Selection and evaluation of FOPID criteria for the X-15 adaptive flight control system (AFCS) via Lyapunov candidates: Optimizing trade-offs and critical values using optimization algorithms

Recently, there has been a growing interest among academics worldwide in studying flight control systems. The advancement of tracking technologies, such as the X-15 adaptive flight control system developed at NASA (National Aeronautics and Space Administration), has sparked significant exploration efforts by scientists. The vast availability of aerial resources further contributes to the importance of studying adaptive flight control systems (AFCS). The successful operation of AFCS relies on effectively managing the three fundamental motions: pitch, roll, and yaw. Therefore, scientists have been diligently working on developing optimization algorithms and models to assist AFCS in achieving optimal gains during motion. However, in real-world scenarios, each motion requires its own set of criteria, which presents several challenges. Firstly, there are multiple criteria available for selecting appropriate optimization values for each motion. Secondly, the relative importance of these criteria influences the selection process. Thirdly, there is a trade-off between the performance of the criteria within a single optimization case and across different cases. Lastly, determining the critical value of the criteria poses another obstacle. Consequently, evaluating and selecting optimum methods for AFCS trajectory controls becomes a complex operation. To address the need for optimizing AFCS for various maneuvers, this study proposes a new selection process. The suggested approach involves utilizing black hole optimization (BHO), Jaya optimization algorithm (JOA), and sunflower optimization (SFO) as methods for detecting and correcting trajectories in adaptive flight control systems. These methods aim to determine the best launch of missiles from the AFCS based on the coordinate location for both long and short distances. Additionally, the methods determine the optimal gains for the FOPID (fractional order proportional integral derivative) controller and enhance protection against enemy attacks. The research framework consists of two parts. The first part focuses on improving the FOPID motion gains by employing optimization algorithms (BHO, JOA, and SFO) that are evaluated based on the FOPID criteria. Lower significant weighting values of the optimization algorithms demonstrate the best missile launching in a cosine wave trajectory within AFCS, while higher significant values indicate the best missile launching in a sine wave trajectory within AFCS. The FOPID controller criteria, including Kp_pitch, Ki_roll, Kd_yaw, λ_pitch, and µ_yaw, are considered in all situations. Furthermore, the study reports the best weights obtained for the "Kp_pitch" criterion across the motions as follows: (0.8147, 66.7190, and 54.4716). For the "Ki_roll" criterion, the best weights are (0.0975, 64.4938, and 64.7311), and for "Kd_yaw" the weights are (0.1576, 35.2811, and 54.3886). The results of the selection process by the BHO, JOA, and SFO algorithms also include λ_pitch (0.1419, 40.0791, and 72.1047) and µ_yaw (0.6557, 13.5752, and 52.2495). To ensure the validity of the proposed research framework, a systematic evaluation and precise analysis were conducted.