1. A diagnostic device for use with an object to be diagnosed, said object having an automatic control system forming a closed loop and including an integration element in said object, said diagnostic device sampling the input and output of said object with a fixed periodic time so as to obtain digital signals, and detecting an abnormal state of said object in accordance with said digital signals so as to indicate the occurrence of the abnormal state, said diagnostic device comprising: mathematical model means simulating an input-output characteristic of said object to be diagnosed; first means for applying to said model means said sampled input of said object in the present period of time when said object output satisfies a predetermined condition for letting the model means execute a calculation to obtain an output of said model means corresponding to the output of said object, and for letting the model means output coincide with the object output in the present period of time without executing the model means calculation when said object output does not satisfy said predetermined condition, said predetermined condition being that a rate of change of said object output is larger than a predetermined value, so that accumulation of errors in the model means calculation when the predetermined condition is not satisfied is avoided; and second means for comparing the output of said model means controlled by said first means with the output of said object in the present period of time, and then for detecting an abnormal state of said object in accordance with a deviation output obtained by the comparison so as to indicate the occurrence of the abnormal state.