Figure 1.
The 3D model of the RIP.
Table 1.
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 |
Figure 2.
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.
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).
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.
Figure 6.
The comparison results during changes in model parameters: (a) the pendulum angle and (b) the arm angle of two controllers.