Norm optimal Cross-Coupled Iterative Learning Control

Barton, Kira; Wijdeven, Jeroen van de; Alleyne, Andrew G.; Bosgra, О.H.; Steinbuch, M Maarten

doi:10.1109/cdc.2008.4738973

Cited by 28 publications

(31 citation statements)

References 14 publications

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“…In [9] it is concluded that the smallest error is achieved if W u = 0, however W u = 0 is used in order to handle model errors. Moreover, it is discussed that the convergence rate mostly depends on λ, where λ = 0 gives deadbeat control w.r.t the iterations and λ → ∞ makes the convergence rate arbitrarily slow.…”

Section: Stability Analysismentioning

confidence: 99%

Estimation-based norm-optimal iterative learning control

Axelsson¹,

Karlsson²,

Norrlöf³

2014

Systems & Control Letters

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The iterative learning control (ilc) method improves performance of systems that repeat the same task several times. In this paper the standard norm-optimal ilc control law for linear systems is extended to an estimation-based ilc algorithm where the controlled variables are not directly available as measurements. The proposed ilc algorithm is proven to be stable and gives monotonic convergence of the error. The estimationbased part of the algorithm uses Bayesian estimation techniques such as the Kalman lter. The objective function in the optimisation problem is modied to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ilc design is independent of the estimation method. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc algorithm. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and veried in a simulation study with a simplied model of an industrial manipulator system. AbstractThe iterative learning control (ilc) method improves performance of systems that repeat the same task several times. In this paper the standard norm-optimal ilc control law for linear systems is extended to an estimation-based ilc algorithm where the controlled variables are not directly available as measurements. The proposed ilc algorithm is proven to be stable and gives monotonic convergence of the error. The estimation-based part of the algorithm uses Bayesian estimation techniques such as the Kalman filter. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ilc design is independent of the estimation method. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc algorithm. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and verified in a simulation study with a simplified model of an industrial manipulator system.

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Section: Stability Analysismentioning

confidence: 99%

Estimation-based norm-optimal iterative learning control

Axelsson¹,

Karlsson²,

Norrlöf³

2014

Systems & Control Letters

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“…Using analysis provided in [72,78] it can be shown that the S weighting matrix should be designed to ensure robust monotonic convergence in the presence of model uncertainty. Assuming a weighting matrix of the form S = sI, the weighting gain s provides constant weighting for uniform model uncertainty.…”

Section: Motivationmentioning

confidence: 99%

“…As is shown in [73], the influence of stochastic disturbances can be minimized by reducing the convergence speed. In [78] the dominating factor in convergence speed was shown to be the R weighting matrix. While a constant weighting gain r in R = rI provides consistent influence on the effect of stochastic disturbances, many applications include external disturbances and noise that change …”

Section: Motivationmentioning

confidence: 99%

“…Previous work has been done to address the deficiencies of time-invariant weighting matrices through the design of time-varying weighting matrices for specific applications, [73,77,78]. In [77], critical and non-critical sections of a given trajectory are weighted separately using a time-varying weighting matrix design.…”

Section: Introductionmentioning

confidence: 99%

“…References [78,120] present some guidelines for designing and tuning the matrices based on performance and robustness requirements. The work in this paper focuses on time-variation in the Q matrix primarily due to a coupled output objective defined as the contour error (J.13).…”

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confidence: 99%

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Precision coordination and motion control of multiple systems via iterative learning control

Barton

Alleyne

2010

Proceedings of the 2010 American Control Conference

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In today's engineering world, many emerging applications ranging from manufacturing to the autonomous vehicle industry require coordination of multiple systems. Traditional approaches for controlling these systems often neglect the underlying coupling in the application. To stay at the forefront of these fields requires the development of innovative approaches to new challenges. The research in this dissertation focuses on designing novel control strategies for coordinated applications. Electrohydrodynamic jet (E-jet) printing, an example of an emerging micro/nano-manufacturing process with applications in biotechnology and flexible electronics, requires multiple systems to work in a coordinated manner to achieve a desired objective. Repetitive execution of processes such as E-jet can be harnessed to achieve high performance. Iterative learning control (ILC) is an adaptive control technique for improving process performance in systems that execute a task repetitively. This research simultaneously exploits the repetitiveness and inherent coupling of the desired outcome by applying a coordinated ILC approach to processes such as E-jet. The versatility of this approach will be demonstrated through applications ranging from robotics to emerging manufacturing processes.ii To Alex and our little family iii

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Iterative learning control for integrated system of robot and machine tool

Chen

2022

Asian Journal of Control

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This study is concerned with the integrated system of a robot and a machine tool. The major task of robot is loading the workpiece to the machine tool for contour cutting. An iterative learning control (ILC) algorithm is proposed to improve the accuracy of the finished product. The proposed ILC is to modify the input command of the next machining cycle for both robot and machine tool to iteratively enhance the output accuracy of the robot and machine tool. The modified command is computed based on the current tracking/contour error. For the ILC of the robot, tracking error is considered as the control objective to reduce the tracking error of motion path, in particular, the error at the endpoint. Meanwhile, for the ILC of the machine tool, contour error is considered as the control objective to improve the contouring accuracy, which determines the quality of machining. In view of the complicated contour error model, the equivalent contour error instead of the actual contour error is taken as the control objective in this study. One challenge for the integrated system is that there exists an initial state error for the machine tool dynamics, violating the basic assumption of ILC. It will be shown in this study that the effects of initial state error can be significantly reduced by the ILC of the robot. The proposed ILC algorithm is verified experimentally on an integrated system of commercial robot and machine tool. The experimental results show that the proposed ILC can achieve more than 90% of reduction on both the RMS tracking error of the robot and the RMS contour error of the machine tool within six learning iterations. The results clearly validate the effectiveness of the proposed ILC for the integrated system.

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Norm optimal Cross-Coupled Iterative Learning Control

Abstract: Abstract-In this paper, we focus on improving contour tracking in precision motion control (PMC)

Cited by 28 publications

References 14 publications

Estimation-based norm-optimal iterative learning control

Estimation-based norm-optimal iterative learning control

Precision coordination and motion control of multiple systems via iterative learning control

Iterative learning control for integrated system of robot and machine tool

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