Iterative Learning Control Law Research Articles

Iterative learning control approach for linear discrete time-varying systems with different initial time points

Different from the existing iterative learning control (ILC) works for dynamical systems with iteration-varying trial lengths, in which the terminal time points are not identical, this paper presents an ILC approach for linear discrete time-varying (LDTV) systems with different initial time points. A piecewise ILC law is designed by using the segment compensation techniques in time axis. Through a rigorous mathematical analysis, it is theoretically proved that as the mathematical expectation of the iterative initial state equals to the desired initial state, the ILC tracking error at the maximum universal time interval can be driven into a bounded region in mathematical expectation sense. Particularly, the mathematical expectation of the ILC tracking error at the maximum universal time interval can even be driven to zero under a certain initial state condition. Numerical simulations are provided to verify the effectiveness of the proposed ILC scheme.

Quantized iterative learning control of communication-constrained systems with encoding and decoding mechanism

In practical applications, due to the limited communication bandwidth, the network control systems (NCSs) are prone to data dropouts when the load is high. In this paper, the problem of quantized iterative learning control (ILC) based on encoding and decoding mechanism for such communication-constrained systems is studied. By combining the encoding and decoding mechanism with the uniform quantizer, the network burden and the impact of quantization error on the tracking performance of the systems are significantly mitigated. Meanwhile, data dropouts are represented as the Bernoulli random variable model, and an ILC law based on gradient is designed. When data dropouts occur, the signals maintain the value of the previous trial, otherwise the signals are updated. For this kind of learning framework, the asymptotic zero-error tracking performance has been rigorously proven for the uniform quantizer. To validate the proposed design, a joint motion of an industrial robot in the horizontal plane is simulated as an example.

Predictive State Observer-Based Set-Point Learning Control for Batch Manufacturing Processes With Delay Response

A predictive state observer (PSO) based iterative learning control (ILC) scheme is proposed for industrial batch manufacturing processes with delay response suffering from nonrepetitive uncertainties and disturbances. Combining with a delay-free output predictor, a PSO based feedback control structure is firstly presented to improve set-point tracking and disturbance rejection performance against nonrepetitive process uncertainties and disturbances for the initial batch run. Then an ILC law is introduced to update the closed-loop system set-point in order to improve the tracking performance from batch to batch. A delay-independent sufficient condition is established to ensure the convergence of output tracking error along the batch-direction, based on double-dynamic analysis. Moreover, another delay-dependent sufficient condition is constructed by linear matrix inequality to assess robust stability of the proposed two-dimensional control system along both the time- and batch-directions. Finally, an illustrative example and a real application to the batch temperature regulation of a 4-litre crystallizer are shown to validate the effect and advantage of the proposed ILC scheme.

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.

Experimental Validation of Iterative Learning Control for DC/DC Power Converters

In order to solve the problem that the parameters of traditional proportional–integral (PI) control are not easy to adjust, an iterative learning control (ILC) technique for a DC/DC power converter is proposed in this paper. Firstly, we have developed a system which is composed of two different states of DC/DC converter in order to obtain its equivalent linear time-varying system, and then the open-loop PD-type ILC law has been used to control it. Secondly, an experimental setup is arranged to verify and compare the simulated results. The experimental results show that, as compared with the traditional PI control, the proposed strategy is easy to implement and optimal with regard to debugging parameters, and it can achieve zero steady-state tracking errors without overshooting. Finally, the experimental results have also proven that our proposed scheme of iterative learning control for a DC/DC power converter is robust as compared to traditional PI control.

Iteration learning control for 2D linear discrete systems with randomly varying trail lengths

This paper considers the problem of randomly varying trial lengths of a class of two-dimensional (2D) linear systems represented by Roesser model, and two new iterative learning control (ILC) schemes are proposed. One is a conventional P-type control rule with a modified tracking error; the other is an ILC law with an iteration-average operator. Both learning control schemes are developed by a 2D stochastic variable to describe varying trial lengths. Under the Bernoulli distribution assumption and the initial state conditions, the convergence analysis is performed rigorously in the probability sense. Finally, illustrative examples have been provided to verify the theoretical results.

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

High-order model-free adaptive iterative learning control

In this paper, a high-order model-free adaptive iterative learning control (HOMFAILC) scheme is proposed for nonlinear non-affine discrete-time systems. The main feature of the proposed HOMFAILC is that not only the control input iterative learning law is designed with higher-order algorithms but also the parameter iterative adaptive updating law has the similar forms. Using additional control knowledge in both the iterative learning control law and the parameter estimation law, the control performance of the proposed HOMFAILC can be improved consequently. Furthermore, the similar structure in the control law and parameter updating law can also help to achieve a better control performance. The convergence is proved with rigorous mathematical analysis. Simulation study shows the effectiveness of the proposed HOMFAILC.

Frequency-Domain Based Iterative Learning Control for 2-D Discrete Systems

In the existing of traditional iterative learning control (ILC) results for two-dimensional (2-D) discrete systems with time-domain based analysis approach, fixed boundary states do not affect the complete convergence of P-type ILC law. However, it does affect the ILC convergence properties in the frequency domain. This paper first investigates the frequency-domain ILC tracking problem for 2-D discrete systems with different boundary states. An extended P-type ILC law is designed and a sufficient convergence condition of which can be derived through a rigorous mathematical proof. A simulation example is given to verify the effectiveness and validation of the proposed extended P-type ILC law. Finally, some comparison results on traditional P-type ILC law and D-type ILC law are presented.

