Weighting matrix design for robust monotonic convergence in Norm Optimal iterative learning control
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In this paper we examine the robustness of norm optimal ILC with quadratic cost criterion for discrete-time, linear time-invariant, single-input single-output systems. A bounded multiplicative uncertainty model is used to describe the uncertain system and a sufficient condition for robust monotonic convergence is developed. We find that, for sufficiently large uncertainty, the performance weighting can not be selected arbitrarily large, and thus overall performance is limited. To maximize available performance, a time-frequency design methodology is presented to shape the weighting matrix based on the initial tracking error. The design is applied to a nanopositioning system and simulation results are presented.Keywords:
Robustness
Iterative Learning Control
Tracking error
In this paper, an initial state learning scheme is proposed to remove the common assumption in the iterative learning control (ILC) that the initial states in each repetitive operation should be inside a given ball centered at the desired initial states, which may not be available. It is shown that the tracking error bound is independent of the initialization errors. By incorporating the current tracking error information in the ILC updating law, the uniform bound of the tracking error as well as the ILC convergence rate can be adjusted to a desired level. A class of nonlinear time-varying uncertain systems are investigated. The effectiveness of the proposed iterative learning controller is illustrated by a simulation.
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In this paper,an open closed loop PD type iterative learning control shceme for a class of nonlinear time varying system is proposed.In this scheme,the system courrent tracking error and previous tracking error are both used to update control input meanwhile.Namly,a feedback loop which based on open loop iterative learning control is introduced to form a feedback and feedfoward iterative learning control law to improve the system's tracking performance.Then sufficient and necessary conditions for the convergence of the proposed learning scheme are given.And finally simulation for a robot system shows the feasibility and effectiveness of our conlusion.
Iterative Learning Control
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Iterative Learning Control
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Iterative Learning Control
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To track the operation performance of a batch process under iterative learning control,we propose an R-adjustment control strategy.The definitions of zero-tracking error and bounded-tracking error are given according to classi-cal control theory.We investigate the iterative learning control strategy for achieving zero-tracking error in the output,and rigorously prove the tracking ability of the system under control.The most important conclusion is that the zero-tracking error can be achieved by the R-adjustment control strategy,which provides the basis for practical applications.
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Summary Initial condition problem is crucial to a conventional iterative learning control (ILC) scheme, which steers the tracking error from arbitrary initial value to zero in the time steps equaling to the relative degree of the system undertaken. The implementation may be difficult, due to the practical limitation for the control amplitude. This paper presents an error‐tracking approach to discrete‐time adaptive ILC designs for tracking nonidentical tasks in the presence of initial repositioning errors, which may be quite large. A prototype iterative learning algorithm is derived for estimating the time‐varying unknowns, and the saturation is introduced for assuring the estimates to keep away from zero. A key technical lemma, tailored for the analysis purpose in the iteration domain, is presented and applied to analysis of the ILC scheme. The tracking performance of the closed‐loop system is evaluated and explored in detail. It is shown that the perfect tracking for the error between the tracking error and the desired error is achieved at every time instant, while the input and output signals remain bounded. By the simulation example, the proposed scheme is verified to be applicable to tracking tasks without restriction on initial repositioning.
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This paper presents an iterative learning control (ILC) method for nonlinear systems where the trial lengths could be randomly varying in the iteration domain. Based on the concept of error tracking, a unique equivalent error is given to deal with the tracking tasks with non-uniform trial lengths, which can effectively mitigate the requirements on classic ILC that all trial lengths must be identical and the initial condition must remain to be a fixed value for each iteration. The learning law is derived from the Lyapunov-like approach, which can guarantee the convergence of the tracking error in mathematical expectation. Several simulations are presented to demonstrate the effectiveness of the proposed ILC scheme.
Iterative Learning Control
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A high-order P-type updating law, in which the current iteration tracking error (CITE) is employed, is proposed for iterative learning control (ILC ) of a class of uncertain nonlinear repetitive systems. Uniform boundedness of the tracking error is established in the presence of uncertainty, disturbance and initialization error. The bound and the ILC convergence rate can be adjusted by tuning the learning gain of the CITE.
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Iterative Learning Control
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Parametrization (atmospheric modeling)
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A simple iterative learning controller (ILC) is proposed for the tracking control of uncertain discrete-time nonlinear systems performing the repetitive tasks. The tracking error of the current learning iteration is utilized in the ILC updating law. It is proven that, under relaxed conditions, the final tracking error is bounded in the presence of uncertainty, disturbance and the initialization error. Furthermore, the tracking error bound and the ILC convergence rate can be tuned by the learning gain of the current iteration tracking error in the ILC updating law. The effectiveness of the proposed ILC scheme is illustrated by a simulation.
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