Design of LQR controller with big bang-big crunch optimization algorithm based on time domain criteria

Abstract

LQR controller is the most popular technique that provides an optimal control law for linear systems among the state space feedback control strategies. However, the conventional LQR controller synthesis is unfortunately an iterative process due to the trial and error approach involved in determining the parameters values of the weighing matrices Q and R. Here, the Big Bang-Big Crunch (BB-BC) optimization algorithm is used that optimizes a time domain fitness function in the design of the state feedback optimal control law and thus avoiding the repeated adjustment process of LQR parameters. In this study, a special performance fitness function that is inversely proportional to the certain time domain step response criteria of a dynamical system is proposed for the optimization procedure. In order to test the performance of the proposed method, firstly a simulation study is done within the MATLAB to stabilize an inverted pendulum on cart. Then, the proposed controller is used in a real time implementation to stabilize a DC-DC boost converter benchmark in the lab. Both MATLAB simulations and laboratory experiments demonstrate the effectiveness of the proposed controller.