Performance comparison of optimization algorithms in LQR controller design for a nonlinear system
Performance comparison of optimization algorithms in LQR controller design for a nonlinear system
The development and improvement of control techniques has attracted many researchers for many years.Especially in the controller design of complex and nonlinear systems, various methods have been proposed to determinethe ideal control parameters. One of the most common and effective of these methods is determining the controllerparameters with optimization algorithms.In this study, LQR controller design was implemented for position control ofthe double inverted pendulum system on a cart. First of all, the equations of motion of the inverted pendulum systemwere obtained by using Lagrange formulation. These equations were linearized by Taylor series expansion around theequilibrium position to obtain the state-space model of the system. The LQR controller parameters required to controlthe inverted pendulum system were determined by using a trial and error method. The determined parameters wereoptimized by using five different configurations of three different optimization algorithms (GA, PSO, and ABC). The LQRcontroller parameters obtained as a result of the optimization study with five different configurations of each algorithmwere applied to the system and the obtained results were compared with each other. In addition, the configurations thatyielded the best control results for each algorithm were compared with each other and the control results were evaluatedin terms of response speed and response smoothness.
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