Simulation and control of a complex nonlinear dynamic behavior of multi-stage evaporator using PID and Fuzzy-PID controllers

The dynamic model of heptads' stage evaporative unit employed in concentrating black liquor in paper industry show tremendous complexity. In this work, linearization of such a complex nonlinear model consisting of 14 first order nonlinear differential equations and determination of the system transfer functions has been explored through an exhaustive state space representation technique. The transfer functions that relate the product concentration change to liquor flow rate deviation have been evaluated and presented through this work for the first time. These serve as an input to design a PID controller and study its response for a set point change in product concentration. The response analysis indicated a noticeable overshoot, undershoot and Integral Square Error (ISE), that may collectively influence the product quality. To overcome this issue and to make controlling of product concentration more robust, an intelligent Mamdani type Fuzzy Logic-Proportional-Integral-Derivative (FLC-PID) controller has been additionally designed and its response simulated. A comparison of response of FLC-PID and PID indicated that the rise time of former is larger than the latter. However, FLC-PID response settles faster with ∼49% smaller settling time than PID, possesses zero undershoot, a ∼93% reduced overshoot and 21% reduced ISE. The results demonstrate improved tracking capability, and hence, better control performance of FLC-PID for transient changes in product concentration.