Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Numerical and experimental identifications of a motor-toggle mechanism

In this paper, the punching machine is made up by a toggle mechanism driven by a permanent magnet (PM) synchronous servomotor. First, Hamilton’s principle, Lagrange multiplier, geometric constraints and partitioning method are employed to derive its dynamic equations. The system parameters are difficult to obtain if the mechanism’s components cannot be taken apart. In this paper, the recursive least-squares (RLS) method is adopted to identify these parameters of the motor-toggle mechanism, which cannot be disassembled and their real values cannot be measured. From the comparison between the numerical simulations and experimental results, it is shown that the RLS identification method is feasible, and the parameters of links’ masses and friction coefficient are identified accurately.     

Comparison between mathematical modeling and experimental identification of a spatial slider–crank mechanism

In this paper, Hamilton’s principle, Lagrange multiplier, geometric constraints, partitioning method and Baumgarte stabilization method (BSM) are employed to derive the dynamic equations of a spatial slider–crank mechanism that is driven by a servomotor. The formulation considers the effects of links masses, external forces and motor electric inputs. Comparing dynamic responses between the experimental results and numerical simulations, dynamic modeling gives a wonderful interpretation for the spatial slider–crank mechanism. In this paper, a new identification method based on real-coded genetic algorithm (RGA) is presented to identify the parameters of a spatial slider–crank mechanism. The method promotes the calculation efficiency very much, and is calculated by real-code without the operations of encoding and decoding. The results of numerical simulations and experimental results prove that the identification method is feasible. The contributions of this paper are that the comparison of mathematical modeling and identification between numerical simulations and experimental results are all realized.     

Ostrowski’s fourth-order iterative method speedily solves cubic equations of state

Pressure-volume-temperature (P-V-T) data are required in simulating chemical plants because the latter usually involve production, separation, transportation, and storage of fluids. In the absence of actual experimental data, the pertinent mathematical model must rely on phase behaviour prediction by the so-called equations of state (EOS). When the plant model is a combination of differential and algebraic equations, simulation generally relies on numerical integration which proceeds in a piecewise fashion unless an approximate solution is needed at a single point. Needless to say, the constituent algebraic equations must be efficiently re-solved before each update of derivatives. Now, Ostrowski’s fourth-order iterative technique is a partial substitution variant of Newton’s popular second-order method. Although simple and powerful, this two-point variant has been utilised very little since its publication over forty years ago. After a brief introduction to cubic equations of state and their solution, this paper solves five of them. The results clearly demonstrate the superiority of Ostrowski’s method over Newton’s, Halley’s, and Chebyshev’s solvers.     

Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer-Kaup equations

A (2+1) dimensional Broer-Kaup system which is obtained from the constraints of the KP equation is of importance in mathematical physics field. In this paper, the Painlevé analysis of (2+1)-variable coefficients Broer-Kaup (VCBK) equation is performed by the Weiss-Kruskal approach to check the Painlevé property. Similarity reductions of the VCBK equation to one-dimensional partial differential equations including Burger’s equation are investigated by the Lie classical method. The Lie group formalism is applied again on one of the investigated partial differential equation to derive symmetries, and the ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.     

Analysis of microwave induced natural convection in a single mode cavity (Influence of sample volume, placement, and microwave power level)

The heating of water layer using microwave oven with a rectangular waveguide has been studied both numerically and experimentally. The mathematical model is validated with the experimental data. The transient Maxwell’s equations are solved by using the Finite Difference Time Domain (FDTD) method to describe the electromagnetic field inside the waveguide and sample. The temperature profile and velocity field within sample are determined by the solutions of the momentum, energy and Maxwell’s equations. In this study, the effects of physical parameters, e.g. microwave power level, placement of sample inside the waveguide, volume of sample, are studied. The distribution of electric field, temperature profile and velocity field are presented in details. The results show good agreement between simulation results and experimental data. Conclusively, the mathematical model presented here correctly explains the phenomena of microwave heating of water layer.     

