Decomposition method for solving integrated problem of cyclic scheduling and PI controller design

We propose a novel integration method to solve the scheduling problem and the closed-loop PI control problem simultaneously. The integrated problem is formulated as a mixed-integer dynamic optimization (MIDO) problem. Solution of the MIDO problem is challenging, especially in a short time period required for online implementation. We develop a fast computational strategy to solve the integrated problem, ensuring its online applications. First, we decompose all dynamic models from the integrated problem by computing the optimal-value function of the transition cost dependent on the transition time. The optimal-value function is then discretized by optimizing a set of controller candidates offline. The optimal controller candidate generates the minimum transition cost for a given transition time. Finally, the integrated problem is transformed into a scheduling problem with controller selection. This is a mixed-integer fractional programming problem. We propose a global optimization method based on the Dinkelbach's algorithm to solve the resulting large-scale problem efficiently. The advantage of the proposed method is demonstrated by a mehyl methacrylate polymer manufacturing process.