  A re-entrant manufacturing system producing a large number of items and
involving many steps can be approximately modeled by a hyperbolic partial
differential equation (PDE) according to mass conservation law with respect to
a continuous density of items on a production process. The mathematic model is
a typical nonlinear and nonlocal PDE and the cycle time depends nonlinearly on
the work in progress. However, the nonlinearity brings mathematic and
engineering difficulties in practical application. In this work, we address the
optimal control based on the linearized system model and in order to improve
the model and control accuracy, a modified system model taking into account the
re-entrant degree of the product is utilized to reflect characteristics of
small-scale and large-scale multiple re-entrant manufacturing systems. In this
work, we solve the optimal output reference tracking problem through
combination of variation approach and state feedback internal model control
(IMC) method. Numerical example on optimal boundary influx for step-like demand
rate is presented. In particular, the demand rates are generated by an known
exosystem.
