Introducing a Model-based Learning Control Software for Nonlinear Systems: RoFaLT

This paper presents RoFaLT, a freely-available, model-based iterative learning control (ILC) tool for nonlinear systems, that strives to close the gap between the theory of nonlinear ILC and successful applications. By providing a simple yet powerful syntax, all phases of the design of a nonlinear ILC - from modeling, tuning and execution, to analysis - are supported. RoFaLT implements an optimization-based two-step approach that yields fast convergence rates for nonlinear systems and is easily tunable to trade convergence speed off for robustness. To demonstrate the efficiency of RoFaLT, an application to a tracking problem of a race car is considered, where a simple kinematic bicycle model is used to iteratively learn the control of complex vehicle dynamics. The results show fast convergence and the effect of different tunings is shown.

Iterative learning control (ILC) is one of the most popular tracking control methods for systems that repeatedly execute the same task. A system model is usually used in the analysis and design of ILC. Model‐based ILC results in general in fast convergence and good performance. However, the model uncertainties and nonrepetitive disturbances hamper its practical applications. One of the commonly used solutions is the introduction of a low‐pass filter, namely, the Q‐filter. However, it is indicated in this paper that the existing Q‐filter configurations compromise the servo performance, although improving the robustness. Motivated by the combination of performance and robustness, a novel Q‐filter configuration in ILC is presented in this paper. Some practical considerations, such as the configuration of ILC in a feedback control system, the time delay compensation, and the learning coefficient, are provided in the implementation of the proposed ILC algorithm. The effectiveness and superiority of the proposed ILC versus existing Q‐filter ILC are demonstrated by both theoretical analysis and experimental verification on a wafer stage.

This work focuses on the model-free iterative learning control (ILC) design with good transient performance and fast convergence rate that is employed for precision control of a wafter stage. First, the experimental setup, the mathematical model, and the desired reference are introduced. Notice that the desired reference and its internal model (IM) are known in advance. Then, based on the internal model principle (IMP), a new ILC scheme, named as 1M-based ILC, is proposed by incorporating the 1M of the reference. The proposed 1M-based ILC is model-free, that is, independent on the system model of the controlled plant. The 1M -based ILC is carefully constructed to track the reference along the time axis while tracking/rejecting repetitive variations along the iteration axis. Precisely because of the tracking capability along the time axis in every iteration, the 1M-based ILC can achieve satisfactory performance even in the 0th iteration and improve the transient performance and the convergence speed. In addition, the 2-D $H_{\infty}$ theory is used to establish the design criterion for the 1M-based ILC. Finally, in the experiments, the efficiency of the 1M-based ILC is illustrated by comparing with a P-type ILC and a model-based one.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

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

The repetitive processing and large quantity of single product represented by 3C products are urgently needed. However, for current processing operations, previous processing data have not been used in the optimization of control input. In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise, the idea of iterative learning was introduced to improve the accuracy of machining. On the control level, since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories, an open-loop iterative learning controller and a position loop feedback controller were introduced, which worked fast with good convergence effects. Aiming at reducing the influence of accidental error, step type iterative learning was put forward. The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity, store the current iterative part of the control input, and make constant value compensation. However, in simulation and experiment, it was found that after superposition of the iterative learning controller, the phenomenon of partial divergence of the system tracking error occurred. Therefore, the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed. High-frequency noise was introduced in frequency domain, which was found to be the cause of the abovementioned phenomenon, and high-frequency components were filtered to solve the problem. To further improve the accuracy of convergence and avoid filtering effective high-frequency information in some area, a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed. Through SIMULINK simulation and dSPACE experimental verification, it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

This paper aims at iterative learning control (ILC) design and analysis for a class of linear distributed parameter systems (DPSs) that may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the linear characteristic of systems, the system equations are first cast into a matrix form in the Laplace transform domain. Then, through determination of a fundamental matrix, the system transfer function is precisely evaluated in a closed form. The derived transfer function clearly demonstrates the input-output relationship of system, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and makes full use of the process repetition, while avoids any simplification or discretization for the 3D dynamics of distributed parameter systems in the time, space, and iteration domains. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

In this study, a two‐dimensional (2D) H ∞ ‐based method is presented for the iterative learning control (ILC) design problem of a class of linear discrete‐time systems with iteratively periodic factors, including initial states, parametric uncertainties, disturbances, measurement noises, and reference trajectories. First, the ILC design problem of the linear systems is described as a controller design problem of 2D uncertain Roesser models. Second, the H ∞ performance of 2D Roesser models is studied under a general boundary condition. Third, an ILC design criterion is presented to achieve the perfect tracking and specified H ∞ performance by using linear matrix inequality approaches. Finally, a numerical example is given to illustrate the efficiency of the proposed ILC design method.

While iterative learning control (ILC) and repetitive control (RC) have much ground in common, they fundamentally differ in the initial conditions at each repetition. This difference has lead to distinct analysis techniques, hereby clouding the interrelations between both control strategies. To facilitate the transfer of results, this paper presents a unified approach to ILC and RC. Both control problems are formulated in the trial domain using so-called system lifting. For a given system, the corresponding ILC and RC trial-domain models differ, and a thorough system theoretic analysis and comparison of these models is performed. To illustrate the value of a unified formulation of ILC and RC, the analysis of the most commonly used ILC and RC structures is harmonized. This analysis reveals central differences and similarities between various stability, monotonic convergence and steady-state performance conditions.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

SummaryBatch process, working as a best choice for low‐volume and high‐value products in manufacturing, has been widely used in chemical industries. The actuator faults and time delays often occur in practical production. This paper develops an iterative learning control (ILC) design for a batch process described by two‐dimensional (2D) Roesser system with packet dropouts and time‐varying delays. The phenomenon of actuator faults is regarded as an arbitrary stochastic sequence satisfying the Bernoulli random binary distribution. Firstly, the ILC design for a batch process is transformed into stability analysis for a 2D stochastic system with time‐varying delays. Secondly, for analyzing the stability of 2D stochastic systems, we derive the stability condition in terms of linear matrix inequality. Then, we give a procedure to get the control gain for the ILC design. An injection modeling process as an example with simulations in different cases of data dropout is given to demonstrate the validity of the proposed method. Furthermore, the proposed method has a better result by comparing the existing methods.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

The piezoelectric micro-positioning platform(PMP) has advantages in high displacement resolution and fast response, however, the serious hysteresis nonlinearity in the PMP restricts its positioning accuracy. This paper presents a discretization of Krasnosel’skii-Pokrovskii model to describe the hysteresis nonlinearity of the PMP. Then, the density function is identified online by the adaptive linear neural network. To compensate the intrinsic hysteresis nonlinearity in the PMP, a feedforward compensation control method is implemented by an innovative iterative learning control algorithm. Moreover, a hybrid control method based on iterative learning and fractional order PID control is proposed to further improve the control accuracy. A series of comparative experiments are carried out to validate the feasibility and effectiveness of the proposed control method.

Method to improve convergence performance of iterative learning control systems with bounded noise

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.