The problem of observer-based boundary control of the sine–Gordon model energy is first posed. A Luenberger-type observer for the sine–Gordon equation is analysed, and explicit bounds on the system parameters ensuring the exponential decay of the estimation error are obtained. With the use of this observer a speed-gradient output feedback for sine–Gordon model energy control is proposed. The achievement of the control goal is established under the assumption that system's energy does not vanish in finite time. It is shown that the transient time in energy is close that the transient time in observation error, i.e. the closed-loop system has a reasonable performance. It is also shown that the conditions on the observer gain sufficient for the state estimation error convergence are “almost” necessary in the sense that violation of these conditions makes the state estimation error transients too long.