Iterative Learning Control: An Expository Overview

A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Theoretical background

In this paper, we present an iterative learning control (ILC) framework for tracking problems with predefined data points that are desired points at certain time instants. To design ILC systems for such problems, a new ILC scheme is proposed to produce output curves that pass close to the desired points. Unlike traditional ILC approaches, an algorithm will be developed in which the control signals are generated by solving an optimal ILC problem with respect to the desired sampling points. In another word, it is a direct approach for the multiple points tracking ILC control problem where we do not need to divide the tracking problem into two steps separately as trajectory planning and ILC controller. The strength of the proposed formulation is the methodology to obtain a control signal through learning law only considering the given data points and dynamic system, instead of following the direction of tracking a prior identified trajectory. The key advantage of the proposed approach is to significantly reduce the computational cost. Finally, simulation results will be introduced to confirm the effectiveness of proposed scheme.

In this article, we discuss iterative learning control (ILC) for systems with input/output (i/o) basis functions. First, we show that various different ILC formulations in the literature can be captured by a common system representation involving i/o basis functions. Analysis of ILC control objectives in this framework yields ILC controller conditions which are required for convergence and optimal performance. Furthermore, analysis reveals how different ILC objectives (monotonic convergence, performance, minimisation of input amplitudes) can be reached by designing separate parts of the ILC controller. The analysis is subsequently expanded by studying the effects of trial-varying disturbances on performance, which results in suggestions for the compensation of these effects. Finally, we use these results to systematically design ILC controllers for the representation under study, and we show that the found results are applicable to existing ILC problem formulations with i/o basis functions, and problem formulations which can be interpreted as such.

The tracking performance of two iterative learning control algorithms is compared to that, which can be achieved by an optimal feedback controller. P-type iterative Learning Control in parallel with a proportional feedback controller is compared with norm-optimal iterative learning control, then both ILC systems are compared with the performance achieved by an optimal feedback controller. Considering that the ILC plus proportional controller requires no prior modelling of the plant and minimal adjustment of gains, the tracking performance in terms of mean squared error (mse) per iteration can be reduced by two orders of magnitude further than can be achieved with the optimal feedback controller. However, the Norm-Optimal ILC improves upon this performance by reducing the mse by an extra order of magnitude. The experimental results are derived from tests performed on a gantry robot.

Two-dimensional Iterative Learning Control for Batch Processes With State Delay and Time-varying Uncertainties

The problem of iterative learning control (ILC) is considered for a class of time-varying systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a remote control system and that packet dropout occurs during the packet transmission between the ILC controller and the actuator of remote plant. The packet dropout is viewed as a binary switching sequence which is subject to the Bernoulli distribution. In order to eliminate the effect of packet dropouts on the convergence property of output error, the hold-input scheme is adopted to compensate the packet dropout at the actuator. It is shown that the hold-input scheme with average ILC can achieve asymptotical convergence along the iteration axis for discrete time-varying linear system. Numerical examples are provided to show the effectiveness of the proposed method.

This paper presents an iterative learning control (ILC) approach for tracking problems with specified data points that are desired points at certain time instants. To design ILC systems for such problems, unlike traditional ILC approaches, an algorithm which updates not only the control signal but also the reference trajectory at each trial will be developed. The relationship between the reference trajectory and ILC control in tracking problems where there are specified data points through which the system should pass is investigated as the rate of convergence. In traditional ILC, the desired data is stored in a tracking profile file. Due to the huge size of the data file containing the target points, it is important to reduce the computational cost. Finally, simulation results of the presented technique are mentioned and compared to other related works to confirm the effectiveness of proposed scheme.

This paper utilizes the improved particle swarm optimization (IPSO) technique for adjusting the gains of PID controller, iterative learning control (ILC) and the bandwidth of Butterworth filter of the ILC. The conventional ILC learning process has the potential to excite rich frequency contents and to learn the error signals. However the learnable and unlearnable error signals should be separated for b ettering control process along with the repetitions. Since producing a high frequency error condition should be avoided before the phase margin cause any trouble. Learnable error signals through a bandwidth tuning mechanism should be adaptively injected into learning control laws and thus reduce the tracking error effectively at every repetition. The filter bandwidth should be changed at every repetition for the shape of compensated errors at frequency response thinking. Thus adaptive bandwidth in the ILC controller with the aid of IPSO tuning is proposed here. Simulation results show the new controller can cancel the errors efficiently as the process is repeated. The correlation coefficient that validates the learnable compensated error signal for the trajectory is adaptively decomposed from previous error history via the bandwidth tuning mechanism in the next repetition. The learnable error signals of the intrinsic mode functions through the empirical mode decomposition correlate efficiently with reduced tracking error with further repetitions. Simulation results validate the effectiveness of the IPSO-ILC for precision motion control of a robot arm link performing high speed maneuvering or computer numerical control commanding axis positioning.

Resource-efficient ILC for LTI/LTV systems through LQ tracking and stable inversion: Enabling large feedforward tasks on a position-dependent printer

This paper presents a model-free adaptive iterative learning control (ILC) scheme called a proportional-type ILC scheme for non-linear systems. The obvious characteristic of the proposed ILC scheme is that we can easily finish the ILC task just utilising the Lipschitz constant of the system. In the proposed ILC scheme, the time-vary learning gain can be produced merely by input and output (I/O) measurements. Moreover, the convergence conclusion can be expressed by the ranges of the pseudo-partial derivative and the learning gain. In actual operation, a reasonable and useful convergence condition by a constant is also provided for selection. At last, the effectiveness of the proposed ILC scheme is shown by simulations.

Passivity-Based Iterative Learning Control for Spacecraft Attitude Tracking on SO(3)

Two-dimensional iterative learning control with deep reinforcement learning compensation for the non-repetitive uncertain batch processes

This paper investigates the performance of iterative learning control (ILC) scheme that is adopted in networked control systems with data dropouts, where a linear discrete-time stochastic system can be rewritten as a super-vector formulation. In this paper, two types of compensation schemes are employed for data dropouts occur in both the output signals and control input signals during the signals transmission from the sensor to the ILC controller and from ILC controller to the actuator, respectively. Through statistical analysis approach, it is shown that ILC can perform well and achieve bounded convergence in the sense of norm. Numerical simulations demonstrate the validity and effectiveness.

Output Feedback Based Iterative Learning Control with Finite Frequency Range Specifications via a Heuristic Approach for Batch Processes with Polytopic Uncertainties

This study explores the incorporation of time-varying sign gain into a parallel iterative learning control (ILC) architecture, augmented by an expert system, to enhance the performance and stability of a robotic arm system. The methodology involves iteratively tuning the learning control gains using time-varying sign gain guided by an expert system. Stability analysis, encompassing asymptotic and monotonic convergence, demonstrates promising results across multiple joints, affirming the effectiveness of the proposed control architecture. In comparison with traditional PID control, fixed gain ILC, and ILC with adaptive learning in the expert system, the analysis focuses on stability, precision, and adaptability, using root mean square error (RMSE) as a key metric. The results show that ILC with adaptive learning from the expert system consistently reduces RMSE, even in the presence of learning transients. This adaptability effectively controls the learning transients, ensuring improved performance in subsequent iterations. In conclusion, the integration of time-varying sign gain with expert system assistance in a parallel ILC architecture holds promise for advancing adaptive control in robotic systems. Positive outcomes in stability, precision, and adaptability suggest practical applications in real-world scenarios. This research provides valuable insights into the implementation of dynamic learning mechanisms for enhanced robotic system performance, laying the groundwork for future refinement in robotic manipulator control systems.