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Integrating Disturbance Handling into Control Strategies for Swing-up And Stabilization of Rotary Inverted Pendulum

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31 mar 2025

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Figure 1.

The 3D model of the RIP.
The 3D model of the RIP.

Figure 2.

The comparison results without external disturbance: (a) the pendulum angle, (b) the arm angle, and (c) the control signal of two controllers.
The comparison results without external disturbance: (a) the pendulum angle, (b) the arm angle, and (c) the control signal of two controllers.

Figure 3.

The Extended State Observer in the first scenario: (a) the pendulum angle velocity, (b) the arm angle velocity of the LQR controller, (c) the pendulum angle velocity, and (d) the arm angle velocity of the LQR-based SMC controller.
The Extended State Observer in the first scenario: (a) the pendulum angle velocity, (b) the arm angle velocity of the LQR controller, (c) the pendulum angle velocity, and (d) the arm angle velocity of the LQR-based SMC controller.

Figure 4.

The comparison results when there is external disturbance (a): the pendulum angle (b), the arm angle (c), and the control signal of two controllers (d).
The comparison results when there is external disturbance (a): the pendulum angle (b), the arm angle (c), and the control signal of two controllers (d).

Figure 5.

The Extended State Observer in the first scenario: (a) the pendulum angle velocity, (b) the arm angle velocity of the LQR controller, (c) the pendulum angle velocity, and (d) the arm angle velocity of the LQR-based SMC controller.
The Extended State Observer in the first scenario: (a) the pendulum angle velocity, (b) the arm angle velocity of the LQR controller, (c) the pendulum angle velocity, and (d) the arm angle velocity of the LQR-based SMC controller.

Figure 6.

The comparison results during changes in model parameters: (a) the pendulum angle and (b) the arm angle of two controllers.
The comparison results during changes in model parameters: (a) the pendulum angle and (b) the arm angle of two controllers.

The parameters of the pendulum_

Symbol Description Values Units
mp Pendulum’s mass 0.125 kg
Lp Pendulum’s length 0.15 m
Lr Rotary arm’s length 0.15 m
Jp Pendulum’s inertia moment 2.3 × 10−4 kgm2
Jr Inertia moment of arm 9.4 × 10−4 kgm2
Bp Viscous friction coefficient of the pendulum rod 9.5 × 10−3 -
Br Viscous friction coefficient of the pendulum arm 0.04 -
Kr Motor torque constant 0.042 Nm/A
Km Motor back EMF constant 0.042 Vs/rad
Rm Terminal resistance 2.6 Ω
Lm Rotor Inductance 0.85 mH
g Gravitational acceleration 9.81 m/s2