Performance evaluation of smoothed functional algorithm based methods for sigmoid-PID control optimization in MIMO twin-rotor systems - Mok, Ren Hao; Mohd Ashraf, Ahmad (Springer, 2024)
This paper explores the tuning of the Sigmoid Proportional-Integral-Derivative (SPID) controller using variations of the Smoothed Functional Algorithm (SFA) for the underactuated Multiple-Input Multiple-Output (MIMO) twin-rotor system. The SPID controller, incorporating a sigmoid function, extends the applicability of traditional PID controllers to complex, non-linear systems. However, SPID tuning presents challenges due to the added control parameters and the inherent non-linearity of the sigmoid function. To effectively tune the SPID controller, SFA is recommended, which stochastically optimizes the parameter space without requiring an explicit mathematical model. However, the standard SFA suffers from unstable convergence issues, necessitating modified approaches such as the Norm-Limited SFA (NLSFA) and Memory-Based SFA (MSFA). NLSFA constrains gradient approximation within boundaries, preventing excessively large approximations that lead to divergence but at the cost of an additional optimization parameter. The MSFA introduces a memory function to consider optimal solutions from previous iterations, promoting continuous convergence. The effectiveness of these SFA variations in optimizing SPID controllers for a MIMO twin-rotor system is compared, offering insights into the control and optimization of complex non-linear systems.