  In this paper, we study the exact boundary controllability of the linear
fourth-order Schr\"odinger equation, with variable physical parameters and
clamped boundary conditions on a bounded interval. The control acts on the
first spatial derivative at the left endpoint. We prove that this control
system is exactly controllable at any time $T>0$. The proofs are based on a
detailed spectral analysis and on the use of nonharmonic Fourier series.
