Proposed Iterative Learning Control Method Research Articles

Frequency‐domain‐based iterative learning control utilizing n‐best adaptive Fourier decomposition for nonrepetitive unknown iteration‐independent and iteration‐varying discrete time‐delay systems

AbstractThe bulk of well‐known control techniques for time‐delay systems are sensitive to the system's uncertainty. For unknown nonrepetitive iteration‐independent and iteration‐varying linear discrete time‐delay (LDTD) systems, an iterative learning control (ILC) design with a frequency domain identification technique is devised. The proposed ILC method is based on a novel n‐best adaptive Fourier decomposition (n‐BAFD) approach for approximating the unknown time‐delay transfer function. An extended anticipatory ILC law is developed that uses anticipatory time to compensate for both iteration‐independent and iteration‐varying time delays in the frequency domain for unknown nonrepetitive LDTD systems. Three examples are used to validate the proposed frequency‐domain‐based ILC method.

Kernel-based Regularized Iterative Learning Control of Repetitive Linear Time-varying Systems

Abstract The selections for the model orders and the number of controller parameters have not been discussed for many data-driven iterative learning control (ILC) methods. If they are not chosen carefully, the estimated model and designed controller will lead to either large variance or large bias. In this paper we try to use the kernel-based regularization method (KRM) to handle the model estimation problem and the controller design problem for unknown repetitive linear time-varying systems. In particular, we have used the diagonal correlated kernel and the marginal likelihood maximization method for the two problems. Numerical simulation results show that smaller mean square errors for each time instant are obtained by using the proposed ILC method in comparison with an existing data-driven ILC approach.

Robust iterative learning control design for linear systems with time-varying delays and packet dropouts

This paper proposes the robust iterative learning control (ILC) design for uncertain linear systems with time-varying delays and random packet dropouts. The packet dropout is modeled by an arbitrary stochastic sequence satisfying the Bernoulli binary distribution, which renders the ILC system to be stochastic instead of a deterministic one. The main idea of this paper is to transform the ILC design into robust stability for a two-dimensional (2D) stochastic system described by the Roesser model with a delay varying in a range. A delay-dependent stability condition, which can guarantee mean-square asymptotic stability of such a 2D stochastic system, is derived in terms of linear matrix inequalities (LMIs), and formulas can be given for the ILC law design. An example for the injection molding is given to demonstrate the effectiveness of the proposed ILC method.

Robust PI based set-point learning control for batch processes subject to time-varying uncertainties and load disturbance

Based on the proportional-integral (PI) closed-loop control widely used in industrial engineering practice, a robust iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties and load disturbance. An important merit is that the proposed ILC design is independent of the PI tuning which maintains the closed-loop system stability, owing to that the ILC updating law is implemented through adjusting the set-point of the closed-loop system and adding a feedforward control signal to the plant input along the batch-to-batch direction. Using the robust H infinity control objective, a robust discrete-time PI tuning algorithm is given in terms of the plant state-space model description with norm-bounded time-varying uncertainties. For the batch-to-batch direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory, which is capable of perfect output tracking against repetitive type load disturbance. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method.

State-Constrained Iterative Learning Control for a Class Of MIMO Systems

In this note, we present a novel iterative learning control (ILC) method for a class of state-constrained multi-input multi-output (MIMO) nonlinear system under state alignment condition with both parametric and nonparametric uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. Barrier Composite Energy Function (BCEF) scheme with a novel Barrier Lyapunov Function is proposed to facilitate the analysis of state tracking error convergence while satisfying the state constraints. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC method.

Robust iterative learning control with rectifying action for nonlinear discrete time-delayed systems

This paper addresses the two-dimensional (2-D) linear inequalities based robust Iterative Learning Control (ILC) for nonlinear discrete systems with time delays. The proposed two-gain ILC rule has a rectifying action to iterative initial error and external disturbances. It guarantees a reduced bound of the ILC tracking error against the iteration-varying initial error and disturbances. For the iteration-invariant initial error and disturbances, the ILC tracking error can be driven to convergence, and a complete tracking to reference trajectory beyond the initial time point is even achieved as the control gain is specifically selected. An example is used to validate the proposed ILC method.

