μ synthesis and LFT gain scheduling with real uncertainties

This paper presents a solution to synthesis of gain scheduling controllers based on μ-analysis and linear fractional transformations (LFTs). The system is assumed to have parameter dependencies described by LFTs. The goal of the controller is, with real-time knowledge of the parameters, to provide disturbance and error attenuation. The paper treats both complex and real parametric dependencies. © 1998 John Wiley & Sons, Ltd.     

Computation of the robustness margin with the skewed μ tool

Methods for the direct computation of the maximal structured singular value (s.s.v.) over the frequency range require a recursive application of μ analysis. Introducing the v measure as a skewed s.s.v., we point out the problem can be solved by a single application of the v tool. A mixed v upper bound is then proposed, which provides a direct solution to the problem. The relationship between the mixed μ and v upper bounds is moreover clarified. The nonnegativity of the sensitivity of the mixed μ upper bound is finally obtained as a corollary.     

The rank one mixed μ problem and ‘kharitonov-type’ analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so-called ‘affine parameter variation’ problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated ‘Kharitonov-type’ results have been proven.     

Synthesis Of μ Controllers Using Statistical Iterations

This paper introduces the integration of robust control and quality control, based on which a statistical iteration scheme of μ synthesis is proposed. In this statistical solution, μ controller structures are fully flexible, and controller orders do not increase during iterations. In addition, it can reveal the directions of parameter changes, which may lead to improvements in the performance of the resulting controllers. Statistical interpretations and systematical procedures for this quality‐oriented control design are also addressed.     

Development of a skew μ upper bound

Exploitation of the NP hard, mixed μ problem structure provides a polynomial time algorithm that approximates μ with usually reasonable answers. When the problem is extended to the skew μ problem, an extension of the existing method to the skew μ formulation is required. The focus of this paper is to extend the μ upper bound derivation to the skew μ upper bound and show its direct computation by way of an Osborne balancing algorithm and an linear matrix inequality (LMI) algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

A Third-Order Representation of the λμ-Calculus

Higher-order logical frameworks provide a powerful technology to reason about object languages with binders. This will be demonstrated for the case of the λμ-calculus with two different binders which can most elegantly be represented using a third-order constant. Since cases of third- and higher-order encodings are very rare in comparison with those of second order, a second-order representation is given as well and equivalence to the third-order representation is proven formally.     

AN AFM PROBE CONTROLLER DESIGN BASED ON μ‐SYNTHESIS

The atomic force microscope (AFM) is one of the most important tools for measuring atomic resolution. The AFM system maintains constant force between a tip and the sample in order to track the sample topography. The controller that maintains the constant interaction force plays a significant role in measurement accuracy. This paper presents a μ‐synthesis controller design to deal with model uncertainty and establish a measurement error bound. The system's nonlinearity and the set‐point drift are lumped into a multiplicative uncertainty. The performance bound allows specification of the error magnitude over the frequency range. Simulation results show that the proposed control can tolerate uncertainties. The error spectrum from the experiments shows consistency with the design specifications. Images were taken to compare μ‐synthesis control with a well‐tuned PID control at a 480μm/s scan rate. The results verify the outstanding performance of the μ‐controller.     

Synchronous and asynchronous handling of abnormal events in the μsystem

This paper presents a general model for dealing with abnormal events during program execution and describes how this model is implemented in the μSystem. (The μSystem is a library of C definitions that provide light-weight concurrency on uniprocessor and multiprocessor computers running the UNIX operating system.) Two different techniques can be used to deal with an abnormal event: an exception, which results in an exceptional change in control flow from the point of the abnormal event; and an intervention, which is a routine call from the point of the abnormal event that performs some corrective action. Users can define named exceptions and interventions in conjunction with ones defined by the μSystem. Exception handlers and intervention routines for dealing with abnormal events can be defined/installed at any point in a program. An exception or intervention can then be raised or called, passing data about the abnormal event and returning results for interventions. Interventions can also be activated in other tasks, like a UNIX signal. Such asynchronous interventions may interrupt a task's execution and invoke the specified intervention routine. Asynchronous interventions are found to be useful to get another task's attention when it is not listening through the synchronous communication mechanism.     

MIXED μ PROBLEMS AND BRANCH AND BOUND TECHNIQUES

The computation of the general structural singular value (μ) is NP hard, so quick solutions to medium sized problems must often be approximate. In many of the cases where the current approximate methods are unsatisfactory, improved solutions are highly desirable. It is shown that, despite their worst-case combinatorial nature, branch and bound techniques can give substantially improved solutions with only moderate computational cost. © 1997 by John Wiley & Sons, Ltd.     

Development of a μ-concentrator Using Dielectrophoretic Forces

We present the simulation, development and experimental validation of a μ-concentrator based on dielectrophoresis, DEP.In a first step dielectrophoretic force fields of various electrodes are computed and compared. The simulation results for various electrode dimensions may serve as a general design rule for DEP devices. Favorable electrode designs were realized in gold on glass substrates. The performance of the DEP chips is validated by concentration of E.-Coli bacteria, a separation efficiency of 99.93% was achieved. Furthermore, we outline how the combination of forced convection and DEP allows for bacteria separation at increased flow rates.     

