An improved neuroendocrine–proportional–integral–derivative controller with sigmoid-based secretion rate for nonlinear multi-input–multi-output crane systems

This paper proposes an improved neuroendocrine–proportional–integral–derivative controller for nonlinear multi-input–multi-output crane systems using a sigmoid-based secretion rate of the hormone regulation. The main advantage of the sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative is that the hormone secretion rate of neuroendocrine–proportional–integral–derivative can be varied according to the change of error. As a result, it can provide high accuracy control performance, especially in nonlinear multi-input–multi-output crane systems. In particular, the hormone secretion rate is designed to adapt with the changes of error using a sigmoid function, thus contributing to enhanced control accuracy. The parameters of the sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative controller are tuned using the safe experimentation dynamics algorithm. The performance of the proposed sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative controller-based safe experimentation dynamics algorithm is evaluated by tracking the error and the control input. In addition, the performances of proportional–integral–derivative and neuroendocrine–proportional–integral–derivative controllers are compared with the proposed sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative performance. From the simulation work, it is discovered that the sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative design provides better control performances in terms of the objective function, the total norm of error and the total norm of input compared to proportional–integral–derivative and neuroendocrine–proportional–integral–derivative controllers. In particular, it is shown the proposed sigmoid-based secretion rate neuroendocrine–proportional–integral–derivative controller contributes 5.12% of control accuracy improvement by changing the fixed hormone secretion rate into a variable hormone secretion rate based on the change of error.