A synthetic approach for robust constrained iterative learning control of piecewise affine batch processes

For industrial nonlinear batch processes that can be practically divided into a series of piecewise affine operating regions, a two-dimensional (2D) closed-loop iterative learning control (ILC) method is proposed for robust tracking of the set-point profile against cycle-to-cycle process uncertainties and load disturbances. Both state feedback and output feedback are considered for the control design, together with the process input and output constraints for implementation. Based on a 2D system description for the batch operation, a few synthetic performance and robust control objectives are proposed for developing the 2D ILC schemes, in combination with the 2D Lyapunov–Krasovskii functions that can guarantee monotonic state energy (or output error) decrease in both the time (during a cycle) and batch (from cycle to cycle) directions. Both the polyhedral and norm-bounded descriptions of process uncertainties are considered to derive the corresponding linear matrix inequality (LMI) conditions for the closed-loop ILC system robust stability. An important merit of these LMI conditions is that there are adjustable convergence indices prescribed for both the time and batch directions, and an adjustable robust control performance level for the closed-loop system. By specifying/optimizing these adjustable parameters to solve these LMI conditions, the 2D ILC controller can be explicitly derived for implementation. The application to a highly nonlinear continuous stirred tank reactor (CSTR) is shown to illustrate the effectiveness and merits of the proposed ILC method.

Flexible Closed-Loop Iterative Learning Control for Industrial Batch Processes With State Delay and Time-Varying Uncertainties

A robust closed-loop iterative learning control (ILC) method is proposed for industrial batch processes with state delay and time-varying uncertainties from cycle to cycle. Based on a two-dimensional (2D) system description of such a batch process, a closed-loop ILC scheme consisting of dynamic output feedback plus feedforward control is established to realize robust tracking of the setpoint trajectory in both the time (during a cycle) and batch (from cycle to cycle) directions. Only measured output errors of current and previous cycles are used for control design to facilitate practical implementation. A flexible 2D difference Lyapunov function that guarantees monotonical state energy decrease in both the time and batch directions is introduced to establish a sufficient condition in terms of the linear matrix inequality (LMI) for holding robust stability of the closed-loop ILC system. Correspondingly, the ILC controller can be explicitly formulated, together with an adjustable robust H infinity performance level. An illustrative example is given to demonstrate effectiveness and merits of the proposed ILC method.

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

AbstractBased on a two-dimensional (2D) system description of a batch process, a robust closed-loop iterative learning control (ILC) scheme is proposed for batch processes with time-varying uncertainties. An important merit is that the proposed ILC method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of the setpoint trajectory in both the time (during a cycle) and batchwise (from cycle to cycle) directions. Only measured output errors of the current and previous cycles are used to design a synthetic ILC controller consisting of dynamic output feedback plus feedforward control. By introducing a comprehensive 2D difference Lyapunov function that can lead to monotonical state energy decrease in both the time and batchwise directions, sufficient conditions are established in terms of linear matrix inequality (LMI) constraints for holding robust stability of the closed-loop ILC system. By solving these LMI constraints, the ILC controller is explicitly formulated, together with an adjustable robust H infinity performance level. An illustrative example is given to demonstrate effectiveness and merits of the proposed ILC method.

Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties

Based on a two-dimensional (2D) system description of a batch process in industry, a robust closed-loop iterative learning control (ILC) scheme is proposed for batch processes with state delay and time-varying uncertainties. An important merit is that the proposed ILC method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of setpoint trajectory in both the time (during a cycle) and batchwise (from cycle to cycle) directions. Only measured output errors of current and previous cycles are used to design a synthetic ILC controller consisting of dynamic output feedback plus feedforward control, for the convenience of implementation. By introducing a comprehensive 2D difference Lyapunov function that can lead to monotonical state energy decrease in both the time and batchwise directions, sufficient conditions are established in terms of linear matrix inequality (LMI) constraints for holding robust stability of the closed-loop ILC system. By solving these LMI constraints, the ILC controller is explicitly formulated, together with an adjustable robust H infinity performance level. An illustrative example of injection molding is given to demonstrate effectiveness and merits of the proposed ILC method.

