A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive-control system (RCS) for a class of single-input, single-output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO-based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO-based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.
KEYWORDSdisturbance rejection, generalized extended state observer, mismatched disturbance, repetitive control
INTRODUCTIONIn control engineering practice, many control tasks are often of a periodic nature, such as optical disk drive, 1 magnetic spacecraft attitude control, 2 active control of vibration in helicopters, 3 and noncircular turning. 4 Repetitive control (RC) is an effective strategy for such control systems, which was originated from the work of Inoue et al, 5 based on the internal model principle. 6 A repetitive-control system (RCS) has a self-learning capability similar to that of human beings. It gradually improves the tracking accuracy through repeated learning actions, which involves adding the tracking error of the previous period to that of the present period to produce a control input. In the past three decades, there has been a significant amount of research progresses made on its theory and application.One problem with an RCS is that the improved periodic performance comes at the price of degraded performance for nonperiodic inputs, ie, due to the Bode Sensitivity Integral, 7 pushing the sensitivity down to zero at the multiples of the periodic input's harmonics increases the sensitivity at intermediate frequencies.To deal with this disadvantage, a so-called high-order RC was proposed by Pipeleers et al 8 that tried to achieve an optimal trade-off between periodic and nonperiodic performance indices. However, the high order of the controller makes it difficult to implement. Strategies to deal with this problem also include sliding-mode-based RC, 9 adaptive RC, 10 and H ∞ RC. 11 In these traditional feedback diagrams (also referred to as single-degree-of-freedom control structures), as pointed out by Chen et al, 12 there are a number of intrinsic design constraints such as tracking versus disturbance rejection and nominal performance versus robustness.Int J Robust Nonlinear Control. 2019;29:3777-3792.wileyonlinelibrary.com/journal/rnc
