Optimal sensor location for the state estimation of distributed parameter systems is studied.First a nonlinear state estimator is developed based on late lumping.The partial differential equations for state estimation and the differential sensitivity matrix are then solved numerically.Optimal sensor locations are obtained by minimizing a integral function over a spacial domain using a nonlinear constraint optimization method. A wall-cooled fixed-bed reactor is used as a working system

and the effects of measurement noise

model parameter errors

and unmeasurable disturbance are studied.Results show that with one or two properly placed temperature sensors

excellent state estimation of the fixed-bed reactor can be achieved.