ILC-based model reference neuro-adaptive technique for stochastic distribution control

The stochastic distribution control is important for certain industrial applications and cases where non-Gaussian noises exist. The problem has been initially solved by controlling the dynamical system formed by neural networks which approximate the output probability density function (PDF). Also, a modified version of iterative learning control (ILC) has been previously introduced by the authors to solve the output PDF shaping problem for linear weight dynamical systems. Looking into unknown non-linear weight dynamics, this paper presents a model reference neuro-adaptive control (MRNAC) approach for PDF shaping in non-Gaussian stochastic systems. The method is based on ILC and employs a neural network framework for modelling and controller. The time domain is first split up to batches. Then the proposed ILC method is implemented in two main domains namely within each batch and between any two adjacent batches. The design is carried out in three stages: a) NN-based non-linear dynamic system identification; b) MRNAC of the weight control loop within each batch; c) tuning the NN centres and widths between any two adjacent batches. Simulations confirm the effectiveness of the method.

Iterative learning control for a class of nonlinear discrete-time systems with multiple input delays

This article, addresses the robust iterative learning control (ILC) problem for nonlinear discrete time-delay systems. The derivation of convergence and robustness for the proposed ILC rule is based on two-dimensional (2D) linear inequalities. For a class of nonlinear discrete-time systems with multiple input delays, it is shown that the ILC tracking errors are bounded in the presence of state, output disturbances and initial state uncertainty. As these disturbances and uncertainty satisfy required conditions, the ILC tracking errors even can be driven to zero. Two numerical examples are used to validate the proposed ILC method.

An iterative learning control based identification for a class of MIMO continuous-time systems in the presence of fixed input disturbances and measurement noises

This article presents an identification method based on an iterative learning control (ILC) for a class of linear MIMO (multi-input, multi-output) continuous-time systems with unknown but fixed input disturbances. For this purpose, a formula of a specific type of ILC which updates the input in an appropriate parameter space is extended to the case of MIMO systems with fixed disturbances. Then a concrete procedure to construct such an ILC is given to apply the ILC to the continuous-time system identification. Finally, numerical examples demonstrate how the parameter estimation can be achieved through the proposed ILC method in the presence of heavy measurement noises.

Noise Tolerant Iterative Learning Control and Identification for Continuous-Time Systems With Unknown Bounded Input Disturbances

This paper considers the problems of both noise tolerant iterative learning control (ILC) and iterative identification for a class of continuous-time systems with unknown bounded input disturbance and measurement noise. To this aim, we first propose a formulation of an extended ILC scheme using sampled input∕output (I∕O) data. The proposed ILC method has distinctive features as follows. Its learning law works in a prescribed finite-dimensional parameter space and employs I∕O data of all past trials efficiently. Also, the time derivative of tracking error is not required. Then, it is presented how the uncertain parameters can be identified by using the proposed ILC algorithm and how robust it is against measurement noise through a numerical example. Furthermore, its experimental evaluation is performed to demonstrate the effectiveness of the proposed identification scheme.

NOISE TOLERANT IDENTIFICATION OF CONTINUOUS-TIME SYSTEMS WITH UNKNOWN CONSTANT INPUT DISTURBANCE USING ILC METHOD

This paper considers the problem of noise tolerant identification of a class of continuous-time systems with unknown constant-input disturbance. To this aim, we first propose an extended formulation of identification method using iterative learning control (ILC) scheme based on sampled I/O data in the presence of measurement noise. The proposed ILC method has distinctive features as follows. Its learning law works in the prescribed finite dimensional parameter space and employs I/O data of all past trials efficiently. Also the time-derivative of tracking error is not required. Then, it is presented how the parameter estimation can be achieved by the proposed ILC method and how robust it is against measurement noise through numerical examples.

An iterative learning control method and mathematical model for robotic manipulation at undesired locations

This paper presents an iterative learning control (ILC) strategy for a robotic manipulator when objects have to be picked up at undesired locations. The proposed ILC method can ensure that a robotic manipulator achieves its task in real time following a predetermined number of control steps. The paper has provided a robotic control strategy and mathematical formulae for the implementation of a proactive assurance control. The proactive assurance control can improve the quality of production in terms of maintaining the production workflow as a fixed value at all times, even though the components to be assembled are not in their desired locations. This can accelerate the production process owing to the possibility of eliminating the task of mounting the components at their exact locations.