Mathematical Model of a Controlled Shaft-Type Dryer Under Parametric Uncertainty

This article presents the development of a state-space mathematical model for controlling the wheat drying process in a shaft-type dryer. The drying process is considered a complex multivariable, nonlinear, and distributed-parameter dynamic object characterized by simultaneous heat and mass transfer, transport delay, external disturbances, and variable raw-material properties. Based on the physical characteristics of the process, state, control, output, and disturbance vectors are formulated. Energy balance equations for wheat grains and the drying agent, together with moisture transfer and air humidity equations, are used to construct a nonlinear dynamic model. The nonlinear equations are linearized around a nominal operating point using the first-order Taylor expansion, resulting in a state-space representation. Transport delay associated with grain movement through the dryer is also incorporated into the model. The developed model provides a mathematical basis for analyzing process dynamics and designing advanced control algorithms aimed at improving drying stability, product quality, and energy efficiency.