Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

The active disturbance rejection control (ADRC) scheme requires a high bandwidth in the extended state observer (ESO), causing heavy noise pollution in the control system. This article develops an effective and simple adaptive ADRC scheme to realize high performance control when ESO bandwidth is limited. The adaptative law is generated by the state tracking error such that all the feedback loops and feedforward channels are activated for active disturbance rejection. An "attached" and "quantified" adaptation is developed to guarantee the easy usage of the proposed scheme. The uniformly ultimate boundedness of all the signals in the closed-loop system is proved in the sense of Lyapunov theory. Finally, two simulation examples are given to demonstrate the results.

Section: Adrc and Problem Statementmentioning

confidence: 99%

Section: Adrc and Problem Statementmentioning

confidence: 99%

Adaptive active disturbance rejection control guaranteeing uniformly ultimate boundedness and simplicity

Nie

Zhang

Wang

et al. 2020

“…In this section, a method is developed to identify the model set (Δ), as given by (3), which constitutes contribution C4. A connection is established between the stochastic disturbances that corrupt the output during the identification process and the resulting uncertainty of the nominal model.…”

Section: Identification Of the Model Setmentioning

confidence: 99%

“…Consider (Δ) as given by(3), under Assumptions 2 and 7, andlet G n ( k ), W y ( k ) and W u ( k ) be set as in Proposition 1. If is such that F( , k ) ≥ , with F( , k ) as presented in Lemma 6, then Pr(G • ( k ) ∈ (Δ, k )) ≥ .…”

mentioning

confidence: 99%

Multivariable nonparametric learning: A robust iterative inversion‐based control approach

Rozario

Oomen

2020

Learning control enables significant performance improvement for systems by utilizing past data. Typical design methods aim to achieve fast convergence by using prior system knowledge in the form of a parametric model. To ensure that the learning process converges in the presence of model uncertainties, it is essential that robustness is appropriately introduced, which is particularly challenging for multivariable systems. The aim of the present article is to develop an optimization-based design framework for fast and robust learning control for multivariable systems. This is achieved by connecting robust control and nonparametric frequency response function identification, which results in a design approach that enables the synthesis of learning and robustness parameters on a frequency-by-frequency basis. Application to a multivariable benchmark motion system confirms the potential of the developed framework. K E Y W O R D S frequency response methods, learning control, multivariable control systems, robust control, System identification 1 INTRODUCTION Learning control methods can increase the performance of systems by using past operational data. Iterative learning control (ILC), 1,2 repetitive control (RC), 3 and iterative inversion-based control (IIC) 4 have been developed to increase the tracking performance of systems that start each task under identical conditions or that operate continuously in a periodic fashion. 5,6 Examples of high-precision applications whose performance has been enhanced through learning control include nanopositioning devices, 7,8 additive manufacturing machines, 9,10 and industrial printing systems. 11,12 Convergence, usually in terms of signal norms, is an essential aspect of learning and is typically subject to the following requirements. 1,13(§5.1.1) (R1) The learning process converges in a way that is free of poor learning transients and converges relatively fast. (R2) The performance upon convergence is improved. These requirements should hold in the presence of uncertain dynamics and unknown disturbances, 14 since learning control is typically employed to increase the performance in the presence of these unmodeled phenomena. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

“…Therefore, the EID approach is directly applicable to both minimum‐ and non‐minimum‐phase plants. Unlike the ESO method, the EID approach approximates and compensates disturbances or uncertainties from the control input channel, thus it avoids the adverse influences caused by mismatched disturbances or uncertainties on state estimation 16 …”

Section: Introductionmentioning

confidence: 99%

Analysis of equivalent‐input‐disturbance‐based control systems and a coordinated design algorithm for uncertain systems

Liu

et al. 2021

Self Cite

The control method based on the equivalent‐input‐disturbance (EID) estimator and the Luenberger state observer has received much attention in recent years. However, the property of EID‐based control systems is still not well investigated. A number of design procedures were proposed but lacked sufficient theoretic justification. In this article, the two‐degree‐of‐freedom nature of an EID‐based control system is revealed. Specifically, the reference‐tracking is determined by an outer loop, while the disturbance rejection and robustness is determined by an inner loop consisting of the EID estimator and state observer. The bandwidth constraints on the inner loop are analyzed for plants having zeros or poles in the open right‐half plane by using the Bode and the Poisson integral formulas. These analyses provide a theoretic justification for conventional design procedures. Further, a coordinated design algorithm is provided for the EID‐based uncertain control systems. In addition, a comprehensive comparison of the EID‐based and the disturbance observer (DOB) based control systems is conducted in the system design aspect. Lastly, comparative studies of the EID‐based and DOB‐based control methods are given for various types of plants to validate the developed design algorithm.