Robustness analysis of an adjoint optimal iterative learning controller with experimental verification

A synthesis algorithm for the filters in a first order ILC is presented and applied on an industrial robot. The proposed ILC synthesis method is evaluated using two experiments on the robot. The first is a one-axis experiment where the system can be seen as a single servo. A modeling experiment is done to give input to the synthesis algorithm and then ILC is applied to the single axis showing a dramatic improvement in trajectory following. In the second experiment ILC is applied to a more complex multi axes motion where the robot draws a circle in a plane. The evaluation of the result is done using a pen mounted on the robot and it is evident that also on the arm-side an improved motion can be achieved. In both experiments the error converges to a stable level in about 5 iterations. Since a model is desired for the synthesis, an extra iteration has to be done for the modeling experiment. In this particular case a good path following can therefore be achieved after 6 iterations.

IEEE-ASME Transactions on Mechatronics, 2008

This paper deals with robust iterative learning control design for uncertain single-input-single-output linear time-invariant systems. The design procedure is based upon solving the robust performance condition using the Youla parameterization and the µ-synthesis approachto obtain a feedback controller. Thereafter, a convergent iterative learning law is obtained by using the performance weighting function involved in the robust performance condition. Experimental results, on a CRS465 robot manipulator, are provided to illustrate the effectiveness of the proposed design method.

Many manipulators at work in factories today repeat their motions over and over in cycles and if there are errors in following the trajectory these errors will also be repeated cycle after cycle. The basic idea behind iterative learning control (ILC) is that the controller should learn from previous cycles and perform better every cycle. Iterative learning control is used in combination with conventional feedback and feedforward control, and it is shown that learning control signal can handle the e ects of unmodeled dynamics and friction. Convergence and disturbance e ects as well as the choice of lters in the updating scheme are also addressed.

Proceedings of 2012 UKACC International Conference on Control, 2012

In many practical applications, constraints are often present on, for example, the magnitudes of the control inputs. Recently, based on a novel successive projection framework, two constrained iterative learning control (ILC) algorithms were developed with different convergence properties and computational requirements. This paper investigates the effectiveness of these two methods experimentally on a gantry robot facility, which has been extensively used to test a wide range of linear model based ILC algorithms. The results obtained demonstrate the effectiveness of the algorithms in solving one form of the general constrained ILC problem.

Asian Journal of Control, 2013

This paper presents a nonlinear iterative learning control (NILC) for nonlinear time-varying systems. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory-tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. A special feature of the algorithm is that the trial-time interval is finite but not fixed as it is for the other iterative learning algorithms. A sufficient condition for convergence and robustness of the bounded-error learning procedure is derived. With respect to the bounded-error and standard learning processes applied to a virtual robot, simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control.

Proc. of the 17th IFAC …, 2008

Abstract: Iterative learning control is a technique especially developed for application to processes which are required to repeat the same operation, or task, over a finite duration and has many applications, such as a gantry robot undertaking a pick and place operation. The exact ...

2002

In this paper, the uncertain model of the robotic system is decomposed into repetitive and non-repetitive parts, and the norm model of the system is taken into account. By using the Lyapunov method, an adaptive robust iterative learning control scheme is presented for the robotic system with both structured and unstructured uncertainty, and the overall stability of the system in

Control Engineering Practice, 2013

Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum. In common with other control algorithm design methods, this can be a very difficult specification to meet but often the control of physical/industrial systems is only required over a finite frequency range. This paper uses the generalized Kalman-Yakubovich-Popov lemma to develop a two-dimensional systems based iterative learning control law design algorithm where frequency attenuation is only imposed over a finite frequency range to be determined from knowledge of the application and its operation. An extension to robust control law design in the presence of norm-bounded uncertainty is also given and its applicability relative to alternative settings for design discussed. The resulting designs are experimentally tested on a gantry robot used for the same purpose with other iterative learning control algorithms.

IEEE Transactions on Systems, Man, and Cybernetics

The authors propose a simple discrete-time design of robust iterative learning controllers taking account of the transient behavior as well as the uncertainty of a plant. Using the impulse response sequence of a plant, we give a simple finite dimensional formulation of the problem. Assuming that a nominal impulse response sequence is given, it is proposed that a design based on the minimization of a quadratic performance index that can be regarded as a measure for the transient performance. Then the effect of the error in the impulse response data is analyzed. It is shown that an excessively high order controller is not robust in the sense that the error severely deteriorates the transient Performance. To obtain a robust controller with a reasonable order, we proposed a design based on a probabilistic modeling of the error in the impulse response data. The controller is obtained by minimizing an averaged quadratic performance index. Simulation examples are presented to illustrate the effectiveness of the proposed methods. 0018-9472/92$03.00 0 1992 IEEE S. Kodama and N. Suda, "Matrix theory for systems and control," Soc. Instrum. Contr. Eng., 1978 (in Japanese). M. Brady et al., Robot Motion: Planning and Control.

Control Engineering Practice, 2010

This paper considers iterative learning control law design for both trial-to-trial error convergence and along the trial performance. It is shown how a class of control laws can be designed using the theory of linear repetitive processes for this problem where the computations are in terms of linear matrix inequalities (LMIs). It is also shown how this setting extends to allow the design of robust control laws in the presence of uncertainty in the dynamics produced along the trials. Results from the experimental application of these laws on a gantry robot performing a pick and place operation are also given.

Proceedings of the 2010 American Control Conference, 2010

This paper uses 2D control systems theory to develop robust iterative learning control laws for linear plants with experimental validation on a gantry robot used for 'pick and place' operations commonly found in industries such as food processing. In particular, the stability theory for linear repetitive processes provides the setting for analysis and this allows design to take account of trial-to-trial error convergence, transient response along the trials and robustness. The mechanism for this is the use of a strong form of stability for repetitive processes/2D linear systems known as stability along the pass (or trial) with the added requirement for maintaining this property in the presence of model uncertainty. The resulting design computations are in terms of Linear Matrix Inequalities (LMIs) and the control laws can be implemented without the need to estimate state vector entries.

2008 American Control Conference, 2008

A number of iterative learning control algorithms have been developed in a stochastic setting in recent years. The results currently available are in the form of algorithm derivation and the establishment of various fundamental systems theoretic properties. As the crucial, in terms of eventual use in applications, next stage this paper compares their performance when implemented on a gantry robot system.

Archives of Control Sciences, 2012

This paper deals with a simulation-based design of model-based iterative learning control (ILC) for multi-input, multi-output nonlinear time-varying systems. The main problem of the implementation of the nonlinear ILC in practice is possible inadmissible transient growth of the tracking error due to a non-monotonic convergence of the learning process. A model-based nonlinear closed-loop iterative learning control for robot manipulators is synthesized and its tuning depends on only four positive gains of both controllers - the feedback one and the learning one. A simulation-based approach for tuning the learning and feedback controllers is proposed to achieve fast and monotonic convergence of the presented ILC. In the case of excessive growth of transient errors this approach is the only way for learning gains tuning by using classical engineering techniques for practical online tuning of feedback gains

IEEE Transactions on Control Systems Technology, 2000

This brief develops a new algorithm for the design of iterative learning control law algorithms in a 2-D systems setting. This algorithm enables control law design for error convergence and performance, and is actuated by process output information only. Results are also given from the experimental application to a gantry robot.

2009

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, ...