Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms

Hexadic tank system represents an extension of quadruple tank system for controlling non-growth-associated product dynamics in bioprocess industries, including two stage continuous fermentations, multiple distillation columns, pharmaceutical, and food processing applications. This study presents a comprehensive analysis encompassing theoretical foundations, simulation frameworks, hardware implementation, and experimental validation of three control algorithms: LQR, Linear MPC, and Robust MPC, evaluated under disturbance and non-disturbance conditions. Among the three control algorithms, Linear MPC with disturbances (LMPC\((_{\text{D}})\)) achieves superior performance with the lowest mean error (1.67), maximum error (2.00), control variance (3.47), and overall sensitivity (2.52), with high settling times. RMPC\((_{\text{D}})\) shows the fastest minimum response (1.93 s) but exhibits higher mean error (2.5) and maximum error (5.0), and overall sensitivity (3.94). LQR controllers exhibit poor performance, with high sensitivity (94.08-226.47), large errors, and longer settling times (especially for LQR\((_{\text{D}})\)), rendering them unsuitable for practical implementation. All controllers maintain zero steady-state error with stable eigenvalues (\((-6.76\times10^{-3})\) to \((-4.34\times10^{-19})\)). This confirms that the model predictive control strategies are optimal for tracking precision, disturbance rejection, and parameter insensitivity in bioprocess applications.