Introduction
The formulation and preliminary
The SMC-based CNF approach for the magnetic ball suspension system
The incremental SMC-based CNF strategy for the inverted pendulum
The nonlinear \( \psi \,(s) \) function in the CNF
The optimization
The main results
The magnetic ball suspension system stability
The stability analysis
The simulation results
Parameters | Magnitudes |
---|---|
Coil resistance (R) | 52 Ω |
Coil inductance (L) | 1.227 H |
Ball mass | 16.5 g |
The initial distance from the core | 50 mm |
x1, ball position (mm) | i, coil current (amp) |
---|---|
30 | 0.114 |
40 | 0.236 |
50 | 0.376 |
60 | 0.523 |
70 | 0.746 |
Pendulum mass (m) | 1 kg |
---|---|
Cart mass (M) |
\( 1\,\,{\text{kg}} \)
|
Friction of the cart |
\( 0.1\,{\text{N/m/s}} \)
|
Length of the pendulum (l) |
\( 0.1\,\,{\text{m}} \)
|
Inertia of the pendulum (i) |
\( 0.006\,\,{\text{kg}} . {\text{m}}^{ 2} \)
|
Gravity (g) | 9.8 m/s2 |
CNF-SMC | SMC | |||
---|---|---|---|---|
Settling time | Over/undershoot | Settling time | Over/undershoot | |
Cart position | 19 | 2.1 | 18.2 | 2.43 |
Pendulum position | 2.2 | 0.24 | 5.3 | 0.41 |