The trade-off between control accuracy， bandwidth， and transmission rate in control systems is an important open question. This paper studies the trade-off relation between information transmission rate and distortion from the perspective of information theory. The actuator part of the control system is analyzed based on rate entropy function. An entropy rate analysis framework for a class of reproducible probability distribution function is established. The derived entropy rate inequality represents the relationship between posterior entropy and desired transmission rate in the finitre impulse rsponse（FIR） actuator. Based on the derived expressions， the mutual information data of the tracking system under different signal-to-noise ratios is simulated， and the simulation results are coordinated with the expression expectations.