A new swing-up law for the Furuta pendulum

Abstract

In this paper the swing-up problem for the Furuta pendulum is solved applying Fradkov's speed-gradient (SG) method [1,9] to a dimension 4 model of the system. The new law is compared with the conventionalÅström-Furuta strategy, based on a dimension 2 model. A comparative analysis, including simulations and experiments, whereby the advantages and effectiveness of the new law for swinging the pendulum up are shown is included.

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

“…For example, some considered the problem of stabilizing the pendulum around the unstable vertical position [1,6,25,26,32]. Some swung the pendulum from its hanging position to its upright vertical position [3,9,14,15,31]. Some others tried to create oscillations around its unstable vertical position [2,12,30].…”

Stabilization of the Furuta Pendulum Based on a Lyapunov Function

“…There are many works related to the second problem. However, most of these works manage the physical model by introducing some non-linear approximations or by reducing the order of the system (see [13,17,18] and references therein).…”

“…For this purpose, an energy control strategy is usually applied. Once the system is closed to the desired top position with enough low speed (the inverted pendulum remains swinging while getting closer and closer to the origin), then by means of a simple change in the controller, from a non-linear to a linear controller, it is possible to keep the pendulum in the desired equilibrium (we recommend to see [3,[9][10][11][12][13]). The second problem consists on the stabilization of the FPS with the pendulum in the upright position and the rotating arm at rest at the origin, assuming that the initial deviation angle of the pendulum is restricted to move from (−π/2, π/2) (see [4,14,15]).…”

Nonlinear stabilization control of Furuta pendulum only using angle position measurements

“…The switch from swing-up controller to balancing controller makes the stabilizing control objective of Furuta pendulum be achieved. Many control methods based on this strategy have been presented, [3][4][5]17]. Although the switch strategy is effective for stabilizing Furuta pendulum sometimes, the stability of switching from swing-up area to balancing area is not guaranteed.…”