In most mechanical devices, e.g., manipulators, servo motors, and offshore steel jacket platforms, nonlinear dynamics is prevalent and has been identified as the epicenter of the difficulties experienced in control design of such systems. In order to track and/or reject a periodic reference/disturbance with high accuracy, repetitive control (RC) has been proven as an effective alternative. Unfortunately, there may still exist some disturbances in other forms. These disturbances have the potential to corrupt control performance of nonlinear systems.
To avert this, some strategies have been developed to enhance the disturbance-rejection performance for nonlinear systems. One popular approach is the equivalent-input-disturbance (EID) approach which is based on stable inversion. This method has been reported to being effective for both matched and mismatched disturbances. Better still, this method has been shown not to require an inverse model of the plant and is robust to model uncertainties. However, the conventional EID estimator brings many constraint conditions for system analysis and design.
In a recent publication, Chiba University scientists: Pan Yu (PhD candidate) and Professor Kang-Zhi Liu together with Professors Jinhua She and Min Wu at China University of Geosciences (Wuhan) and also Professor Yosuke Nakanishi at Waseda University developed an improved EID (IEID) approach to deal with a larger class of nonlinearities in a modified RC system (MRCS) perturbed by an exogenous disturbance. They focused on developing a simple structure of IEID estimator that can eliminate requirements on the existence of the generalized inverses of the input and the observer gain matrices. Their work is currently published in International Journal of Robust and Nonlinear Control.
In brief, they started by providing an overview of the configuration of the IEID estimator. Next, they analyzed the IEID-based nonlinear MRCS and established a continuous-discrete two-dimensional hybrid system model and presented a design algorithm for the closed-loop control system. Then, they conducted comparisons of the developed method with the GESO and conventional EID methods in structural analysis. Finally, numerical methods to validate the developed method and compare it with the GESO and conventional EID methods were undertaken.
The authors avoided the restrictive commutative condition so as to reduce the conservativeness of system design. As such, they adopted a general form of Lyapunov functions for the system design. This way, a design algorithm based on two LMIs, which considered the relation of all the control gains, was devised.
In summary, an IEID-based disturbance-rejection method was developed for a nonlinear MRCS. Specifically, the researchers took advantage of stable inversion, to develop an improved equivalent-input-disturbance (EID) estimator, which was more relaxed than the conventional EID estimator for system design, for the purposes of estimating and canceling out the influence of the disturbance and nonlinearity in the low-frequency domain. Altogether, simulations demonstrated and proved the validity and the advantages of the developed approach.
Pan Yu, Kang-Zhi Liu, Jinhua She, Min Wu, Yosuke Nakanishi. Robust disturbance rejection for repetitive control systems with time-varying nonlinearities. International Journal of Robust and Nonlinear Control. 25 March, 2019; Volume29, Issue5, Pages 1597-1612.Go To International Journal of Robust and Nonlinear Control