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which upon substitution of the dynamics, <math>\ddot{q}</math>, gives
:<math>
\left(\ddot{q}_d-\frac{u-K_0q-K_1q^3-b\dot{q}}{m(1+q^2)}+\alpha \dot{e}\right) = -\frac{\kappa}{2}(\dot{e}+\alpha e)
</math>
Solving for <math>u</math> yields the control law
:<math>
u= m(1+q^2)\left(\ddot{q}_d + \alpha \dot{e}+\frac{\kappa}{2}r
</math>
with <math>\kappa</math> and <math>\alpha</math>, both greater than zero, as tunable parameters
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