Optimization of Programmed Trajectories of Moving Objectʼs Stabilization Based on Control Systems of Variable Structure

Abstract

The article considers optimal systems that provide dynamic systems with highcontrol quality indicators: speed, accuracy, and low energy consumption. An approach to the synthesis of robust-optimal systems based on the use of feedbackwith a variable structure is being developed and includes the following mainstages: planning of the programmed optimal trajectory; determination of moments of switching of control functions in feedback loops of the object; synthesis of control functions in the corresponding feedback loops of a multidimensional object. The application of the proposed order of synthesis of systems witha variable structure for various types of objects based on the preliminary construction of optimal programmed trajectories of stabilization of dynamic processes allows optimizing the stabilization processes of nonlinear non-stationarysystems of high order. Optimal programmed stabilization trajectories are formedfrom segments established relative to the corresponding derivative of the motioncoordinate, based on polynomial forms for given boundary conditions and theoptimality criterion, taking into account limited control values, and are solvedfor the time of moments of switching of control and the time of the end of thetransition process based on a system of algebraic equations. Control synthesis iscarried out taking into account the initial values based on the equations of thebalance of forces and moments efforts on the moving object and their derivatives. The optimal trajectory and control are formed in such a way that, duringthe synthesis of an additional robust control circuit (with feedback from theoutput of the object) to compensate for the incomplete certainty of the mathematical model and uncontrolled (unmeasured) disturbances and noises, sufficiently limited areas of changing the coordinates of the moving object relative to given values. In the future, this allows the construction of sufficientlyeffective and practical in the implementation of robust-optimal control systems, for example, marine mobile objects, quadcopters, that function in conditions of considerable uncertainty.