Control strategies of the on–off type can be used to bring batch reactor temperature to the set point in minimum time. A practical controller implementing this control strategy in industry is the dual-mode controller. When well-tuned, this controller shows excellent control performances for various batch reactors. However, the dual-mode controller may be sensitive to process changes. For improved robustness, the dual-mode controller is modified and equipped with an iterative learning technique. This iterative learning dual-mode controller requires minimal information from the previous batch runs and can be incorporated in the existing dual-mode controller with minimal effort.
In an exothermic batch reactor, temperature overshoot is usually avoided because it can cause runaway due to the large amount of heat released at elevated reactor temperatures. On the other hand, reactor temperature should be increased as quickly as possible to the operating set point. Control actions to achieve this objective can be obtained by solving the time-optimal control problem (Cott and Macchietto, 1989). The resulting control actions are usually on–off controls, although sometimes a singular arc is optimal (Kirk, 1970). The minimum time control strategy can be implemented by a so-called dual-mode (DM) controller (Shinskey, 1996). Maximum heating is applied until the reactor temperature reaches within a specified number of degrees of the set point, and then maximum cooling is followed to bring the error to zero. When the reactor temperature has reached its desired set point, a standard PID controller is switched on and used to maintain the reactor temperature. Although the DM controller with two changes in input will not emulate the time-optimal control strategy perfectly, a well-tuned DM controller provides excellent system performance approximating the time-optimal control strategy. However, because the time-optimal control and its approximate DM control are model based, they are difficult to implement on new systems having robustness concerns.
For control strategies with improved robustness, several authors (Aziz, Hussain, & Mujtaba, 2000; Cott & Macchietto, 1989; Juba & Hamer, 1986; Jutan & Uppal, 1984) have proposed control systems that estimate the amount of heat being released in the reactor and use it to counterbalance the effect of the heat released. Although the estimation of heat release has some error and time delay, it compensates for the major nonlinearity in the reactor dynamics and control system. To design the estimator, the reactor temperature and its time derivative, the jacket temperature and some process parameters are required.
Iterative learning control (Lee, Bang, Yi, Son, & Yoon, 1996; Lee & Lee, 2007) has been used to control the temperature in an exothermic batch reactor. It uses previous batch information to eliminate the tracking error and reject repetitive disturbances. Because the iterative learning control cannot handle random disturbances, feedback control is also incorporated to reduce the effects of such random disturbances and to accelerate the convergence of the iteration. Because initial control actions for heating the batch reactor are usually on–off, iterative learning controls based on constrained optimization are required.
In order to obtain a simpler and more easily understandable method, the conventional DM controller is modified and incorporated with the iterative learning technique. Specifically, the cooling period is adjusted to prevent thermal runaway or overcooling, and switching criteria are adjusted iteratively from the previous batch runs (run-to-run control) to maintain the system performances. Minimal information from previous batch runs is required. Simulations show that the improved DM controller can avoid thermal runaway for various process changes and the iterative learning technique achieves satisfactory control performances.
In DM control that implements nearly time-optimal control for batch reactor temperature, full heating is applied first to raise quickly the reactor temperature and then full cooling is followed to reduce the rate of temperature increment and for the reactor temperature to approach the set point smoothly. When there are some process changes, the fixed cooling period in the DM controller can be too short and large overshoot can result. On the other hand, for some cases, the cooling period can be too large and undershoot can result. To mitigate such problems, a technique to modify the cooling period according to the reactor temperature trend is derived. This improved DM controller shows improved performance for various process changes.
Further, to maintain control performance, an iterative learning technique is applied to the improved DM controller. The heating period is adjusted based on the previous batch runs so that the reactor temperature reaches the set point without overshoot, and then the cooling period is adjusted so that the reactor temperature does not show undershoot. Simulations show that the proposed iterative learning technique restores the control performances in about 3 runs. Because minimal information from previous batch runs is required, this iterative learning technique can enhance the conventional DM control with modest efforts.
