The aim of this paper is to suggest a methodical smooth control method for improving the stability of two wheeled self-balancing robot under effect disturbance. To promote the stability of the robot, the design of linear quadratic regulator using particle swarm optimization (PSO) method and adaptive particle swarm optimization (APSO). The computation of optimal multivariable feedback control is traditionally by LQR approach by Riccati equation. Regrettably, the method as yet has a trial and error approach when selecting parameters, particularly tuning the Q and R elements of the weight matrices. Therefore, an intelligent numerical method to solve this problem is suggested by depending PSO and APSO algorithm. To appraise the effectiveness of the suggested method, The Simulation result displays that the numerical method makes the system stable and minimizes processing time.