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

Abstract

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.

Novel feedforward‐feedback‐based continuous process transition strategy for chemical industry

“…Therefore, the process control strategy remains the first choice for chemical processes, 19,20 and the main control method is also limited to the conventional PID regulation. 21,22 The process transition strategy will be adopted to ameliorate the transition performance only when the transition requirements cannot be fulfilled by the process control strategy. It means that the process control strategy and process transition strategy need to be switched frequently in different stages of the production process.…”

Transient Modeling and Simulation of a Multiple‐Stage Evaporator in the Paper Industry

“…Since the last eight decades, many research articles based on the steady‐state energy modeling of MSE have been published 3, 6–13. These articles represent a wide range of solution approaches for solving the set of nonlinear algebraic equations (SNLAE), such as different solvers (fsolver) 13, iterative methods (Gauss elimination, Gauss‐Seidel, Newton‐Raphson methods) 3, pinch analysis (composition and grand composition curve) 14, 15, the interior‐point method 16, genetic algorithms 17, differential evolution, particle swarm optimization 18, the water cycle algorithm 19, the artificial electric field algorithm 20, 21, etc., in the MATLAB environment. The introduction of different new deterministic (nonlinear programming) and stochastic approaches (metaheuristic approaches) to find the optimal value makes it essential to check the best solution obtained in the minimum time period.…”

Petviashvili Method for the Fractional Schrödinger Equation

“…For instance, one of the recent studies investigates the usage of fractional calculus for damping and hybrid base isolation system [11]. Other applications are also present in the literature, for example for PID controllers [12], acoustic waves in complex media [13][14][15], fractional wave equation [2], fractional epidemic model [16], disease transmission model [17], prey-predator model [18] and financial systems with time delay [19].…”