  This paper addresses the management of water flow in a rectangular open
channel, considering the dynamic nature of both the channel's bathymetry and
the suspended sediment particles caused by entrainment and deposition effects.
The control-oriented model under study is a set of coupled nonlinear partial
differential equations (PDEs) describing conservation of mass and momentum
while accounting for constitutive relations that govern sediment erosion and
deposition phenomena. The proposed boundary control problem presents a fresh
perspective in water canal management and expands Saint-Venant Exner (SVE)
control frameworks by integrating dynamics related to the transport of fine
particles. After linearization, PDE backstepping design is employed to
stabilize both the bathymetry, the water dynamics together with the
concentration of suspended sediment particles. Two underflow sluice gates are
used for flow control at the upstream and downstream boundaries with only the
downstream component being actuated. An observer-based backstepping control
design is carried out for the downstream gate using state measurement at the
upstream gate to globally exponentially stabilize the linearized system to a
desired equilibrium point in $\mathscr{L}^2$ sense. The stability analysis is
performed on the linearized model which is a system of four coupled PDEs, three
of which are rightward convecting and one leftward. The proposed control design
has the potential to facilitate efficient reservoir flushing operations.
Consistent simulation results are presented to illustrate the feasibility of
the designed control law.
