Abstract
This paper presents the performance analysis on a benchmark control problem, the ball on sphere (BoS) system using, linear quadratic regulator (LQR) controller. Mathematical modelling was done by the use of Euler-Lagrange formulation. Linear quadratic regulator controller was used for stabilizing the ball on the sphere. Simulation was done in MATLAB 2022a environment, and the simulated results showed that the state weighting matrix Q had a higher penalty on the ball’s position on the x-axis and on the ball’s velocity on the y-axis. Also, as the diagonal element of the state weighting matrix increases, the optimal controller K becomes better for smaller values, the reduced ricatti matrix P is better for higher values and the estimated Eigen values E is better also for smaller values of Q.
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