Novel digitally controlled drive for the vibratory conveyors

The vibratory conveyors are used in the industry for continuous transportation of loose substances over short distances (2–10 m). The presented conveyor is designed for transportation in aseptic conditions. To obtain high efficiency for granulated mass with different size of grain and different physical properties it is necessary to set the appropriate vibration amplitude independently of vibration frequency. This is not possible with the conveyors currently being used. Therefore it was proposed to apply the novel drive made up of rotary exciter with digital controller. Moreover some methods for dynamic stiffening of the panels were developed and their effectiveness was ascertained. A digitally controlled exciter allowed dynamic panel stiffening by using light closed panels in construction of the conveyor. The control system with encoders for measuring the vibration amplitude of the panel was also established. A study of the conveyor's prototype shows the effectiveness of the drive system. The possibility of digitally setting the vibration amplitude of the light panel to obtain the maximum productivity for particular materials was also shown in results of the research. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto-Structural analysis of rotating electrical machines

The vibrations of the stator core of a rotating electrical machine induce acoustic noise. These oscillations of the stator yoke are excited of the force density due to the magnetic field in the air gap. This requires a transient magnetic field analysis coupled with a dynamic mechanical analysis. Coupling these two different physical fields results in a high numerical effort and usually one direction of the interaction is disregarded. This paper presents a method to calculate the vibrations of a stator core under design operating conditions. For this purpose, harmonic electromagnetic excitation forces have been calculated in a linear magnetic field analyses using the finite element method. The resulting forces have been applied to a linear structural dynamic FE model in the frequency domain. The results of the calculations are harmonic velocities specified by amplitude and phase from the structural surface of the stator core. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance analysis of assembly systems with unreliable machines and finite buffers

An unreliable assembly system is studied in which different types of components are processed by two separate work centers before merging to an assembly station with random breakdown. Blocking at the work centers and starvation at the assembly station may occur because of finite buffer sizes and uncertainties in job arriving times and processing/assembly times. We derive the system stability condition, and obtain formulas for the system state probabilities, blocking probabilities, starvation probability, stockout probability, system availability in the steady state. We also obtain the distributions of blocking times and first failure times, respectively. Through numerical examples, we elaborate on the monotonous properties of the performance measures, and draw the insights into the impacts of the system parameters on its various performance indices, which provide important guidance for design of assembly systems.     

An energy-based analysis of reduced-order models of (networked) synchronous machines

Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced techniques for the analysis and controller design of power networks. Although there are widely accepted reduced-order models to describe the power network dynamics, they are commonly presented without details about the reduction procedure. The present article aims to provide a modular model derivation of multi-machine power networks. Starting from first-principle fundamental physics, we present detailed dynamical models of synchronous machines and clearly state the underlying assumptions which lead to some of the standard reduced-order multi-machine models. In addition, the energy functions for these models are derived, which allows to represent the multi-machine systems as port-Hamiltonian systems. Moreover, the systems are proven to be shifted passive, which permits for a power-preserving interconnection with other passive components.     

Minimal data rates and entropy in digitally networked systems

In digitally networked systems the assumption of classical control theory that information can be transmitted instantaneously, lossless and with arbitrary precision is violated. This raises the question about the smallest data rate above which a control task can be solved. For a single control loop and the problem to make a set Q of states invariant, the minimal data rate can be described by an entropy-like quantity, the so-called invariance entropy. Under some controllability and hyperbolicity assumptions, the invariance entropy can be expressed in terms of Lyapunov exponents. Furthermore, one can show that for making Q invariant with a data rate close to the smallest, no strategies more complicated than stabilization at periodic trajectories are necessary. For a network with n subsystems, which can all communicate with each other, there are different ways to formulate the question about the smallest data rate for the invariance problem, but also in this setting entropy-like quantities yield important information. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adjoint machines,state-behavior machines,and duality

A process X: $\text{K}$→$\text{K}$ is output if Dyn(X)→$\text{K}$ has a right adjoint; state-behavior if Dyn(X)→X has both left and right adjoints; and adjoint if X has a right adjoint and $\text{K}$ has countable coproducts. Output processes provide the proper setting for a general theory of state observability. We give a minimal realization theory using image factorization of a total response map. We give an adjointness theory for state-behavior machines and a duality theory for adjoint machines which clarifies classical linear system duality and yields an improved duality for nondeterministic automata. Adjoint machines (machines with adjoint input processes) provide the first integration of classical sequential machines (the only state-behavior machines in the category, Set, of sets), metric machines, topological machines, linear systems, nondeterministic automata and Boolean machines. There exist state-behavior machines which are not adjoint (but not in Set).     

Heavy traffic analysis of controlled multiplexing systems

The paper develops the mathematics of the heavy traffic approach to the control and optimal control problem for multiplexing systems, where there are many mutually independent sources which feed into a single channel via a multiplexer (or of networks composed of such subsystems). Due to the widely varying bit rates over all sources, control over admission, bandwidth, etc., is needed to assure good performance. Optimal control and heavy traffic analysis has been shown to yield systems with greatly improved performance. Indeed, the heavy traffic approach covers many cases of great current interest, and provides a useful and practical approach to problems of analysis and control arising in modern high speed telecommunications. Past works on the heavy traffic approach to the multiplexing problem concentrated on the uncontrolled system or on the use of the heavy traffic limit control problem for applications, and did not provide details of the proofs. This is done in the current paper. The basic control problem for the physical system is hard, and the heavy traffic approach provides much simplification. Owing to the presence of the control, as well as to the fact that the cost function of main interest is “ergodic”, the problem cannot be fully treated with “classical” methods of heavy traffic analysis for queueing networks. A basic result is that the optimal average costs per unit time for the physical problem converge to the optimal cost per unit time for the limit stationary process as the number of sources and the time interval goes to infinity. This convergence is both in the mean and pathwise senses. Furthermore, a “nice” nearly optimal control for the limit system provides nearly optimal values for the physical system, under heavy traffic, in both a mean and pathwise sense. This revised version was published online in June 2006 with corrections to the Cover Date.     

