Effective Algorithm to Design PID-regulator by Numerical Optimization

摘要

Automatic control systems are used in all areas of technology, their accuracy determines the accuracy of the work of robots, manipulators on conveyors, transport systems and high-precision measuring systems. Static error is always minimized through the use of integrating link in regulator. High dynamic accuracy can be ensured by the correct calculation of the proportional and derivative links. If the coefficients are not calculated correctly, the system may lose stability. The minimum dynamic error is ensured only with the most correctly designed regulator. The best design method in the case of a relatively complex mathematical model of the object is a method of numerical optimization. There are software tools for modeling such systems and optimizing regulator, such as VisSim, SimInTech, Simulink + MATLAB, Mathcad, and others. These systems do not use the best algorithms for the specific purpose of the synthesis of PID-regulator, but simply the most well-known numerical optimization algorithms, such as Powell, Polak-Ribiere, Fletcher-Reeves, Monte-Carlo. As a result, in some cases, the coefficients calculated by the regulator are not efficient enough. The paper proposes an improvement in the numerical optimization algorithm. The proposed algorithm was studied by numerical simulation using an example of an object taken from an article by other authors, which allowed us to compare the results obtained by these authors with the results of using this algorithm. Comparison showed that the proposed method is more effective than all the previously described methods. The choice of the best cost (goal) function for these purposes and optimization of the task and simulation time are also necessary. All recommendations are combined into a formal description of the proposed methodology for solving the problem.