Vyaznikov

pp. 279-290

The article deals with a problem of optimal control of caterpillar machine movement with regard to the driver as a feedback loop of the dynamic system. In order to build a control algorithm a mathematical model of caterpillar machine motion which takes into account non-holonomic links between caterpillars and soil was used. External control action was formalised in the form of an objective function. State parameters of an object were determined by the measuring system which was also subject to random perturbations. The maximum principle of P.S. Pontryagin was used for synthesising optimal control of a caterpillar machine. During optimization of an object one wants to find a vector of control action considering constraints from the minimum of composed functions expressing specified criteria. A problem of synthesizing time optimal control was considered. It was noticed that a system is time optimal if minimal transition time is provided, considering restrictions imposed on control and output coordinates. The principle of forcing dynamic processes at certain time intervals by increasing control signal within the specified range was used to reduce duration of the transition process.

This article considers the question of stability rating of a tracklaying vehicle’s curvilinear motion, considering the lateral drift. Methods of the theory of ordinary differential equations were used to determine stability boundaries of a dynamic model. The solution obtained by the numerical method with the specified step of integration is presented with a discrete sequence of points in a metric space. It was shown that the phase trajectory tends to an isolated limit set which, in the model, is a local integral manifold. Stability conditions of the limit set are emphasized. The developed algorithm of numerical stability assessment of solution of a system of equations is based on the Poincare-Bendixson theorem for differentiable manifolds. Also, the author considers an approach to solving the problem of motion stability on the basis of mapping the dynamic regimes on the parameter plane and defining the boundary of the domain of possible motion parameters of a tracklaying vehicle.