To the Optimal Use of Technological Capabilities of the Excavator – Dragline in Construction

The mathematical model of motion of system “boom on a turning platform – bifilar suspended bucket” was created. As a control function, we choose the moment of force relatively non-movable base. The length of suspension of the bucket is assumed to be constant. The bucket of excavator is suspended bifilar. The bucket and the arrow needs to be moved from initial rest final rest position. The results of solution of the problem of rapid movement of bucket of excavator dragline are presented. The structure of an optimal control law has been calculated by means of maximum Pontryagin' s principle and the method of control parameterization. A simple technique of calculations of optimal bucket trajectories has been developed. The dynamic of optimal control laws of the bucket and the arrow has been studied. Special software is created.


Introduction
At present technological capabilities of the heavy walking excavator -dragline, for a variety of reasons, are used not fully [1][2][3]. Relevance of a problem of performance improvement of the excavatordragline doesn't raise doubts.
In [4][5][6][7][8] developed mathematical optimal control theory. In [9] described an effective method for analysis of maneuvering capabilities of controlled mechanical systems and results of its application for solving the problem of optimum maneuvering of aircraft and spacecraft. In [10] described a numerical method for optimization of high dimensionality systems. These methods based on [4][5][6][7][8].
In [1], using methods of [9][10], provides the results of application of the developed technology to the problem of maximum turn angle dragline -excavator boom within a fixed time interval, with finite damping of occurring oscillations of a bucket, which bifilar attached to a boom of excavator.
This article provides the results of application of the method [9][10] to solve the problem about the fastest movements of a dragline excavator bucket and arrow to a given point with finite damping of occurring oscillations of a bucket attached to a boom. The considered problem is reciprocal for the problem of maximum boom swing within a fixed time interval. The results obtained in the article are in complete agreement with the results of solving the problem turn the excavator to the maximum angle within the required time [1].

Problem definition
Movement of the model "boom on a turning platformbifilar suspended bucket" (Fig.1) under certain circumstances may be described by the following system of differential equations [2-3]: where: M -a angle of turning of platform around vertical axis, V -bucket deflection from the boom plane, normalized to the turntable swing axis, J -normalized moment of system inertia in relation to the turntable swing axis, M -moment of force around the axis of the turntable, l -normalized length of the suspension, g -gravitational acceleration, t -time of motion. ( The control function Its required to minimize the total time of motion: from the rest state (2) to the desired rest state: Control function ) (t M should provide that the maximum angular speed of turn of an arrow shan't exceed the given value 1 The formulated problem of optimum control may be reduced to the standard problem of optimum control with limitations for the control function and phase variable [5,10]. Note that the formulated problem is similar to the problem of minimum time of movement of a mathematical pendulum with a movable suspension point from one equilibrium position to another equilibrium position [8].

Algorithms of the method of controls parameterization
Qualitative analysis of the optimum control structure is provided in [1][2]. Optimal controls laws were founded. These functions takes the form as shown at the Fig. 2. In order to get these functions were founded the algorithms of the method of controls parametrization. The provided below algorithms use the essential properties of the symmetry of control function. The control laws shown at the Fig. 2а will be parametrized as  Table 1. Key parameters of optimal motion of bucket and boom.

Conclusion
The main results of the investigation can be summarized as follow: 1. The method of investigation of maneuvering capabilities of controllable mechanical systems was adapted for the problem of increasing performance of excavator -dragline. 2. Efficiency of the developed method was demonstrated through solving the problem of operating speed during swing of boom of dragline excavator to the required angle with finite damping of occurring oscillations of a bucket bifilarly attached to a boom. Obtained results are in complete agreement with the results of solving the problem turn the excavator to the maximum angle within the required time [1]. 3. The developed model is the base of special purpose software. The described model is included into the automated management system of enterprise. The model is used for calculation of optimal booms trajectories of dragline -excavator. To solve the optimal control problem at computer it takes less 2 second.