The scheduling problem in Continuous Annealing Line (CAL) can be described as a combinatorial optimization problem. Because of the vastness of the search area and the complicated problem structure, it is difficult to solve the problem only using the optimization algorithms. In this paper, a solving algorithm that combines the heuristic knowledge and optimization algorithms is presented and the new methodology how to use the heuristic knowledge in solving the scheduling problem is also discussed. The conventional expert system development methodology, which usually aims to built the expert problem solving model in detail and realize the model in the computer system, is nearly impossible to treat the numerous problem patterns and trial-error process that is necessary to solve the scheduling problem. The methodology described in this paper makes much account of practical use of the optimization algorithm and classify the heuristic knowledge considering its relation with the optimization algorithm in order to determine how to use the knowledge in constructing the solving algorithm. The scheduling algorithm developed through the methodology can offer a useful solution ten times faster than the human expert and shows good maintainability.
In this paper, we investigate the stochastic behavior of an elevator system from mathematical point of view. We formulate it as a queueing model and analyse its performance to derive the p.g.f. (probability generating function) of the queue length and to obtain the mean queue length. Based on the analytical results, we calculate the above performance measures under various types of scenarios and find that the mean queue length at each floor depends on its relative position to other floors as well as the arrival rate to the floor and the attainable speed of the elevator.
In Japan, a gravity sewer system is designed so that it satisfies the following conditions : the flow velocity is in the range from 0.6m/s to 3.0m/s and increases gradually to the downstream the slope becomes gradually gentle to the downstream. This paper presents methods to find out the minimum-cost or a close to the minimum-cost design which satisfies the above conditions : If a design flow and a design velocity are given to a section, a commercially available diameter that minimizes the slope of the section is uniquely determined. Then, in case of a relatively flat region, by connecting such pipes and slopes chosen for each section, the total amount of the covering soil over the sewers, therefore the total cost, is minimized. In case of a region where steep downhills are included, the problem can be reduced to a one-dimensional nonlinear programming program, and the solution can be found by the golden section search.
We consider the stability criterion of Popov for multivariable Lur'e systems. To derive the criterion using a Liapunov function, we need to restrict the class of nonlinearity in the system. The largest class reported so far is that of differentiable nonlinearities with symmetric Jacobian matrices. In this paper, we extend the class by removing the assumption of differentiability from a part of the nonlinearity. For nonlinearities which are not in this class, the Popov criterion is not valid. Therefore, we propose modified criteria to apply to systems with such nonlinearities. To do this, we take the symmetric part of the nonlinearity as nominal and treat the residual as a perturbation.
In this paper, modeling and vibration control of a flexible solar array paddle are considered. This problem has arisen, in particular, in the area of control of satellites and space stations which have large solar array paddles. We consider the flexible solar array paddle which is in zero gravity field and is rotated about two axes of the flexible plates by motors, respectively. We first derive partial differential equations and two sets of boundary conditions which represent vibration of the paddle and ordinary differential equations which represent the dynamics of angles of rotation of motors. Solving the related eigenvalue problem, the eigenvalues and the corresponding eigenfunctions are obtained. On the basis of a finite-dimensional modal model of the distributed-parameter system, a controller for the flexible solar array paddle is constructed. Simulation results confirm that the controller performs remarkably well.