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Showing papers in "Mathematical Problems in Engineering in 1996"


Journal ArticleDOI
TL;DR: In this article, a new definition of production systems bottlenecks is formulated and analyzed, and a method based on indirect but real-time data is developed to identify the bottleneck machine in a serial production line.
Abstract: In this work, a new definition of production systems bottlenecks is formulated and analyzed. Specifically, a machine is defined as the bottleneck if the sensitivity of the system's performance index to this machine's production rate in isolation is the largest. Although appealing from the systems point of view, this definition suffers a deficiency due to the fact that the sensitivities involved cannot be either measured on-line or efficiently calculated off-line. To avoid this, the paper develops a method based on indirect but real-time data. From this point of view, the main result of the work is as follows: The bottleneck machine in a serial production line can be identified by analyzing relationships between the so-called manufacturing blockage and manufacturing starvation of each machine. This leads to a simple rule for bottleneck identification. The rule requires neither the calculation of the production rate sensitivities nor the production rate itself. When the probabilities of manufacturing blockages and starvations are not available from on-line measurements, the paper presents their analytical estimates which, under certain conditions, can be used for bottleneck identification. Finally, a case study at an automotive component plant is described.

159 citations


Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamic systems, but on which only discrete-time actions are exercised.
Abstract: Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

142 citations


Journal ArticleDOI
TL;DR: The theory shows that sequential trim cannot work for free flight, and is exercised with periodic shooting to show how free-flying rotorcraft can be trimmed in a variety of ways by use of the general theory.
Abstract: In this paper we offer a general theory of rotorcraft trim. The theory is set in the context of control theory. It allows for completely arbitrary trim controls and trim settings for multi-rotor aircraft with tests to ensure that a system is trimmable. In addition, the theory allows for “optimal trim” in which some variable is minimized or maximized rather than set to a specified value. The theory shows that sequential trim cannot work for free flight. The theory is not tied to any particular trim algorithm; but, in this paper, it is exercised with periodic shooting to show how free-flying rotorcraft can be trimmed in a variety of ways (zero yaw, zero pitch, zero roll, minimum power, etc.) by use of the general theory. The paper also discusses applications to harmonic balance and auto-pilot trim techniques.

107 citations


Journal ArticleDOI
TL;DR: In this article, the problem of Lyapunov analysis of sliding motions was studied and the results of the analysis were applied to the design of a realistic bounded control of a sliding motion.
Abstract: The results concern the fundamental problem of Lyapunov analysis of sliding motions. It consist first to estimate the useful part of the sliding surface (the so-called “sliding domain”) and second to estimate the useful part of the state domain that is the domain of all initial conditions for which the corresponding solutions converge to the sliding domain. The application of such results concern the design of a realistic bounded control. Several examples are exposed in order to illustrate the obtained results.

106 citations


Journal ArticleDOI
TL;DR: In this article, the boundary value problem is considered and sufficient conditions for the existence of positive solutions are established for the special case λ = 1, sufficient conditions are also established for λ ≥ 0.
Abstract: We shall consider the boundary value problem y ( n ) + λ Q ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 2 ) ) = λ P ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 1 ) ) , n ≥ 2 , t ∈ ( 0 , 1 ) , y ( i ) ( 0 ) = 0 , 0 ≤ i ≤ n − 3 , α y ( n − 2 ) ( 0 ) − β y ( n − 1 ) ( 0 ) = 0 , γ y ( n − 2 ) ( 1 ) + δ y ( n − 1 ) = 0 , where 0,\alpha ,\beta ,\gamma$ " xmlns:mml="http://www.w3.org/1998/Math/MathML"> λ > 0 , α , β , γ and δ are constants satisfying 0,\beta , \delta \ge 0, \beta + \alpha > 0$ " xmlns:mml="http://www.w3.org/1998/Math/MathML"> α γ + α δ + β γ > 0 , β , δ ≥ 0 , β + α > 0 and 0$ " xmlns:mml="http://www.w3.org/1998/Math/MathML"> δ + γ > 0 to characterize the values of λ so that it has a positive solution. For the special case λ = 1 , sufficient conditions are also established for the existence of positive solutions.

36 citations


Journal ArticleDOI
TL;DR: In this paper, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived and the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations.
Abstract: Chebyshev polynomials are utilized to obtain solutions of a set of pth order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations. The Floquet Transition Matrix (FTM) can then be computed and its eigenvalues (Floquet multipliers) subsequently analyzed for stability. Two straightforward methods, the ‘differential state space formulation’ and the ‘differential direct formulation’, are presented and the results are compared with those obtained from other available techniques. The well-known Mathieu equation and a higher order system are used as illustrative examples.

31 citations


Journal ArticleDOI
TL;DR: All major characteristics for the queueing process in an analytically tractable form are obtained, based on the theory of first excess processes developed by the first author.
Abstract: The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than r and not greater than R(≥r). The server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.

