MOEA/D-DE based bivariate control sequence optimization of a variable-rate fertilizer applicator

To realize precise control for a bivariate control system of a variable-rate applicator, it is essential to determine the optimal control sequence, which depends on quantifying the appropriate combination of the active feed-roll length (L) and the rotational speed of the drive shaft (N). This paper presents a novel method to optimize the control sequence (L, N) to improve fertilization accuracy and uniformity, while guaranteeing the rapidity of equipment adjustment. First, the variable-rate fertilization process model was formed using an improved General Regression Neural Network (GRNN), in which the optimum spread parameter (sigma = 2.0304) was calculated using a differential evolutionary (DE) algorithm. Next, a three-objective problem model was developed, and the Pareto set of the control sequence was obtained using a Multi-Objective Evolutionary Algorithm based on a Decomposition (MOEA/D) algorithm. Finally, a group of control sequences representing different target fertilization rates at the weight vector of (0.90, 0.08, 0.02) was chosen and an indoor test was conducted. Results revealed that the optimized control sequence overall outperformed the traditional method. It decreased the mean relative error (RE) from 8.239% to 5.977% and coefficient of variation (CV) from 13.512% to 13.187%, while constraining the response time to around two seconds.