Optimal Tuning of Thermodynamic-Based Decentralized PI Control Loops: Application to the Tennessee Eastman Process

The need of designing decentralized control loops emerges to ensure the global stability of a given process plant. To that purpose, the authors have proposed in recent works a systematic approach to derive robust decentralized controllers, which is based on the link between thermodynamics and passivity theory as well as on the fundamentals of process networks. This Thermodynamic-Based Control (TBC) methodology has several steps: i) Decomposition of the considered process system into abstract mass and energy inventory networks; ii) design of conceptual mass and energy inventory control loops to guarantee the convergence of the states of the plant to a compact convex region defined by constant inventories, where input-output stability follows; iii) definition of intensive variable control loops (if needed) to achieve global stability; iv) realization of the conceptual inventory and intensive variable control loops over the available degrees of freedom in the system by using, for instance, PI controllers. In this work, we develop a tool to tune these PI control loops, based on the solution of a nonlinear programming optimization problem (NLP), in order to complete the proposed hierarchical and systematic TBC design. The aim is to minimize a given cost function, subject to both the system dynamics as well as the linear and nonlinear constraints (no disturbances affecting the system are considered), where the vector of decision variables will be formed by the parameters of the PI controllers used in the defined decentralized control loops. We will test this tuning procedure in several control designs developed for the challenging benchmark of the Tennessee Eastman Process (TEP) by Ricker (1996) and Larsson et al. (2001) as well as in two TBC candidates, concluding that the best candidate among the proposed ones (in terms of final cost function) will be one of these TBC designs. For solving the NLP problem, two local (FMINCON and NOMADm) solvers and a new global (MITS) one are used, comparing their performances. Finally, the dynamic analysis of the optimal tuned closed loop systems is carried out, finding that the presented TBC control candidates will be stable while the other control structures considered exhibit complex dynamic behaviors or even instability when disturbances affecting the process are considered.