A control apparatus which can improve the accuracy of control of a controlled variable by a control input exhibiting a periodic fluctuating behavior. The control apparatus calculates an air-fuel ratio correction value DKCMD such that the output from an oxygen concentration sensor converges to a target output, and calculate a modulated value DKCMD_DSM by modulating DKCMD with an algorithm to which is applied a Δ Σ modulation algorithm. Further, the control apparatus calculates a reference air-fuel ratio KCMDBS according to an exhaust gas volume, calculates a model modification coefficient KTRQFF using a modification coefficient calculated such that DKCMD become equal to 0, calculates an adaptive reference air-fuel ratio KCMDADP by the equation of KCMDADP=KCMDBS×KTRQFF, and calculates a target air-fuel ratio KCMD by the equation of KCMD=KCMADP+DKCMD_DSM.