SELECTION OF THE SET OF ALLOWABLE VALUES OF THE VARIABLE PARAMETERS OF THE STABILIZER OF A COMPLEX DYNAMIC OBJECT

Abstract

Topicality. One of the most important tasks in the application of computational methods for the parametric synthesis of controllers of complex dynamic objects is the task of determining the set of permissible values of the variable parameters of the controller, where the target function is calculated based on the solutions of the mathematical model of the disturbed motion of the dynamic object with its subsequent minimization. The purpose of the work is to construct the set of permissible values of variable parameters of the stabilizer of a complex dynamic object when applying the algorithmic combined method of parametric synthesis of stabilizers of complex dynamic objects, the essence of which is the direct calculation of the integral quadratic functional on the solutions of a closed dynamic system with subsequent finding of its global minimum through a sequential combination of two algorithms – the Sobol grid algorithm and the Nelder-Mead algorithm. Results. With the help of the Sobol grid construction algorithm, the starting point of the computational process is brought to the node of the Sobol grid, which is located in the small vicinity of the point of the global minimum. At the second stage of optimization, the found Sobol grid node is selected as the starting point for applying the Nelder-Mead method, which is implemented by the Optimization Toolbox software product of the MATLAB package or the Minimize software product of the MATHCAD package and leads the computational process to the point of the global minimum. Conclusion. The paper proves a theorem according to which the stability region of a closed system of the first approximation can be taken as such a set, and also gives an example of a solution to the problem of parametric synthesis of the stabilizer of the car's course stability system during its emergency braking.