This work addresses the design of an optimized control system for an acrylic acid plant through the lens of the Stochastic Plant-Wide Optimizing Control (S-PWOC) framework. The S-PWOC employs stochastic optimization methods and advanced computer modeling to optimize plant performance by dynamically adjusting operational parameters under varying uncertainties. A comparison between the proposed S-PWOC model and two conventional approaches, the two-level identification method and the typical plant-wide decentralized control structure, highlights the advantages of S-PWOC despite its higher computational demands. Experimental results demonstrate significant improvements, including a 15% increase in process efficiency, a 10% reduction in energy consumption, enhanced product quality consistency, and greater economic viability. Additionally, S-PWOC proves effective in reducing safety risks and improving control efficiency, making it a robust solution for handling uncertainties in real-world plant operations.