It is very necessary to adjust and maintain the hypnosis depth in anesthesia. If the propofol amount is less it results to insufficient anesthesia and if amount is higher, it may be dangerous for patient. Hence BIS (BISPECTRAL INDEX) is used for regulating the propofol depth. Here in this paper, we are studying the anesthesia process and for which the patient model is designed depending upon pharmacodynamics and pharmacokinetic model (PK/PD) in MATLAB/Simulink. A first-order plus dead time model is designed and approximated for anesthesia process. With the aid of various filters and the Smith Predictor, this work intends to evaluate the effectiveness of an Internal Model Control Proportional-Integral-Derivative (IMC-PID) controller with a dead time compensator (Both Integer and fractional order). We are constructing an IMC-PID controller with a dead time compensator utilizing a fractional and integer order filter in this study because the unwanted delay generates oscillations, instability, and uncertainty into the system. The robustness of the controller against model uncertainty and disturbances is demonstrated through sensitivity analysis. To show the effectiveness of the controller with compensator employing a fractional and integer order filter, simulations of the anesthesia model are given.