Design of a control system for a self-erecting inverted pendulum process

Obrnuto rotacijsko njihalo reprezentira primjer dinamički nelinearnog i nestabilnog sustava sa dva stupnja slobode gibanja. U ovom radu je implementiran te prikazan hibridni regulator s ciljem dovođenja sustava u okolinu ravnotežnog položaja te stabilizacije njihala u ravnotežnom položaju. Sustav je opisan pomoću matematičkog modela koji je zbog svoje nelinearne dinamike jako složen. Pri opisu matematičkog modela korištena je Lagrange-ova metoda kojoj je glavna ideja očuvanje momenta i energije. Za slučaj dovođenja sustava u okolinu ravnotežnog položaja projektiran je swing-up regulator, dok za slučaj stabilizacije njihala u ravnotežnom položaju projektiran je regulator pomoću metode polova. Swing-up algoritam je dizajniran jer stabilizirajući regulator djeluje samo kad je kut otklona njihala u okolini ravnotežnog položaja te se temelji na energetskom principu tako da sustav računa trenutnu energiju sustava te mu u svakom trenutku daje dodatnu energiju kako bi došao u ravnotežni položaj. Za projektirani regulator pomoću metode polova provedena je linearizacija matematičkog modela te sinteza regulatora na lineariziranom i nelinearnom modelu. U konačnici, hibridni regulator je provjeren simulacijski unutar Matlab okruženja te eksperimentalno na laboratorijskom postavu.Inverted rotating pendulum represents an example of a dynamically nonlinear and unstable system with two rotational degrees of freedom. What is implemented and shown in this paper is a hybrid controller to bring the system into the balanced position and stabilization of the pendulum in a balanced position. The system is described by a mathematical model which, due to its nonlinear dynamics, is very complex. In the description of the mathematical model, Lagrange’s method was used, whose main idea is conservation of momentum and energy. In the case of bringing the system into the balanced position the model has been designed with a swing-up controller, and in the case of stabilization of the pendulum in a balanced position, controller has been designed using the method of poles. Swing-up algorithm was developed because the stabilizing controller only works when the deflection angle of the pendulum is around the balanced position and is based on the energy principle, so that the system calculates the current energy of the system, and provides him, at any time, with extra energy to reach the balanced position. For the designed controller using the method of poles, linearization of the mathematical model and the synthesis of the controller on the linear and nonlinear model was performed. Ultimately, a hybrid controller is verified by simulation in Matlab environment and experimentally in the laboratory setup