Trajectory planning based on minimum absolute input energy for an LCD glass-handling robot

The main idea of this paper is to design a novel point-to-point (PTP) trajectory based on minimum absolute input energy (MAIE) for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The mechatronic system is described by a mathematical model of electrical and mechanical coupling equations. To generate the MAIE PTP trajectory, we employ a high-degree polynomial and compare with the trapezoidal, cycloidal and zero-jerk trajectories for various constraint conditions, which satisfy their corresponding desired constraints of angular displacement, speed, acceleration and jerk at the start and end times. The real-coded genetic algorithm (RGA) is used to search for the coefficients of high-degree polynomials for the PTP trajectories, and the inverse of absolute input electrical energy is adopted as a fitness function. From numerical simulations, it is found that either increasing the degree number of polynomials or decreasing the constraints at the start and end times will decrease the absolute input electrical energy. The proposed methodology for designing the MAIE PTP trajectory can also be applied to any mechatronic system driven by a PMSM.     

Fleet-sizing and service availability for a vehicle rental system via closed queueing networks

In this paper, we address the problem of determining the optimal fleet size for a vehicle rental company and derive analytical results for its relationship to vehicle availability at each rental station in the company’s network of locations. This work is motivated by the recent surge in interest for bicycle and electric car sharing systems, one example being the French program Vélib (2010). We first formulate a closed queueing network model of the system, obtained by viewing the system from the vehicle’s perspective. Using this framework, we are able to derive the asymptotic behavior of vehicle availability at an arbitrary rental station with respect to fleet size. These results allow us to analyze imbalances in the system and propose some basic principles for the design of system balancing methods. We then develop a profit-maximizing optimization problem for determining optimal fleet size. The large-scale nature of real-world systems results in computational difficulties in obtaining this exact solution, and so we provide an approximate formulation that is easier to solve and which becomes exact as the fleet size becomes large. To illustrate our findings and validate our solution methods, we provide numerical results on some sample networks.     

Recrystallization behavior of a Nb-microalloyed steel during hot compression

Using a Thermecmastor-Z hot simulator, dynamic recrystallization (DRX) and static recrystallization (SRX) behavior of a Nb-microalloyed steel was investigated by single-hit compression tests and double-hit compression tests, respectively. The experimental results show that DRX will more easily occur at higher deformation temperature and lower strain rate. The deformation activation energy and stress exponent for the Nb-microalloyed steel are calculated to be 379.29 ± 23.56 kJ/mol and 5.76 in temperature range of 950 °C to 1100 °C by regression analysis, respectively. Furthermore, a semi-empirical model is developed to identify the peak stress and strain for DRX. It is found that SRX kinetics follows Avrami’s law, and the softening fraction predicted by the model agrees well with experimental results.     

Comments on “A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect”

The purpose of this paper is to point out that if there are some machines that do not process any job then the mathematical programming model provided by Eren [T. Eren, A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect, Applied Mathematics and Computation 209 (2009) 186-190] may not be a valid one. A simple way to fix this problem is given. Furthermore, based on the idea of Eren’s model, a general mathematical programming model is proposed.     

Analysis and numerical solution of a piezoelectric frictional contact problem

We consider a mathematical model which describes the frictional contact between an electro-elastic–visco-plastic body and a conductive foundation. The contact is modelled with normal compliance and a version of Coulomb’s law of dry friction, in which the stiffness and the friction coefficients depend on the electric potential. We derive a variational formulation of the problem and we prove an existence and uniqueness result. The proof is based on a recent existence and uniqueness result on history-dependent quasivariational inequalities obtained in [15]. Then we introduce a fully discrete scheme for solving the problem and, under certain solution regularity assumptions, we derive an optimal order error estimate. Finally, we present some numerical results in the study of a two-dimensional test problem which describes the process of contact in a microelectromechanical switch.     

An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity

To attract more sales suppliers frequently offer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity W. In this paper, we generalize [Goyal, S.K., 1985. EOQ under conditions of permissible delay in payments. Journal of the Operational Research Society 36, 335–338] economic order quantity (EOQ) model with permissible delay in payment to reflect the following real-world situations: (1) the retailer’s selling price per unit is significantly higher than unit purchase price, (2) the interest rate charged by a bank is not necessarily higher than the retailer’s investment return rate, (3) many items such as fruits and vegetables deteriorate continuously, and (4) the supplier may offer a partial permissible delay in payments even if the order quantity is less than W. We then establish the proper mathematical model, and derive several theoretical results to determine the optimal solution under various situations and use two approaches to solve this complex inventory problem. Finally, a numerical example is given to illustrate the theoretical results.     

