Performance indexes.

This paper suggests a novel optimal inverse Radial Basis Function (RBF) neural network model for the control of Twin Rotor Aerodynamic Systems (TRAS), such as Multi-Input–Multi-Output (MIMO) systems with high nonlinearity and coupling effects between channels. After analyzing and linearizing the dynamic model, TRAS is decoupled into two Single Input Single Output (SISO) systems, thereby creating vertical (pitch model) and horizontal (yaw model) systems. The relationship between the output angle of each subsystem and the input voltage is modeled using the inverse RBF neural network. The weights, biases, centers and widths of the Gaussian function are unknown parameters of the proposed inverse neural model, and they are obtained using Atom Search Optimization (ASO). A combination of the proportional derivative controller and the proposed inverse neural model fed forward controller is then applied to control the angles of each subsystem with different conditions. The simulation results showed that the proposed controller demonstrates noticeable performance improvements over the Fractional Order PID (FOPID) and Particle Swarm Optimization-PID (PSO-PID) controllers. Compared to FOPID, it achieves an 88.3% faster rise time, a 96.0% faster settling time, and a 93.8% lower overshoot for the Yaw model, along with a 42.8% faster rise time, a 73.9% faster settling time, and an 86.8% lower overshoot for the Pitch model. In comparison to PSO-PID, the Yaw model shows a 36.2% faster rise time, an 86.7% faster settling time, and a 59.7% lower overshoot, while the Pitch model exhibits a 58.4% slower rise time but compensates with a 59.9% faster settling time and a 71.2% lower overshoot. Additionally, integral performance indices are notably reduced for the proposed controller.