Observer-based technique is an alternative to deal with uncertainties, which estimates the uncertainties by designing a state/disturbance observer. In Ref. [37], a high gain observer-based robust output feedback control approach was proposed for a single-link FJM with matched disturbances and parametric uncertainties. In Ref. [38], a nonlinear disturbance observer (NDO) based DSC approach was proposed for the FJM with input saturation and unknown nonlinear disturbance, where the NDO was applied to estimate the unknown external disturbance and compensate the saturation constrain. However, only matched disturbances were considered in these control methods. Extended state observer (ESO), which regards internal and external disturbances as an extended system state variable, is another effective and practical disturbance estimation and attenuation approach [39]. As for FJMs in the presence of disturbances, an ESO-based feedback linearization control method was proposed in Ref. [40], and a cascaded-ESO based sliding-model control strategy was proposed in Ref. [41]. However, the conventional ESO is only applicable for integral chain systems, which should satisfy the so-called matching conditions. Although the ESOs in Refs. [40; 41] can transform a mismatched disturbance into a matched one, they require a series of complex coordinate transformations, which make the control algorithms computationally complicated. In addition, the order of the constructed ESOs is greater than the system. For high-order systems like the FJM, it may bring about some negative effects of the high gain action, such as noise amplification and the peaking phenomenon [41]. Unlike conventional ESO, the reduced-order ESO (RESO) [42], which makes full use of the measurable system state information, can attenuate the peaking phenomenon and yield a better estimation performance. More importantly, the RESO can be applied to non-integral chain systems with matched and mismatched disturbances. Due to these advantages, the RESO has been widely used for the control of various engineering systems, such as missiles [43], gear-shifting actuators [44], underwater vehicles [45], DC-DC buck converters [46], all-clamped plates [47], etc. However, the application of RESO on FJMs has not been reported. Based on the above literature review and analysis, it is noted that there are still many crucial problems worthy of being further investigated in the control of FJMs, which can be summarized as follows. 1. The FJMs in practical applications inevitably encounter various uncertainties including matched and mismatched disturbances. Unfortunately, the current researches focus on the matched disturbances, while the mismatched ones are not considered. Although the conventional ESO can transform a mismatched disturbance into a matched one, it requires a series of complex coordinate transformations, which make the control algorithms computationally complicated;
2. The backstepping technique employed for the control design of FJMs suffers from the drawback of \"explosion of complexity\". Although the DSC or SCFCB can deal with the computation problem, the potential errors caused by the introduction of filters are not considered, which may greatly reduce the tracking accuracy. Motivated by the above considerations, this paper aims to propose an efficient model-assisted composite control approach for the high precision tracking control of FJMs in the presence of lumped matched and mismatched disturbances by integrating the techniques of RESO and the SCFB. More specifically, the uncertain model of a single-link FJM is first given, where all the uncertainties affecting the system including friction/damping terms and external disturbances are lumped as matched and mismatched disturbances. Then, two model-assisted RESOs are constructed to estimate the matched and mismatched disturbances in real time.