Table 1 The rotary inverted pendulum parameters.

From: Enhancing stability control of inverted pendulum using Takagi–Sugeno fuzzy model with disturbance rejection and input–output constraints

Gravity \((ms^{-2})\)

g

9.81

Mass of the pendulum rod (kg)

m

0.125

Length of the pendulum rod (m)

l

0.335

Length of the pendulum arm (m)

\(r_a\)

0.215

Equivalent moment of inertia of the pendulum arm and gears \((kgm^2)\)

\(J_{eq}\)

\(3.5842\times 10^{-3}\)

Moment of inertia of the motor rotor \((kgm^2)\)

\(J_m\)

\(3.87\times 10^{-7}\)

Friction coefficient of the pendulum arm \((Nmsrad^{-1})\)

\(B_a\)

0.004

Friction coefficient of the pendulum rod \((Nmsrad^{-1})\)

\(B_r\)

0.0095

Torque constant \((NmA^{-1})\)

\(K_t\)

\(7.67\times 10^{-3}\)

Back EMF constant \((Vsrad^{-1})\)

\(K_v\)

\(7.67\times 10^{-3}\)

Motor armature resistance \((\Omega )\)

R

2.6

Gearbox ratio

\(K_g\)

70

Gearbox efficiency

\(n_g\)

0.9

Motor efficiency

\(n_m\)

0.69

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