The present work presents spatiotemporal modeling of the paper machine spatial distributed system. The basis weight is taken as the profile parameter of the paper sheet. PID controllers are used to keep the minimum variability in the basis weight profile by adjusting the consistency profiling dilution actuators. In the context of the control systems for spatial distributed systems, nature-inspired algorithms (NIAs) are rarely used to tune controllers. To minimize the integral of the square value of error (ISE) and to enhance the robust stability, genetic algorithm (GA) was utilized for tuning. It is determined that GA-PID tuned controller outperforms the conventional two-dimensional loop shaping controller. The developed controller is tested on several other criteria, including transient response characteristics. A GA-tuned PID controller has high robustness and a wide variety of stability margins for the feedback loop’s uncertainty.