Performance comparison of optimization algorithms in LQR controller design fora nonlinear system

Abstract

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 determine the ideal control parameters. One of the most common and effective of these methods is determining the controller parameters with optimization algorithms.In this study, LQR controller design was implemented for position control of the double inverted pendulum system on a cart. First of all, the equations of motion of the inverted pendulum system were obtained by using Lagrange formulation. These equations were linearized by Taylor series expansion around the equilibrium position to obtain the state-space model of the system. The LQR controller parameters required to control the inverted pendulum system were determined by using a trial and error method. The determined parameters were optimized by using five different configurations of three different optimization algorithms (GA, PSO, and ABC). The LQR controller parameters obtained as a result of the optimization study with five different configurations of each algorithm were applied to the system and the obtained results were compared with each other. In addition, the configurations that yielded the best control results for each algorithm were compared with each other and the control results were evaluated in terms of response speed and response smoothness.

The Bees Algorithm Approach to Determining SMC Controller Parameters for the Position Control of a SCARA Robot Manipulator

“…The population size and crossover and mutation rates given as inputs are the important parameters which affects the performance of the algorithm. The GA may not succeed in a perfect solution because it does not produce a lot of different states to attain the best but it is one of the best algorithm taking time constraints into consideration (Önen, Cakan, & Ilhan, 2019).…”

A hybrid model based on the convolutional neural network model and artificial bee colony or particle swarm optimization-based iterative thresholding for the detection of bruised apples

“…It uses only three control parameters predetermined by the user, which are population size, maximum iteration number, and limit [22]. This method has been used for optimization in different areas [23][24][25][26]. The steps of the ABC-based iterative thresholding approach are listed as follows:…”

İki serbestlik dereceli bir robot kolun konum kontrolü için PID kontrol parametrelerinin arı algoritması (AA) kullanılarak belirlenmesi

“…Konum kontrolü, yörünge takibi gibi çalışmalar uzun yıllardır araştırmacıların robotik çalışmalarına konu olmuştur. Bu yüzden PID, LQR, Kayan Kipli Kontrol gibi çeşitli kontrolcüler geliştirilerek, farklı amaçlar için uygulanmıştır [9][10][11][12][13]. Kontrolcü tasarımında genellikle geleneksel yöntemler kullanılmaktadır, bu yöntemlerle elde edilen kontrol parametreleri hangi parametrenin ne derece etkili oldukları konusunda bakış açısı sağlamaktadır [14].…”