exponential convergence: $\tilde{E} \rightarrow 0.$
      This is true for any $\dot\theta$, except for $\dot\theta=0$ (so it will
      not actually swing us up from the downright fixed point... but if you
      nudge the system just a bit, then it will start pumping energy and will
      swing all of the way up).  The essential property is that when $E > E^d$,
      we should remove energy from the system (damping) and when $E < E^d$, we
      should add energy (negative damping).  Even if the control act