Analysis & Control of Inverted Pendulum System Using PID Controller

Abstract

This Analysis designs a two-loop proportional-integral-derivative (PID) controller for an inverted cartpendulum system via pole placement technique, where the (dominant) closed-loop poles to be placed at the desired locations are obtained from an Linear quadratic regulator (LQR) design. It is seen that in addition to yielding better responses (because of additional integral action) than this LQR (equivalent to two-loop PD controller) design, the proposed PID controller is robust enough. The performance and of the PID compensation are verified through simulations as well as experiments.

Traditional stilts as an alternating incomplete inverted pendulum controlled by hand and a physical pendulum pivoting at the hand

“…We can generate the stability of an inverted pendulum by applying an external excitation. The excitation is in the form of an external oscillation that is applied to the pivot either in the horizontal [16][17][18][19][20][21][22] or the vertical [23][24][25][26][27][28][29][30][31][32][33] direction.…”

“…Just as additional information, the problems of the inverted pendulum subjected to vertical excitation have been widely discussed [23][24][25][26][27][28][29][30][31][32][33]. For small deviation angles, the basic equation is Mathieu's equation which can be written as d 2 θ dt 2 + k (1 − m cos ωt) θ = 0 with k = g/Lω 2 , m = a/L, a is the amplitude of the pivot oscillation, L is the length of the pendulum, and ω is the excitation frequency [34].…”