LQR controller design and performance comparison with metaheuristic algorithms for the gantry crane system

In the thesis, the design and performance analysis of Genetic algorithm (GA), Artificial Bee Colony (ABC), Vibrating Particle System (VPS) and Big Bang-Big Crunch (BB-BC) and Thermal Exchange Optimization (TEO) algorithms for the control parameters of the Linear Quadratic Regulator (LQR) controller for the pendulum type gantry crane system are presented in detail. The aim of the optimization is to design an LQR controller to follow the command of the desired position as soon as possible and eliminate pendulum oscillations. To address this problem and to provide a solution, is designed the novel multi-objective function considers the significant parameters of the control responses. Vibrating Particle System, Big Bang-Big Crunch and Thermal Exchange Optimization algorithms, which are among the algorithms used for optimization, were used for the first time for the motion control of the single pendulum gantry system and compared with the traditional of Genetic algorithm and Artificial Bee Colony algorithms. To achieve the most successful optimization results, six distinct populations or particle size values (10-60) of Genetic algorithm, Artificial Bee Colony, Vibrating Particle System and Big Bang-Big Crunch and Thermal Exchange Optimization algorithms have been examined for 100 iterations. In addition, the initial parameters of ABC, BB-BC, and VPS algorithms were obtained by examining two independent variables. GA, ABC, VPS, BB-BC, and TEO algorithms were compared with each other and with non-optimized LQR. The best configurations obtained by simulation studies are verified experimentally. The results obtained by the study were evaluated by examining the control response parameters (rise time, settling time, overshoot, peak time, etc.) and important statistical performance evaluation criteria (Mean Absolute Error, Mean Squared Error, Root Mean Square Error). According to the pre-design results, the steady-state error of the pendulum cart was eliminated and 52.46% improvement was achieved in settling time. In addition, an improvement of up to 73,81% was achieved in the settling time of the pendulum angle.