23 citations


Journal ArticleDOI
TL;DR: In this article, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters are investigated.
Abstract: In this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic and convex modeling of acoustic excitation appears to be most suitable, since there is an insufficient information available on the acoustic excitation parameters, to justify the totally probabilitic analysis. Specifically, we postulate that the uncertainty parameters in the acoustic loading belong to a bounded, convex set. In the special case when this convex set is an ellipsoid, closed form solutions are obtained for the most and least favorable mean square responses of both the transverse displacement and bending moment of the structure. Several finite-span beams are exemplified to gain insight into proposal methodology.

21 citations


Journal ArticleDOI
TL;DR: In this article, a simple assembly system consisting of two components and one assembly machine is developed, and it is shown that the assembly is unimprovable with respect to workforce if each component machine is blocked as frequently as the assembly machines are starved for parts produced by this particular assembly machine.
Abstract: Improvability theory for a simple assembly system consisting of two components and one assembly machine is developed. Both constrained and unconstrained formulations are addressed. In the constrained case, it is shown that the assembly is unimprovable with respect to workforce if each component machine is blocked as frequently as the assembly machine is starved for parts produced by this particular assembly machine. The system is unimprovable with respect to work-in-process if, roughly speaking, all buffers have equal average steady state occupancy. In the unconstrained improvability case, it is shown that the bottleneck machine can be identified by analyzing the probabilities of the so-called manufacturing blockages and starvations. A generalization to n component—one assembly machine system is also included.

19 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the guaranteed cost property of the proposed control strategy for the linear case can be proved for the nonlinear case as well as for the continuous case.
Abstract: This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

17 citations


Journal ArticleDOI
TL;DR: It is shown that PLS can yield physical insight into the system from which empirical data has been collected and when there exists a non-linear cause-and-effect relationship between the independent and dependent variables, the PLS calibration model can yield prediction errors that are much less than those for CLS.
Abstract: In this paper we present partial least-squares (PLS), which is a statistical modeling method used extensively in analytical chemistry for quantitatively analyzing spectroscopic data. Comparisons are made between classical least-squares (CLS) and PLS to show how PLS can be used in certain engineering signal processing applications. Moreover, it is shown that in certain situations when there exists a linear relationship between the independent and dependent variables, PLS can yield better predictive performance than CLS when it is not desirable to use all of the empirical data to develop a calibration model used for prediction. Specifically, because PLS is a factor analysis method, optimal selection of the number of PLS factors can result in a calibration model whose predictive performance is considerably better than CLS. That is, factor analysis (rank reduction) allows only those features of the data that are associated with information of interest to be retained for development of the calibration model, and the remaining data associated with noise are discarded. It is shown that PLS can yield physical insight into the system from which empirical data has been collected. Also, when there exists a non-linear cause-and-effect relationship between the independent and dependent variables, the PLS calibration model can yield prediction errors that are much less than those for CLS. Three PLS application examples are given and the results are compared to CLS. In one example, a method is presented using PLS for parametric system identification. Using PLS for system identification allows simultaneous estimation of the system dimension and the system parameter vector associated with a minimal realization of the system.

Journal ArticleDOI
TL;DR: A variety of signal processing functions are performed by Underwater Acoustic Systems as discussed by the authors, such as detection to determine presence or absence of information signals in the presence of noise, or an attempt to describe which of a predetermined finite set of possible messages {mi,i,...,M} the signal represents; estimation of some parameter θˆ associated with the received signal (i.e. range, depth, bearing angle, etc.).
Abstract: A variety of signal processing functions are performed by Underwater Acoustic Systems. These include: 1) detection to determine presence or absence of information signals in the presence of noise, or an attempt to describe which of a predetermined finite set of possible messages {mi,i,...,M} the signal represents; 2) estimation of some parameter θˆ associated with the received signal (i.e. range, depth, bearing angle, etc.); 3) classification and source identification; 4) dynamics tracking; 5) navigation (collision avoidance and terminal guidance); 6) countermeasures; and 7) communications. The focus of this paper is acoustic communications.

Journal ArticleDOI
TL;DR: In this article, the authors considered the general linear programming problem over the cone of positive semi-definite matrices and provided a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution.
Abstract: We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.

