A fundamental nonlinear model of the Kamyr digester is developed as an extension of the original Purdue model. This model is linearized and reduced using Hankel-norm approximation to obtain a low order linear model. The reduced linear model is used for linear model predictive control (LMPC) with state estimation to control the Kappa number, a key product quality variable for the Kamyr digester. The use of the nonlinear model for past input contribution in MPC with state estimation and the reduced linear model for future predictions is also demonstrated in a nonlinear model predictive control (NLMPC) scheme. The performance of the two MPC structures for setpoint tracking and unmeasured disturbance rejection are compared.