Indirect Iterative Learning Control Research Articles

An Enhanced 2D-PID Adaptive Strategy for Batch Processes through Set-point-Tuning Indirect Iterative Learning Control

An Enhanced 2D-PID Adaptive Strategy for Batch Processes through Set-point-Tuning Indirect Iterative Learning Control

Data-Driven Indirect Iterative Learning Control.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

Cross-coupling indirect iterative learning control method for batch processes with time-varying uncertainties

For batch time-varying processeswith non-repetitive disturbances, a cross-coupling indirect iterative learning control (CC-iILC) is proposed. The set trajectory of the system on the single axis is accurately tracked by an indirect iterative learning control strategy with a PI controller for its time direction and a closed-loop feedback control strategy for the batch direction. Under the asymptotically stable condition of the two-dimensional (2D) dynamic model, the optimal control law is obtained by optimizing the H-infinity control function. To avoid the contour error during coupling, the cross-coupling technique is used to distribute the contour error to each axis for compensation. The stability condition of the indirect iterative learning controller is analyzed by a two-dimensional Fornasini-Marchesini (FM) batch dynamics model and two-dimensional robust H-infinity control theory. The feasibility and superiority of the proposed control method are verified by numerical simulation and experimental tests.

Repetitive process based indirect-type iterative learning control for batch processes with model uncertainty and input delay

This paper develops an indirect iterative learning control scheme for batch processes with time-varying uncertainties, input delay, and disturbances. In this paper, a predictor based on a state observer is designed to estimate the future state and to compensate for the input delay. Then a feedback controller based on the estimated state and the set-point error is used to track the specified reference trajectory, where, of the options available, a robust H∞ controller is designed in the presence of time-varying uncertainties and load disturbances. Then a proportional plus derivative type iterative learning control law is designed. An injection molding process model demonstrates the new method’s effectiveness, and a comparison with a direct-type design is given.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.

Indirect iterative learning control for robot manipulator with non‐Gaussian disturbances

In this study, a novel indirect iterative learning control (ILC) strategy is presented for a robotic manipulator that performs repeat operation and is also subjected to non-Gaussian disturbances. The performance index about the entropy of tracking error and the related optimisation method are used to update the local parameters of controller between any two adjacent batches. Moreover, the entropy is employed as it is a unified probabilistic measure of uncertainty quantification regardless whether the random disturbances are Gaussian distribution or not. Thus, an innovative performance index about tracking error entropy that represents the relationship between the entropy of error and controller gains is proposed in order to obtain the controller which can drive the uncertainty of output error as small as possible with the increase of the batch number. Then the non-linear stochastic optimal method is presented so as to obtain updated gains for the next batch. Stability of closed-loop system is analysed. Finally, a comparison between a classic ILC and the proposed approach is given. Moreover, the effectiveness and feasibility of the proposed control schemes is verified by some simulation results of robotic trajectory tracking.

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser's system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.

Advanced PI control with simple learning set-point design: Application on batch processes and robust stability analysis

According to the literature statistics, less than 10% of reported iterative learning control (ILC) methods are of the indirect form. Under an indirect ILC, the closed-loop system consists of two loops. Despite of the advantages in controller design and practical implementation, analysis on the corresponding system's stability and robustness becomes troublesome compared with the direct ILC methods. To address this open issue, a combination of PI control and ILC, referred to ILC-based PI control, is therefore developed in this study. Under the proposed ILC-based PI controller, the closed-loop system can be transformed into a 2-dimensional (2D) Roesser's system. Based on the 2D system formulation, a sufficient condition for robust asymptotical stability is first derived for multi-input multi-output linear batch processes. Correspondingly, an advanced PI control with ILC-based set-point is developed which requires smaller memory for operation together with less degree of freedom to design. Moreover, the proposed control algorithm can lead to superior steady-state tracking performance and good robustness against load disturbance and measurement noise, without requiring the internal state information of the process. Finally, the effectiveness and merits of the proposed method are illustrated by application to an injection molding process and a batch reactor, in comparison with a typical PI-type direct ILC method recently developed.

