Water cycle algorithm tuned robust fractional-order Proportional–Integral–Derivative controller for energy optimization and control of nonlinear Multiple Stage Evaporator: A case study of paper mill

In paper industries, Multiple Stage Evaporator (MSE) is used to concentrate black liquor. Due to the energy intensive nature of MSE, the global energy scenario stresses on optimizing its energy efficiency. Moreover, the necessity of a tight control of product quality demands superior understanding of system dynamics for controller design. This paper presents a robust fractional-order Proportional–Integral–Derivative (FOPID) controller for concentration control of black liquor in Heptad's effect MSE. First, the steady-state unknown process parameters are estimated by solving the nonlinear steady-state model. Thereafter, these optimal process parameters are utilized to simulate the nonlinear dynamic model to obtain the transfer functions. By using these transfer functions, the FOPID controller is designed whose parameters are tuned via Water Cycle Algorithm (WCA). The competence of WCA toward controller tuning is validated by comparing with other optimization techniques (Genetic Algorithm [GA], Simulated Annealing [SA], Particle Swarm Optimization [PSO], and Krill Herd [KH]). Moreover, the performance of the proposed FOPID controller in concentration control, set-point tracking, and noise suppression is validated by comparing with conventional PID, two-degree of freedom-PID (2-DOF-PID), and Internal Model Control (IMC) controllers. The results demonstrate that FOPID controller reduces the Integral Square Error (ISE) by 91.05%, 89.81%, and 78.84%, respectively, with respect to PID, 2-DOF-PID, and IMC. Also, the proposed FOPID controller improves the system transience with high robustness.