Repetitive control of tracking systems with time-varying periodic references

Position‐dependent disturbance rejection using spatial‐based adaptive feedback linearization repetitive control

“…The control law given by (9) is valid under the condition that L g L r −1 f h(x) = 0. Therefore, it is imperative to preserve this condition when implementing the proposed control system design.…”

“…Although design methods for the linearized system are simple and straightforward, it is unclear whether the overall control system (which is nonlinear) will operate at varying speed or could sustain large velocity fluctuation without stability concern. For tracking of spatially periodic references, Mahawan and Luo [9] proposed and proved the feasibility of operating the repetitive kernel in spatial domain and the stabilizing controller in the time domain. Thus, no reformulation of the open-loop system is required.…”

Spatially Sampled Robust Repetitive Control

“…Although effective for small angular velocity fluctuations, the effectiveness of a linearized approach is limited when the application requires a large variation in operating speed. (Mahawan & Luo, 2000) demonstrated the feasibility of augmenting a spatially sampled repetitive controller to a time-sampled stabilizing controller, where no reformulation and linearization of the openloop plant model is required. However, the complexity of the method lies in the need to solve an optimization problem in real-time to synchronize the hardware and software interrupts associated with time and spatial sampling, respectively.…”

“…In addition, although reasonable for trajectory tracking, the assumption of a known mapping between time and angular displacement is rarely applicable for disturbance rejection applications. The lack of considerations to modeling uncertainty is another area that can be improved from the methods proposed in (Nakano et al, 1996) and (Mahawan & Luo, 2000). Instead of linearizing the resulting nonlinear plant model, (Chen and Chiu, 2008) shows that the nonlinear plant model can be formulated into a quasi-linear parameter varying (quasi-LPV) system, where the angular speed is one of the measurable varying parameters.…”

Robust Adaptive Repetitive and Iterative Learning Control for Rotary Systems Subject to Spatially Periodic Uncertainties

“…However, the overall system might lack the stability of operating at a variable speed or coping with large velocity fluctuation. For tracking of spatially periodic references, Mahawan and Luo [26] have validated the idea of operating the repetitive kernel in angular domain and the stabilizing controller in time domain. Doing so does not require reformulation of the open-loop system.…”