Optimal Structure of Learning-Type Set-Point in Various Set-Point-Related Indirect ILC Algorithms

Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology, Clear Water Bay,Kowloon, Hong KongABSTRACT: According to the literature statistics, only less than 10% of reported iterative learning control (ILC) methods havebeendevotedtotheindirectapproach.Motivatedbythefullpotentialofresearchopportunitiesinthisfield,anumberofstudiesonindirectILCwereproposedrecently,whereILC-basedP-typecontrolandlearning-typemodelpredictivecontrol(L-MPC)aretwosuccessfulstories.AllindirectILCalgorithmsconsistoftwoloops:anILCintheouterloopandalocalcontrollerintheinnerloop.Thelocalcontrollersare,respectively,aP-typecontrollerintheILC-basedP-typecontrolandamodelpredictivecontrol(MPC)inthe L-MPC. Logically, this leads to the question of what type of ILC should be chosen respectively for the two above-mentionedindirectILCmethods.Inthisstudy,P-typeILCandanticipatoryP-type(A-P-type)ILCarestudiedandcompared,becausetheyaretypical and widely implemented. Based on mathematical analysis and simulation test, it has been proved that the A-P-type ILCshouldbeusedintheILC-basedP-typecontrolandwhiletheP-typeILCshouldbeusedintheL-MPC.Furthermore,animprovedL-MPC with batch-varying learning gain was proposed to handle the trade-off between convergence rate and robustnessperformance. The simulation results on injection molding process and a nonlinear batch process validated the feasibility andeffectiveness of the proposed algorithm.1. INTRODUCTIONIntelligentmachinesincludingindustrialcomputerscanbeledfrom repeated trainingto reach superiorperformance of a speci-fied task. Scholars and engineers have therefore developediterative learning control (ILC) methods to formulate the learn-ingproceduresystematically.ILCwasfirstpresentedinJapanesein 1978

An Enhanced ILC-based PI Controller for Batch Processes

AbstractA novel combination of PI control and iterative learning control (ILC), referred to ILC-based PI control, is proposed in this study. This algorithm belongs to set-point-related (SPR) indirect ILC. Based on a 2-dimensional (2D) Roesser's system description, a sufficient condition for asymptotical stability of multi-input multi-output linear batch processes under the ILC-based PI controller was derived in this paper. Applications on injection packing pressure control show that the proposed method can achieve the design objective well, with performance improvement along both time and batch direction, and also owns good robustness to disturbances and measurement noises.

Indirect Iterative Learning Control for a Discrete Visual Servo Without a Camera-Robot Model

This paper presents a discrete learning controller for vision-guided robot trajectory imitation with no prior knowledge of the camera-robot model. A teacher demonstrates a desired movement in front of a camera, and then, the robot is tasked to replay it by repetitive tracking. The imitation procedure is considered as a discrete tracking control problem in the image plane, with an unknown and time-varying image Jacobian matrix. Instead of updating the control signal directly, as is usually done in iterative learning control (ILC), a series of neural networks are used to approximate the unknown Jacobian matrix around every sample point in the demonstrated trajectory, and the time-varying weights of local neural networks are identified through repetitive tracking, i.e., indirect ILC. This makes repetitive segmented training possible, and a segmented training strategy is presented to retain the training trajectories solely within the effective region for neural network approximation. However, a singularity problem may occur if an unmodified neural-network-based Jacobian estimation is used to calculate the robot end-effector velocity. A new weight modification algorithm is proposed which ensures invertibility of the estimation, thus circumventing the problem. Stability is further discussed, and the relationship between the approximation capability of the neural network and the tracking accuracy is obtained. Simulations and experiments are carried out to illustrate the validity of the proposed controller for trajectory imitation of robot manipulators with unknown time-varying Jacobian matrices.

INDIRECT ITERATIVE LEARNING CONTROL OF TAKAGI-SUGENO FUZZY SYSTEMS

An indirect iterative learning control is proposed to update the gains of a Parallel Distributed Compensation controller when the trajectory is repetitive. The corresponding Takagi-Sugeno fuzzy system, to be controlled, is supposed to exhibit time-varying matrices in the consequent part. When the membership functions are fixed, it will be possible to estimate the consequent system for every time, using different control gains for each trial. Finally, when the system parameters are considered as properly estimated, it will be possible to derive a controller which will not only be stable but will also exhibit good tracking properties.