te of the model parameters, $m,$ $l,$ and $g.$ In
      fact, the only place that the model enters our control equation is in the
      calculation of $\tilde{E} = \frac{1}{2} m l^2 \dot\theta^2 - mgl(1 +
      \cos\theta)$, and the only property of this estimate that impacts
      stability is the location of the orbit when $\tilde{E} = 0$, which is
      $\frac{1}{2}l\dot\theta^2 = g(\cos\theta + 1).$ Therefore, we could have
      used $\frac{E - E_d}{m} = \frac{1}{2} l^2 \dot\theta^2 - gl(1 +
      \cos