Flowchart machines

Let denote a conventional flowchart. Any algorithm can be represented by a flowchart. If action nodes in call then is a recursive flowchart. We show how to decompose arbitrary non-self-modifying programs into structure and atomic parts. We specifically give the synthesis procedure for a controller . can serve as the only sequencer in an execution of . If is recursive then is a pushdown machine, otherwise is a finite state machine. The next-state functionf and the output functiong of represent respectively all of the structure-, i.e. the programmer-oriented-, and all of the atomic-, i.e. the data-oriented-, parts of .f defines the flow or pattern of computations andg the actual transformations or operations on data. Thus we construct and analyze programs by constructing and analyzing their sequencers .     

Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines

This paper examines a model of a serial flow line with two workstations and an intermediate buffer. Each workstation consists of multiple unreliable parallel machines which are not necessarily identical, viz., the processing times, failure times and repair times of the parallel machines at each workstation are assumed to be exponentially distributed with non-identical mean rates. The system under consideration is solved via exact Markovian analysis. More specifically, a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity is developed and all possible transition equations are derived and solved analytically. Once the transition equations are solved the performance measures of the model under consideration can be easily evaluated. This model may be used as a decomposition block for solving larger flow lines with parallel unreliable machines at each workstation.     

Representation and analysis of transfer lines with machines that have different processing rates

A transfer line is a tandem production system, i.e. a series of machines separated by buffers. Material flows from outside the system to the first machine, then to the first buffer, then to the second machine, the second buffer, and so forth. In some earlier models, buffers are finite, machines are unreliable, and the times that parts spend being processed at machines are equal at all machines. In this paper, a method is provided to extend a decomposition method to large systems in which machines are allowed to take different lengths of time performing operations on parts. Numerical and simulation results are provided.     

Bifurcation analysis of a Lyapunov-based controlled boost converter

Lyapunov-based controlled boost converters have a unique equilibrium point, which is globally asymptotically stable, for known resistive loads. This article investigates the dynamic behaviors that appear in the system when the nominal load differs from the actual one and no action is taken by the controller to compensate for the mismatch. Exploiting the fact that the closed-loop system is, in fact, planar and quadratic, one may provide not only local but also global stability results: specifically, it is proved that the number of equilibria of the converter may grow up to three and that, in any case, the system trajectories are always bounded, i.e. it is a bounded quadratic system. The possible phase portraits of the closed-loop system are also characterized in terms of the selected bifurcation parameters, namely, the actual load value and the gain of the control law. Accordingly, the analysis allows the numerical illustration of many bifurcation phenomena that appear in bounded quadratic systems through a physical example borrowed from power electronics.     

OnTL-finite state machines

In this paper we introduce the notions of aTL-finite state machine,TL-retrievability,TL-separability,TL-connectivity and discuss their basic properties.     

Synergy in machines

The capability of a finite state machine constructed of component machines in a composition with feedback is shown to be greater than the capabilities of series-parallel (or cascade) compositions of these same components. A measure of the amount of feedback in a construction is defined and a hierarchy of classes of machines is obtained by increasing the amount of feedback permitted in the members of each class.     

Stochastic analysis of machine interference of a production system wit[hdot] identical machines

This paper examines the transient and steady–state interference characteristics of a production system with one operator and n identical, semi–automatic and reliable machines. A stochastic model is developed to describe the system and analytical expressions for the percentage interference and mean output rate permachine with arbitrary distribution of concurrent time and exponential distribution of procssing time of each machine, have been obtained by using a state–space method and the regeneration point technique. A particular case is investigated and numerical results are presented illustrating some features of this machine inter ference problem     

Semismooth support vector machines

Support vector machines can be posed as quadratic programming problems in a variety of ways. This paper investigates a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint under a duality construction. The quadratic term is a small rank update to a diagonal matrix with positive entries. The optimality conditions of the quadratic program are reformulated as a semismooth system of equations using the Fischer-Burmeister function and a damped Newton method is applied to solve the resulting problem. The algorithm is shown to converge from any starting point with a Q-quadratic rate of convergence. At each iteration, the Sherman-Morrison-Woodbury update formula is used to solve the key linear system. Results for a large problem with 60 million observations are presented demonstrating the scalability of the proposed method on a personal computer. Significant computational savings are realized as the inactive variables are identified and exploited during the solution process. Further results on a small problem separated by a nonlinear surface are given showing the gains in performance that can be made from restarting the algorithm as the data evolves.Accepted: December 8, 2003This work partially supported by NSF grant number CCR-9972372; AFOSR grant number F49620-01-1-0040; the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38; and Microsoft Corporation.     

Register machines with counters

Register machines with counters (RC machines) are studied. It is shown that any computable function can be strictly computed on RC machines with a bounded number of counters and programs. The place in the Kleene–Mostowski hierarchy of certain algorithmic problems related to RC machines is determined.     

OnTL-subsystems ofTL-finite state machines

In this paper we introduce the notions ofTL-subsystems, strongTL-subsystems and discuss their basic properties.