Particle Swarm Optimization Based LQR Control of an Inverted Pendulum

Abstract

Development of new control methods and the improvement of existing control techniques have been interest of researchers for many years. Inverted pendulum systems have been used to test the performance of various control methods in many studies due to their unstable and nonlinear structures. In this work, the use of Particle Swarm Optimization algorithm is presented for the parameter optimization of a Linear Quadratic Regulator controller designed to stabilization and position control of an inverted pendulum. Equations of motion of the cart pendulum derived by Lagrange formulation have been linearized and presented as state-space model. A Linear Quadratic Regulator controller has been designed for position control and stabilization of pendulum system. Parameters of the controller have been optimized by Particle Swarm Optimization algorithm to obtain best control results. Simulation studies were carried out in the MATLAB/Simulink environment and performance of the designed controller has been evaluated through simulation results.

Determination of Parameters of Linear Quadratic Regulator using Global Best Inertia Weight Modified Particle Swarm Optimization Algorithm

“…Its performance or behaviour, is determined by the state weighting matrix Q and the control weighting matrix R [3]. The values of Q and R, are traditionally ascertained by trial-and-error method [3], and using traditional control methods can be so laborious that at times, it can be so difficult to achieve the best parameters [4], [5], [6]. Due to the aforementioned reason, researchers used various evolutional algorithms such as particle swarm optimization (PSO) algorithm, Bees algorithm, and Ant Colony among others, to determine the weighting parameters Q and R of an LQR [4].…”

“…The values of Q and R, are traditionally ascertained by trial-and-error method [3], and using traditional control methods can be so laborious that at times, it can be so difficult to achieve the best parameters [4], [5], [6]. Due to the aforementioned reason, researchers used various evolutional algorithms such as particle swarm optimization (PSO) algorithm, Bees algorithm, and Ant Colony among others, to determine the weighting parameters Q and R of an LQR [4]. PSO is an Optimization algorithm which is the result of research by Dr. Russell Eberhart and James Kennedy in 1995 [7].…”

Optimal Tuning of a LQR Controlled Active Quarter Car System Using Global Best Inertia Weight Modified Particle Swarm Optimization Algorithm

“…It is designed by utilizing linear optimization methods. LQR controllers are designed for multi-variable and dynamic systems that are both linear and sometimes non-linear [5]. It has applications in a variety of fields, including aerospace systems [6], high-performance motion control applications for direct current (DC) motors [7], unmanned aerodynamic vehicles (UAV) [8], control of radar antenna systems [2], and autopilots for racing yachts [9].…”

“…Tuning LQR to attain optimality, is laborious and time-consuming when using traditional control methods [6]. Hence, to find the best values for Q and R, researchers have used a variety of evolutionary optimization techniques, including the Bees Algorithm (BA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) Algorithm, among others, to identify the best weighting matrices for LQR controllers [10], [5], and [11]. PSO has surpassed other computational techniques like GA and BA [12]- [14].…”

Análisis de estabilidad del péndulo triple invertido entre un regulador lineal cuadrático LQR y un sintonizador de ganancia mediante el algoritmo PSO

“…Por ello, en los últimos años se han desarrollado y aplicado con éxito métodos de inteligencia bioinspirada para ajustar los controladores de un péndulo invertido, como la optimización por enjambre de partículas (PSO) [14], [15], [16].…”