Zeitkonstante dieser Stoffwandlung ergibt in Verbindung mit den Anwendungsforderungen an die Schichten ein vakuumtechnisches Konzept für die Anlagenentwicklung, das auch großtechnische Anwendungen möglich erscheinen läßt.
Modifizierung der Gasabgabe von Edelstahloberflächen durch Ionenimplantation
Authors: Garke B. , Edelmann Chr. , Günzel R. , Brutscher J.
Published: July 2007

Ein seit einigen Jahren neu etabliertes Ionenimplantationsverfahren, die sogenannte Plasmaimmersionsimplantation (PIII), wurde bei Edelstahlproben angewandt, um definiert Sauerstoff‐ und Stickstoffionen in die Oberfläche zu implantieren und damit oxidische bzw. nitridische Barriereschichten für die Gasdiffusion zu erzeugen. Mit Hilfe oberflächenanalytischer Methoden konnte gezeigt werden, daß unterhalb der äußersten Oberfläche Sauerstoff bzw. Stickstoff über einen bestimmten Tiefenbereich homogen eingebaut wurde. Einige Meßergebnisse zum Gasabgabeverhalten dieser so plasmabehandelten Oberflächen werden vorgestellt und auf die Oberflächenmodifikation durch die Plasmabehandlung bzw. die Wirkung der Implantationsschicht zurückgeführt.
Mit Hochfrequenz angeregte Niederdruckplasmen: Prinzipien und Strukturierung von Halbleitern. Teil I
Authors: Franz Gerhard
Published: July 2007

In zwei Teilen wird die Funktionsweise der Erzeugung von kalten Niederdruckplasmen durch kapazitive und induktive Kopplung sowie durch resonante Anregung beschrieben und im dritten Teil gezeigt, wie die Kenntnis dieser Größen ausgenutzt werden kann, um Halbleiteroberflächen zu modifizieren.
Spektralfotometrische Messungen an optischen Schichten
Authors: Liekmeier Wilfried
Published: July 2007

Die Transmissions‐ und Reflexionseigenschaften optischer Schichtsysteme werden mit Spektrometern überprüft. Der Artikel beschreibt die möglichen Meßprinzipien mit ihren Grenzen und praktischen Anforderungen.