Abstract
We present a sensitivity-based predictor-corrector path-following algorithm for fast nonlinear model predictive control (NMPC) and demonstrate it on a large case study with an economic cost function. The path-following method is applied within the advanced-step NMPC framework to obtain fast and accurate approximate solutions of the NMPC problem. In our approach, we solve a sequence of quadratic programs to trace the optimal NMPC solution along a parameter change. A distinguishing feature of the path-following algorithm in this paper is that the strongly-active inequality constraints are included as equality constraints in the quadratic programs, while the weakly-active constraints are left as inequalities. This leads to close tracking of the optimal solution. The approach is applied to an economic NMPC case study consisting of a process with a reactor, a distillation column and a recycler. We compare the path-following NMPC solution with an ideal NMPC solution, which is obtained by solving the full nonlinear programming problem. Our simulations show that the proposed algorithm effectively traces the exact solution.
Highlights
The idea of economic model predictive control (MPC) is to integrate the economic optimization layer and the control layer in the process control hierarchy into a single dynamic optimization layer.While classic model predictive control approaches typically employ a quadratic objective to minimize the error between the setpoints and selected measurements, economic MPC adjusts the inputs to minimize the economic cost of operation directly
We present a small example to demonstrate the effect of including the strongly-active constraints as equality constraints in the quadratic programming (QP)
QPs (12) that are solved in our path-following algorithm are similar to the ones proposed and solved in the real-time iteration scheme
Summary
The idea of economic model predictive control (MPC) is to integrate the economic optimization layer and the control layer in the process control hierarchy into a single dynamic optimization layer. Instead of solving the full nonlinear optimization problem when new measurements of the state become available, these approaches use the sensitivity of the NLP solution at a previously-computed iteration to obtain fast approximate solutions to the new NMPC problem. These approximate solutions can be computed and implemented in the plant with minimal delay. The framework of asNMPC was applied by Jäschke and Biegler [24], who use a multiple-step predictor path-following algorithm to correct the NLP predictions Their approach included measures to handle active set changes rigorously, and their path-following advanced-step NMPC algorithm is the first one to handle non-unique Lagrange multipliers.
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