Robustness against model uncertainties of norm optimal iterative learning control

Designing an optimal iterative learning control is a huge challenge for linear and nonlinear dynamic systems. For such complex systems, standard Norm optimal iterative learning control (NOILC) is an important consideration. This paper presents a novel NOILC error convergence technique for a discrete-time method. The primary effort of the controller is to converge the error efficiently and quickly in an optimally successful way. A new iterative learning algorithm based on feedback based on reliability against input disruption was proposed in this paper. The illustration of the simulations authenticates the process suggested. The numerical example simulated on MATLAB@2019 and the mollified results affirm the validation of the designed algorithm.

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.

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

The injection stretch blow moulding (ISBM) process is widely used to manufacture plastic bottles for the beverage and consumer goods industry. The majority of the production processes are open-loop systems, often suffering from high raw material and energy waste. In this paper, a heuristic based norm-optimal terminal iterative learning control (ILC) method is proposed to control the preform temperature profiles in the reheating process. The reheating process is a batch process, and ILC can achieve improved tracking performance in a fixed time interval. The terminal ILC (TILC) is a useful strategy when only the terminal temperature profile can be measured in a batch process like the preform reheating in ISBM. To balance the control performance and energy cost, a norm-optimal method is applied, leading to a proposal of the new norm-optimal TILC method in this paper. Heuristic methods including the swarm optimisation (PSO), differential evolution (DE) and teaching-learning based optimization (TLBO) are used to calculate the sequence of norm-optimal control inputs for this non-linear batch process. Simulation results confirm the efficacy of the proposed control strategy.

Iterative learning control (ILC) is applicable to systems that are required to repeatedly track a desired trajectory of finite duration. Norm-optimal ILC can be characterised as a combined feedforward and feedback learning approach, where the tracking error from the previous trial and the tracking error of the current trial are employed to reduce the tracking error from trial to trial. In this paper, a high speed rack feeder typically used in automated warehouses is considered, which represents a flexible beam structure with a vertically moving mass. Due to kinematic constraints such as a maximum velocity and a maximum acceleration, standard ILC is not applicable if the desired trajectory violates these constraints. One possible solution would be an offline trajectory planning subject to the given kinematic constraints. This paper, however, addresses modifications of the ILC algorithm itself to cope with infeasible trajectories. Two alternative algorithms are given for this purpose and compared with each other in experiments on a test rig that replicates the dynamics of a high speed rack feeder.

In this paper, we consider the norm-optimal iterative learning control (NO-ILC) framework and study its robust monotonic convergence (RMC) against model uncertainties in single-input-single-output linear time-invariant systems. Modeling errors in general degrade the convergence performance of NO-ILC, and hence ensuring RMC against model uncertainties is important. Although the robustness of NO-ILC has been studied in the literature, determining the allowable range of modeling errors for a given NO-ILC design is still an open research question. To fill this gap, a frequency-domain analysis with a multiplicity formulation of model uncertainty is developed in this paper to quantify and visualize the allowable modeling errors. Compared with the traditional formulation, the proposed new uncertainty formulation provides a less conservative representation of the allowable model uncertainty range by taking additional phase information into account and thus allows for a more complete evaluation of the robustness of NO-ILC. The analysis also clarifies how the RMC region changes as a function of NO-ILC weighting parameters and therefore can be used as a frequency-domain design tool to achieve RMC for given model uncertainties. Simulation examples are given to confirm the theoretical conclusions and demonstrate the utility of the developed analysis.

In this paper we present an approach to deal with trial-varying initial conditions in norm-optimal iterative learning control (ILC). Varying initial conditions generally degrade the performance of conventional learning algorithms. We therefore introduce a worst-case optimization problem that accounts for trial-varying of initial conditions. The optimization is then reformulated as a convex minimization problem, which can be solved efficiently to generate the control signal. We investigate the relationship between the proposed approach and classical norm-optimal ILC; where we find that our methodology is equivalent to classical norm-optimal ILC with trial-varying parameters. Finally, simulation results of the presented technique are given.

Iterative Learning Control of a Left Ventricular Assist Device

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.

Newton-method based iterative learning control method for nonlinear systems

STABILITY ANALYSIS OF ITERATIVE LEARNING CONTROL SYSTEM WITH INTERVAL UNCERTAINTY

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.

Since they were first introduced by Arimoto, iterative learning control (ILC) methods have received lots of attention because of their effectiveness and briefness. In this paper, an open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common, as in other ILC research papers on the convergence problem, sufficient conditions for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for a similar ILC scheme.

A coordinate descent approach to optimal tracking time allocation in point-to-point ILC

The classical problem setup of iterative learning control (ILC) is to enforce tracking of a reference profile specified at all time points in the fixed task duration. The removal of the time specification releases significant design freedom in how the path is followed but has not been fully exploited in the literature. This article unlocks this extra design freedom by formulating the ILC task description to handle repeated path-following tasks, e.g., welding and laser cutting, which aim at following a given “spatial” path defined in the output space without any temporal information. The general ILC problem is reformulated for ILC design with the inclusion of an additional performance index, and the class of piecewise linear paths is characterized for the reformulated problem setup. A two-stage design framework is proposed to solve the characterized problem and yields a comprehensive algorithm based on an ILC update and a gradient projection update. This algorithm is verified on a gantry robot experimental platform to demonstrate its practical efficacy and robustness against model uncertainty.