## 1 Introduction  
In recent years, advancements in aerial research have led to various applications that are now part of everyday human life. These applications involve acquiring real-world images in dangerous locations such as active volcanoes, earthquake-prone regions, and wildfire-affected areas, as well as tracking industrial activities and national borders and predicting atmospheric conditions. In reality, these operations can be performed by aircraft and drones, with the twin rotor \(MIMO\) system (\(TRMS\)) being the most commonly used [1, 2]. It has encouraged researchers in the control field by serving as a tool for many experiments and enabling real-time adjustments to aeronautical vehicles [2]. In most cases, the \(TRMS\) control system is required to accurately measure two angles: pitch and yaw. These are frequently controlled by calculating two ideal \(DC\) voltages, where each one supplies power to an individual \(DC\) motor [3]. As a result, the system possesses two degrees of freedom, allowing both horizontal and vertical movements. Therefore, the given performance is often restricted by the adequate selection of two main keys [4]. The first key is the determination of a modeling strategy that produces an accurate multi-input, multi-output model (\(MIMO\)). The second key is the correct choice of a controller synthesis technique. On this topic, a novel evolutionary proportional-integral-derivative (\(PID\)) controller design for \(TRMS\) using a simplified genetic algorithm was presented [5]. The proposed controller achieves a good response and excellent performance on the \(MIMO\)\(TRMS\) system. In [6], the behavior dynamics of the \(TRMS\) system was decoupled into two single-input, single-output (\(SISO\)) systems. Each unit is controlled separately using time-optimal, robust \(SISO\) regulators. The cross-coupling impact is regarded as a disturbance or the change of system parameters. In this approach, each \(SISO\) regulator guarantees an optimal Nyquist plot (\(NP\)) margin against these uncertainties. Later, various traditional control methods and advanced control techniques were applied [7] to the \(MIMO\)\(TRMS\) system. These techniques ensure that the \(TRMS\) beam moves rapidly and precisely, enabling it to track a trajectory and reach specific positions. A fuzzy \(PID\) control scheme was proposed in [8] for \(TRMS\), in which a new control structure allows the \(TRMS\) to achieve a target position more efficiently than previously. All the gain values of the \(PID\) regulator are obtained by the real coded genetic algorithm (\(RGA\)) with the system performance index as a fitness function. A feedback model predictive control strategy was proposed in [9] for the nonlinear \(TRMS\), in which the control scheme makes the \(TRMS\) beam move rapidly and precisely to the target positions (pitch and yaw angles). In addition, its structure was tested under disturbance, where an external force was manually applied to the system to assess its performance under significant disturbance conditions. It is evident that the yaw and pitch angles shift from their intended positions due to the applied external force. However, the control system successfully restores stability, ensuring the beam returns to its desired angles. In [10], a decoupled compensator was designed for a physical \(TRMS\) by decoupling its actual behavior using a minimal open-loop decoupler. The resulting decoupled \(SISO\) units are adjusted using two independent two degrees of freedom (\(2 DOF-SISO\)) controllers, ensuring reference tracking dynamics while maintaining closed-loop robustness and mitigating the cross-coupling effect. In a recent study, [PERSON]. [11] introduced a linear quadratic regulator (\(LQR\)) with an integral controller, resulting in a novel robust \(LQI\) controller. The effectiveness of this controller was evaluated against several existing controllers from the literature, and its performance was validated through experimental testing. Later, Ref.