Vibration Suppression of a Flexible Appendage and Pitch Angle Fuzzy Regulation of a Spacecraft

In this work, the large-angle rotational movement and vibration suppression of a flexible spacecraft are carried out based on an adjustable system. First the spacecraft model is transformed into a canonical affine control form, then two fuzzy systems are used: The first (of Takagi–Sugeno type) estimates the feedback linearization control law as a whole, while the second (of Mamdani type) adjusts and stabilizes the control parameters using the gradient descent technique and based on the minimization of the control error rather than the tracking error. Stability results are presented in terms of Lyapunov’s theory, and simulation tests illustrate the significant transient robustness of the closed-loop system against perturbations, the accurate trajectory control, and vibration suppression of the flexible spacecraft. Consequently, as will be shown later, the error will stay confined and converges quickly to zero, confirming the smoothing property of the proposed method using fuzzy logic systems.