Discrete-Time Rule-based Time Optimal Controller

Abstract

The article presents a discrete rule-based optimal control (D-RBOC) algorithm, as an alternative to known solutions for discrete time optimal control of a double integrator plant, which is the simplest positioning process. The algorithm was designed for a double integrator system, with the step response invariant discretization, using rules developed for the movement in the state space. The comparison of the proposed solution with fhan solutions, which are widely spread in the literature, proves the correctness of the former. The article shows that the developed D-RBOC behavior is very close to other optimal regulators. Because in the real physical system implementation, the control loop is affected by time delay due to processing, conversions, transport, etc. in the second part of article, the D-RBOC algorithm is adapted for this situation. The adaptation is based on time delay compensation and can also be used for other optimal control algorithms. The experiments were performed with two dSPACE systems.