Optimization of the Control System Parameters with Use of the New Simple Method of the Largest Lyapunov Exponent Estimation. - Balcerzak, Marek; Dąbrowski, Artur; Kapitaniak, Tomasz; Jach, Anna (Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2013)
This text covers application of Largest Lapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a simulated control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [3] is compared to classical CPA criteria used in control engineering [1]. Introduction contains references to previous publications on Lyapunov stability. Later on, description of classical criteria for CPA along with formulae is presented. Significance of LLE in control systems is explained. Moreover, new efficient formula for calculation of LLE [3] is shown. In the second part simulation of the control system used for experiment is described. The next part contains results of the simulation in which typical criteria for CPA are compared with criterion based on value of LLE. In the last part results of the experiment are summed up and conclusions are drawn.
Keywords: Largest Lapunov Exponent; LLE; control system; parameters; optimization; controller; PID; inverted pendulum; IAE; ISE; ITAE; największy wykładnik Lapunowa; system sterowania; parametry; optymalizacja; kontroler; wahadło odwrócone