Completeness of Continuation Models for λμ-Calculus

We show that a certain simple call-by-name continuation semantics of Parigot's λ_μ-calculus is complete. More precisely, for every λ_μ-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of λ_μ, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any λ_μ-category in the sense of L. Ong (1996, in “Proceedings of LICS '96,” IEEE Press, New York) is isomorphic to a continuation model (Y. Lafont, B. Reus, and T. Streicher, “Continuous Semantics or Expressing Implication by Negation,” Technical Report 93-21, University of Munich) derived from a cartesian-closed category of continuations. We also extend this result to a later call-by-value version of λ_μ developed by C.-H. L. Ong and C. A. Stewart (1997, in “Proceedings of ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Paris, January 1997,” Assoc. Comput. Mach. Press, New York).     

The μ-calculus as an assertion-language for fairness arguments

Various principles of proof have been proposed to reason about fairness. This paper addresses—for the first time—the question in what formalism such fairness arguments can be couched. To wit: we prove that Park's monotone first-order μ-calculus, augmented with constants for all recursive ordinals can serve as an assertion-language for proving fair termination of do-loops. In particular, the weakest precondition for fair termination of a loop w.r.t. some postcondition is definable in it. The relevance of this result to proving eventualities in the temporal logic formalism of Manna and Pnuelis (in “Foundations of Computer Science IV, Part 2,” Math. Centre Tracts, Vol. 159, Math. Centrum, Amsterdam, 1983) is discussed.     

μC++: Concurrency in the object-oriented language C++

We present a design, including its motivation, for introducing concurrency into C++. The design work is based on a set of requirements and elementary execution properties that generate a corresponding set of programming language constructs needed to express concurrency. The new constructs continue to support object-oriented facilities such as inheritance and code reuse. Features that allow flexibility in accepting and subsequently postponing servicing of requests are provided. Currently, a major portion of the design is implemented, supporting concurrent programs on shared-memory uniprocessor and mulitprocessor computers.     

Novel analog pulse‐width‐modulated 15‐μm SiGe micromirrors

Abstract— A novel six‐electrode SiGe micromirror pixel enabling analog pulse‐width modulation (PWM) in display applications is presented. Instead of utilizing bitplanes, arbitrary duty cycles can be realized, resulting in an analog gray‐level distribution. This eliminates the posterization (contouring) effect that is typical for digital micromirrors. Moreover, the pixel design does not require the incorporation of electronic comparators and the gamma compensation can be processed externally. Two out of the six electrodes are used as landing electrodes. The other four attracting electrodes are driven by two anti‐phase saw‐tooth signals and two fixed analog voltage signals. By applying this signal scheme, the duty cycle of the mirror is modulated in an analog manner. Test vehicles were manufactured where SiGe is the microelectromechanical systems (MEMS) material. The use of SiGe as a structural layer is advantageous to build MEMS since the CMOS and MEMS layers can be deposited in a monolithic manner. Measurements using a Laser Doppier Vibrometer (LDV) have confirmed the feasibility of analog PWM for 15‐μm SiGe micromirrors.     

The μ-basis of a planar rational curve—properties and computation

A moving line L(x,y;t)=0 is a family of lines with one parameter t in a plane. A moving line L(x,y;t)=0 is said to follow a rational curve P(t) if the point P(t₀) is on the line L(x,y;t₀)=0 for any parameter value t₀. A μ-basis of a rational curve P(t) is a pair of lowest degree moving lines that constitute a basis of the module formed by all the moving lines following P(t), which is the syzygy module of P(t). The study of moving lines, especially the μ-basis, has recently led to an efficient method, called the moving line method, for computing the implicit equation of a rational curve [3 and 6]. In this paper, we present properties and equivalent definitions of a μ-basis of a planar rational curve. Several of these properties and definitions are new, and they help to clarify an earlier definition of the μ-basis [3]. Furthermore, based on some of these newly established properties, an efficient algorithm is presented to compute a μ-basis of a planar rational curve. This algorithm applies vector elimination to the moving line module of P(t), and has O(n²) time complexity, where n is the degree of P(t). We show that the new algorithm is more efficient than the fastest previous algorithm [7].     

Using Assumptions to Distribute Alternation Free μ-Calculus Model Checking

In this work we extend the approach used in [6] to perform distributed-memory AFMC model checking. The part of a system held in one computer is modeled as a Kripke structure with border states. Moreover, we use assumptions about the truth of a formula in each state. Each process then repeatedly executes a slight modification of a standard sequential algorithm and exchanges its results with other processes. In the paper we define the AFMC semantics for structures with border states and assumptions, present the distributed algorithm and show the main ideas behind the proof of its correctness. Complexity and experimental results are provided as well.     

Optimal buffer allocation in short μ-balanced unreliable production lines

In this work, we investigate the optimal buffer allocation in short μ-balanced production lines consisting of machines that are subject to breakdown. Repair times and times to failure are assumed exponential, whereas service times are allowed to follow the Erlang-k distribution (with k=1, 2, 4 and 8). By an improved enumeration procedure and applying the evaluative algorithm of Heavey et al. (European Journal of Operational Research 1993;68:69–89) for the calculation of throughput, we have examined in a systematic way several systems with 3, 4, 5, 6 and 7 stations and with a different total number of buffer slots. We have been able to give answers to some critical questions. These include the effect of the distribution of the service and repair times, the availability of the stations and the repair rates on the optimal buffer allocation and the throughput of the lines.     

Methods of displaying the behaviour of the mapping z → z + μ

Variations in the display of the computer-generated patterns associated with the mapping z → z² + μ can be achieved by studying changes in the escape radius utilised to test the values of the real and imaginary parts of z. Additional graphic effects can be achieved by sorting the values of z generated for points within the main body of the Mandelbrot set.