Mathematical modelling and analysis of temperature effects in MEMS

This article is concerned with the mathematical analysis of models for Micro-Electro-Mechanical Systems (MEMS). These models arise in the form of coupled partial differential equations with a moving boundary. Although MEMS devices are often operated in non-isothermal environments, temperature is often neglected in the mathematical investigations. In light of this finding the focus of our modelling is to incorporate temperature and the related material properties. We derive a full model for this coupling and discuss a simplified version as well. Lastly, we prove local well-posedness in time and also global well-posedness under additional assumptions on the model’s parameters.     

Stability Analysis of a Reduced Heat Exchanger Model

We consider the mathematical model of a heat exchanger in a heat pumping system using carbon dioxide as refridgerant. From the Euler equations of compressible fluid flow we derive a reduced model, called the zero Mach-number limit, by eliminating time scales associated with soundwaves. The reduced model is a highly nonlinear partial differential-algebraic equation (PDAE). We analyse the stability of this model and show that it is possible to use simple spatial discretisations within the method of lines (MOL), a standard practice in many system simulation software, to simulate the system. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Valuation of guaranteed annuity options using a stochastic volatility model for equity prices

Guaranteed annuity options are options providing the right to convert a policyholder’s accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970’s and 1980’s when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990’s. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant.     

Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.     

Neural network control of seat vibrations of a non-linear full vehicle model using PMSM

In this paper, the dynamic behaviour of a non-linear eight degrees of freedom vehicle model having active suspensions and passenger seat using Permanent Magnet Synchronous Motor (PMSM) controlled by a Neural Network (NN) controller is examined. A robust NN structure is established by using principle design data from the Matlab diagrams of system functions. In the NN structure, Fast Back-Propagation Algorithm (FBA) is employed. The user inputs a set of 16 variables while the output from the NN consists of f₁–f₁₆ non-linear functions. Further, the PMSM controller is also determined using the same NN structure. Various tests of the NN structure demonstrated that the model is able to give highly sensitive outputs for vibration condition, even using a more restricted input data set. The non-linearity occurs due to dry friction on the dampers. The vehicle body and the passenger seat using PMSM are fully controlled at the same time. The time responses of the non-linear vehicle model due to road disturbance and the frequency responses are obtained. Finally, uncontrolled and controlled cases are compared. It is seen that seat vibrations of a non-linear full vehicle model are controlled by a NN-based system with almost zero error between desired and achieved outputs.     

An interactive method for parametric identification of the mathematical model of a parachute system using computer graphics

A simple mathematical model of the motion of a parachute system in space is described and an interactive algorithm for parametric identification of the model is proposed. The algorithm selects the model parameters that minimize the deviation of the calculated dependences from experimental observations on the computer graphic monitor.Moscow. Translated from Dinamicheskie Sistemy, No. 10, pp. 106–111, 1992.     

永磁同步电机伺服系统的有限时间位置控制

研究了永磁同步电机伺服系统的位置跟踪问题.利用反馈线性化的思想,对永磁同步电机的数学模型进行分析,实现了电机模型的精确线性化和解耦.首先,将永磁同步电机位置跟踪系统采用反馈线性化技术变换为两个线性子系统,分别对其设计相应的基于连续状态反馈线性化的有限时间控制器,并设计了有限时间负载观测器来观测估计外部负载扰动.对永磁同步电机位置跟踪的闭环系统进行了稳定性的分析.与对应的渐近稳定控制的方案相比,基于有限时间的控制方案实现了永磁同步电机对期望信号的有限时间跟踪,获得了更好的动态响应和抗扰动性能.仿真结果表明了该控制方案的有效性.     

A comprehensive extension of an integrated inventory model with ordering cost reduction and permissible delay in payments

Huang (2010) [1] proposed an integrated inventory model with trade credit financing in which the vendor decides its production lot size while the buyer determines its expenditure to minimize the annual integrated total cost for both the vendor and the buyer. In this paper, we extend his integrated supply chain model to reflect the following four facts: (1) generated sales revenue is deposited in an interest-bearing account for the buyer, (2) the buyer’s interest earned is not always less than or equal to its interest charged, (3) the total number of shipments in one lot size is the vendor’s decision variable to minimize the cost, and (4) it is vital to have a discrimination term which can determine whether the buyer’s replenishment cycle time is less than the permissible delay period or not. We then derive the necessary and sufficient conditions to obtain the optimal solution, and establish some theoretical results to characterize the optimal solution. Finally, numerical examples are presented to illustrate the proposed model and its optimal solution.