## 1 Introduction
Yet, the proposed control approach was not applied on manipulators with two or three links, whereas the system's complexity rises and its control becomes harder. [PERSON] et al. [7] utilized synergetic control theory and fractional calculus to develop a fractional synergetic control (FSC) strategy for a four-DOF robot manipulator; the synergetic control approach was implemented to obtain fast convergence to the equilibrium point. The results of combining synergetic control and fractional calculus in control system design showcased good tracking performance in both joint space and workspace trajectories. However, the method's robustness had not been investigated. [PERSON] et al. [8] utilized Time Delay Estimation (TDE)-based model-free control to estimate the external disturbance and the unknown friction parameters of a Puma 560 rigid manipulator, and terminal SMC to obtain system robustness. The system responses show that the control method can suppress the effect of uncertainty and produce effective tracking. However, the effect of measurement noise that can affect the overall control performance has not been considered. Likewise, the effect of measurement noise was not determined by [PERSON] et al. [9] when they incorporated a fixed-time adaptive sliding mode observer into the fixed-time non-singular terminal SMC design for the Puma 560 manipulator. For the single-link manipulator, [PERSON] et al. [10] proposed an adaptive tracking controller based on the mismatched disturbance observer. The adaptive approach and disturbance-observer design contribute to effective disturbance rejection and smoother control of the robotic manipulator link. The closed-loop signals are found to be globally uniformly bounded with asymptotically stable tracking error, though the proposed control method is not generalized to more complex multi-link systems. In the same context, [PERSON] et al. [11] developed a disturbance observer-based adaptive fuzzy control method for the single-link manipulator; the proposed control system acquires finite-time prescribed performance, by which the tracking error enters a prescribed bounded set within finite time, even though the prescribed performance control strategy which is debated may not fully account for all practical prospects. Flatness-based control has been employed by [PERSON] et al. [12] in successive loops for both the three-DOF rigid-link robotic manipulator and three-DOF autonomous underwater vessel. The proposed method separates the controlled system into two differentially flat subsystems, connected in cascade. The response of the two case studies exhibits fast and precise tracking of the desired set points; still, the robustness to uncertainty has not been inspected. [PERSON] et al. [13] proposed a modified backstepping control method to stabilize the rotary double-inverted pendulum, where the control law is a combination of the backstepping control action and uncertainty compensation control action. The simulation results show the control system's ability for exponential stabilization in the presence of uncertainties and disturbances. Yet, the proposed method involves complex design steps and lacks tunability to become consistent within practical applications. [PERSON] et al. [14] used pole placement to obtain the feedback gain that stabilizes the single-link inverted pendulum at the desired position of the cart. The results show that placing the poles at more negative locations yields faster response at the expense of higher overshoot and greater control action, yet does not afford robustness. [PERSON] et al. [15] employed a Multi Input/Multi Output (MIMO) decoupled control system method to implement the push-recovery strategy for the triple inverted pendulum by simplifying the control design into three serial Single Input Single Output (SISO) systems with known and uncertain disturbance models in each inverted pendulum, where the PID controller was used in each link to damp the external force applied on it.