Feedback control of decoupled bending and torsional vibrations of flexible beams

In this article, we consider a flexible beam with a rigid body, of which the bending vibration and the torsional vibration are decoupled. Therefore we need two control motors to suppress the vibrations. Each set of dynamic equations is treated in the form of an appropriate Hilbert space. A stabilizing feedback control law of each rotation motor will be established on the basis of modal analysis. A set of experiments has been carried out, and the results demonstrate the effectiveness of the dynamic model and the proposed control law. © 1994 John Wiley & Sons, Inc.     

Interactive multiobjective fuzzy random programming through the level set-based probability model

This paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients. A new fuzzy random programming model is proposed by extending the ideas of level set-based optimality and a stochastic programming model. The original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model. An interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined Pareto optimal solutions. It is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method.     

COMPUTATIONAL METHODS THROUGH GENETIC ALGORITHMS FOR OBTAINING STACKELBERG SOLUTIONS TO TWO-LEVEL MIXED ZERO-ONE PROGRAMMING PROBLEMS

In this paper, we develop computational methods for obtaining Stackelberg solutions to two-level mixed zero-one programming problems in which the decision maker at the upper level controls zero-one variables and the decision maker at the lower level controls real variables. To illustrate two-level mixed zero-one programming problems, we formulate a facility location and transportation problem as a two-level mixed zero-one programming problem. We develop computational methods through genetic algorithms for obtaining Stackelberg solutions. To demonstrate the feasibility and efficiency of the proposed methods, computational experiments are carried out and comparisons between the methods based on the branch-and-bound techniques and the proposed methods are provided.     

INTERACTIVE FUZZY PROGRAMMING BASED ON FRACTILE CRITERION OPTIMIZATION MODEL FOR TWO-LEVEL STOCHASTIC LINEAR PROGRAMMING PROBLEMS

In this article, we focus on two-level linear programming problems involving random variable coefficients in objective functions and constraints. Following the concept of chance constrained programming, the two-level stochastic linear programming problems are transformed into deterministic ones based on the fractile criterion optimization model. After introducing fuzzy goals for objective functions, interactive fuzzy programming to derive a satisfactory solution for decision makers is presented as a fusion of a stochastic approach and a fuzzy one. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.     

Cooling load prediction in a district heating and cooling system through simplified robust filter and multilayered neural network

Cooling load is a heat value of cold water used for air conditioning in a district heating and cooling system. Cooling load prediction in a district heating and cooling system is one of the key techniques for smooth and economical operation. In this article, cooling load prediction in such a district heating and cooling system is considered. Unfortunately, since actual cooling load data usually involve measurement noises, outliers, and missing data for several reasons, a prediction method considering the effect of the outliers and missing data is desirable. In this article, a new prediction method using a simplified robust filter to improve a numerical stability problem of a robust filter and a three-layered neural network, is proposed. Applications of the proposed method and some other methods to actual cooling load data in a district heating and cooling system involving outliers and missing data show the usefulness of the proposed method.     

Feedback stabilization of a class of distributed systems and construction of a state estimator

In this paper, we study feedback stabilization of a class of distributed systems governed by partial differential equations of parabolic type and its application to constructing a state estimator for asymptotic state identification. It is proved that, when a controller (an observation) can be arbitrarily constructed, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant. As an application of this result, it is shown that a state estimator can be constructed, the output of which approaches asymptotically the real state of the system with an arbitrary convergence rate.     

Optimal control of container cranes

A dynamical model of container cranes is derived by using Lagrange's equation. When a ship is loaded or unloaded with containers, the total motion of the container load is divided into five fundamental sections. For each fundamental type of motion, the optimal control is calculated such that the corresponding trajectory satisfies the specified boundary conditions and that the swing of the container load during the transfer is minimized. A new algorithm which is employed for computing the optimal control is explained in detail. Some results of numerical computation are also shown.     

Modeling and feedback control of a flexible arm

When a flexible arm is rotated by a motor about an axis through the arm's fixed end, transverse vibration may occur. The motor torque should be controlled in such a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested as soon as possible at the end of rotation. In this paper, we first derive a partial differential equation and a set of boundary conditions governing the vibration. Then, a feedback control system which incorporates a dynamic compensator is designed using sensor outputs. A set of experiments has been constructed to demonstrate control strategies for a flexible arm, where a strain gage was used as a vibration sensor and a microcomputer was equipped as a controller. Several satisfactory experimental results are shown.     

Modeling and control of coupled bending and torsional vibrations offlexible beams

An evolution equation which governs coupled bending and torsional vibrations of flexible beams with a tip body is derived based on Lagrangian dynamics. A feedback control scheme is shown for suppressing the vibrations