ΔΣ modulators have been utilized for analog-to-digital converters (ADCs). The performance of a ΔΣ modulator can be enhanced if it is designed by taking into account the characteristics of the system that uses the ΔΣ modulator. This paper considers ΔΣ modulators for discrete-time closed loop control systems. In the control system, quantization may degrade control performance and leads to oscillations of the system outputs, whereas saturation of the control input may cause windup phenomena such as overshoots of the system outputs and instability of the control system. This paper jointly mitigates the effects of quantization and saturation in a discrete-time closed loop control system, by minimizing the norm of the quantization error at the system output under a stability condition on the closed-loop system. Numerical examples are provided to see the effectiveness of our proposed design.