Nonlinear MIMO Control of a Continuous Cooling Crystallizer

Abstract

In this work, a feedback control algorithm was developed based on geometric control theory. A nonisothermal seeded continuous crystallizer model was used to test the algorithm. The control objectives were the stabilization of the third moment of the crystal size distribution (μ3) and the crystallizer temperature (T); the manipulated variables were the stirring rate and the coolant flow rate. The nonlinear control (NLC) was tested at operating conditions established within the metastable zone. Step changes of magnitudes ±0.0015 and ±0.5°C were introduced into the set point values of the third moment and crystallizer temperature, respectively. In addition, a step change of ±1°C was introduced as a disturbance in the feeding temperature. Closed-loop stability was analyzed by calculating the eigenvalues of the internal dynamics. The system presented a stable dynamic behavior when the operation conditions maintain the crystallizer concentration within the metastable zone. Closed-loop simulations with the NLC were compared with simulations that used a classic PID controller. The PID controllers were tuned by minimizing the integral of the absolute value of the error (IAE) criterion. The results showed that the NLC provided a suitable option for continuous crystallization control. For all analyzed cases, the IAEs obtained with NLC were smaller than those obtained with the PID controller.