Journal ArticleDOI
TL;DR: The proposed distributed algorithms are theoretically interesting and computationally attractive and used to provide robust and computational efficient solutions to the discrete Riccati equation.
Abstract: In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Journal ArticleDOI
TL;DR: In this paper, the possibility of using 1:1 and 1:2 IR to enhance the coupling in the system is established analytically using the perturbation method of multiple scales.
Abstract: Several recent studies have shown that vibrations in a two-degree-of-freedom system can be suppressed by using modal coupling based control techniques. This involves making the first two natural frequencies commensurable (e.g, in a ratio of 1:1 or 1:2) to establish a state of Internal Resonance (IR). When the system exhibits IR, vibrations in the two directions are strongly coupled resulting in a beat phenomenon. Upon introducing damping in one direction, oscillations in both directions can be quickly suppressed. In this paper we consider vibration suppression of a flexible two-degree-of-freedom gyroscopic system using 1:1 and 1:2 IR. The possibility of using 1:1 and 1:2 IR to enhance the coupling in the system is established analytically using the perturbation method of multiple scales. The results of IR based control strategy are compared with a new method, which is based on tuning the system parameters to make the mode shapes identical. Results indicate that this new technique is more efficient and easy to implement than IR based control strategies. Another advantage of this method is that there is no restriction on the frequencies as in the case of IR. Finally, a control torque is obtained which on application automatically tunes the system parameters to establish modal coupling.

Journal ArticleDOI
TL;DR: Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs.
Abstract: Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven by the adaptive control law and bounded discontinuous control. The discontinuous control driven by the sliding control law is then obtained so that the output error quickly converges to zero. Finally, the performance improvements obtained by adding the sliding mode control input are shown through computer simulations.

Journal ArticleDOI
TL;DR: In this article, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing.
Abstract: LIDAR (Laser Integrated Radar) is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF), which has been the standard nonlinear filter in past engineering applications.

Journal ArticleDOI
TL;DR: In this paper, a technique for evaluation of eigenvalues in the solution of the differential equation d2y/dr2 was developed for evaluating the eigenvalue of the solution.
Abstract: A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2

Journal ArticleDOI
TL;DR: In this article, a self-consistent Boltzmann-Poisson-Schrodinger solver for high-electron mobility transistors is presented, where the quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzman equation along with the Schrodinger and Poisson equations, selfconsistently.
Abstract: A self-consistent Boltzmann-Poisson-Schrodinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrodinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current-voltage characteristics, transconductance, gate capacitance, and unity-gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7 μ m , and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity-gain frequency of 47.8 GHz.

Journal ArticleDOI
TL;DR: New distributed algorithms, which are able to locally process the information and which deliver identical results to those generated by their centralized counterparts are presented.
Abstract: The multisensor estimation problem is considered in this paper. New distributed algorithms, which are able to locally process the information and which deliver identical results to those generated by their centralized counterparts are presented. The algorithms can be used to provide robust and computationally efficient solutions to the multisensor estimation problem. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Journal ArticleDOI
TL;DR: In this article, a self-consistent Boltzmann-Schrödinger-Poisson simulator for HEMT was presented, in which only electrons in the first subband were assumed to be quantized with their motion restricted to 2 dimensions and the second and higher subbands were treated as bulk system behaving as 3 dimensional electron gas.
Abstract: In Part I of this paper we reported a self-consistent Boltzmann-Schrödinger-Poisson simulator for HEMT in which only electrons in the first subband were assumed to be quantized with their motion restricted to 2 dimensions. In that model, the electrons in the second and higher subbands were treated as bulk system behaving as a 3 dimensional electron gas. In Part II of this paper, we extend our simulator to a self-consistent full-quantum model in which the electrons in the second subband are also treated as quantized 2 dimensional gas. In this model, we consider the electrons in the lowest two subbands to be in the quantum well forming the 2-dimensional electron gas, and the electrons in the third and higher subbands to behave as bulk electrons with no restrictions in their motion. We have further incorporated an additional self-consistency by calculating the field-dependent, energy-dependent scattering rates due to ionized impurities and polar optical phonons. The two higher moments of Boltzmann transport equation are numerically solved for the two lowest subbands and the bulk system; six transport equations, four for the two subbands and two for the bulk system. The Schrödinger and Poisson equations are also solved self-consistently. The wavefunctions obtained are used to calculate the ionized impurity scattering and the polar optical phonon scattering rates. The rates of transfer of electrons and their energies to and from each subband are calculated from these intersubband and intrasubband scattering rates.

Journal ArticleDOI
TL;DR: In this article, an analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented, and it is shown that the trajectories of these systems are uniformly bounded with an ultimate bound under certain conditions.
Abstract: An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.

Journal ArticleDOI
TL;DR: In this paper, a generalization of the classical solution expression for linear, constant-coefficient, homogeneous difference equations that accommodates the most general case of repeated zero-valued characteristic roots is presented.
Abstract: Linear, constant-coefficient difference equations play a central role in many areas of engineering, where cases involving repeated zero-valued characteristic roots are sometimes of particular interest. Unfortunately, the classical solution expression presented in the mathematical literature of difference equations is not valid for this latter case. In this paper we develop a unique generalization of the classical solution expression for linear, constant-coefficient, homogeneous difference equations that accommodates the most general case of repeated zero-valued characteristic roots, thereby “completing” the classical theory. A worked example is presented to illustrate our result.