Uncertain disturbance rejection and attenuation for semi-Markov jump systems with application to 2-degree-freedom robot arm

This paper studies the composite refined anti-disturbance control problem of a 2-degree-of-freedom robot arm system modeled by a semi-Markov jump system with multiple disturbances, which includes harmonic disturbances with unknown frequency and amplitude as well as energy bounded disturbances. Firstly, the semi-Markov jump system model is proposed to construct a novel linear model of the 2-degree-of-freedom robot arm subject to two types of disturbances. Next, in order to estimate the uncertain harmonic disturbance, a novel higher order disturbance observer is introduced to convert the uncertain harmonic disturbance into some parameter uncertainty and then estimate the parameter uncertainty. In addition, a corresponding composite anti-disturbance control scheme is formulated to reject and attenuate the above two types of disturbances, respectively. Furthermore, sufficient conditions that can guarantee that the system is stochastically stable are given. Finally, a simulation study of the obtained model is carried out to illustrate the validity of the composite control design method proposed in this paper.