Repetitive process based design of PD-type iterative learning control laws for batch processes with time-delays

This paper uses linear matrix inequality techniques and the Kalman-Yakubovich-Popov lemma to design an iterative learning control law for a class of batch processes with state delays. The design procedure is based on the stability theory for repetitive processes, a class of 2D systems. A numerical example illustrates the new design and demonstrates that the design has advantages compared to the existing alternatives.

Networked Iterative Learning Control Under Changing Operating Mode of Agents and Configuration of Information Network

The paper considers the iterative learning control (ILC) design problem of a network system under changing operating mode of subsystems (agents) and configuration of information network. The network system consists of identical agents, which are discrete linear dynamic plants operating in a repetitive mode. The operating modes of agents depend on their parameters and the reference trajectory, which must be tracked with required accuracy at output of system. The configurations of information network define the group of functioning agents and the type of information exchange between them. The mode and the configuration change takes place in accordance with certain external rules. The control design is based on the divergent method of the vector Lyapunov function. For reducing the transient error caused by the mode change and the connection of new agents, a special rule for switching the ILC law is proposed. The results of modeling the obtained control law for a group of manipulators with flexible link are presented.

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.

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

SummaryThis article first investigates robust iterative learning control (ILC) problem of a class of large‐scale interconnected systems, which consist of many subsystems described by two‐dimensional linear discrete first Fornasini–Marchesini systems with iteration‐dependent uncertainties arising from not only boundary states, disturbances, but also reference trajectory. A decentralized P‐type ILC law without any information exchanges with other subsystems is proposed such that the ultimate ILC tracking error of each subsystem can converge to a bounded range, the bound of which depends continuously on the bounds of all iteration‐dependent uncertainties considered. Especially, if these iteration‐dependent uncertainties are convergent progressively along the iteration direction, perfect ILC tracking on 2‐D reference trajectory can be obtained. Additionally, a modified ILC law with compensation technique is used to a class of large‐scale interconnected systems composed of many subsystems represented by two‐dimensional linear discrete second Fornasini–Marchesini systems. Two simulation examples are used to demonstrate the effectiveness and validity of the obtained ILC results. Finally, some comparative discussions are given.

Iterative Learning Control for Actuator Fault Uncertain Systems

An iterative learning fault-tolerant control method is designed for an actuator fault intermittent process with simultaneous uncertainties for the system parameters. First, an intermittent fault tolerance controller is designed using 2D system theory, and the iterative learning control (ILC) intermittent process is transformed into a 2D Roesser model. Secondly, sufficient conditions for the controller’s existence are analyzed using the linear matrix inequality (LMI) technique, and the control gain matrices are obtained by convex optimization with LMI constraints. Under these conditions for all additive uncertainties for the system parameters and admissible failures, the controller can ensure closed-loop fault-tolerant performance in both the time and batch directions, and it can also meet the H∞ robust performance level against outside disturbances. Eventually, the algorithm’s computational complexity is analyzed, and the effectiveness of the algorithm is verified by simulation with respect to an injection molding machine model. Compared with traditional ILC laws, which do not consider actuator faults, the proposed algorithm has a better convergence speed and stability when the time-invariant and time-variant actuator faults occur during implementation.

AILC for Rigid-Flexible Coupled Manipulator System in Three-Dimensional Space with Time-Varying Disturbances and Input Constraints

In this paper, an adaptive iterative learning control (AILC) law is developed for two-link rigid-flexible coupled manipulator system in three-dimensional (3D) space with time-varying disturbances and input constraints. Based on the Hamilton’s principle, a dynamic model of a manipulator system is established. The conditional equation that is coupled by ordinary differential equations and partial differential equations is derived. In order to achieve high-precision tracking of the revolving angles and vibration suppression of the elastic part, the iterative learning control law based on the disturbance observer is considered in the process of the design controller. The composite Lyapunov energy function is proposed to prove that the angle errors and elastic deformation can eventually converge to zero with the increase of the number of iterations. Ultimately, the simulation results to rigid-flexible coupled manipulator system are given to prove the convergence of the control objectives under the adaptive iterative learning control law.

Practical design of a time-varying iterative learning control law using fuzzy logic

Iterative Learning Control (ILC) is an intelligent control algorithm that can effectively handle a tracking error in any system that operates in a repetitive manner. In practice, it is hardly possible to implement a single gain learning control law to improve the tracking performance due to the existence of large transient growth. To prevent the growth, this paper proposes a time-varying learning control design using the unique concept of fuzzy logic control to track the desired trajectory as well as the desired control input signal. The proposed control design is developed on both serial and parallel ILC configurations. The two configurations are initially constructed and implemented on a robotic manipulator with the use of a single gain learning control law. To avoid bad transients, the gain adjustment mechanism based on fuzzy logic control is introduced to vary the learning gain in each time step for enhancing the robustness of the system. According to the simulation and experiment on a robotic manipulator, both ILC structures with the proposed mechanism achieve the desired learning performance without bad transients.

A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems.

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.

A Fuzzy System Based Iterative Learning Control for Nonlinear Discrete-Time Systems with Iteration-Varying Uncertainties

In this paper, we consider an iterative learning control problem for a class of unknown discrete-time nonlinear systems with iteration-varying initial error, iteration-varying system parameters, iteration-varying external disturbance, iteration-varying desired output, and iteration-varying control direction. These iteration-varying uncertainties are not required to take any particular structure such as the high-order internal model and only need to satisfy certain boundedness conditions. We propose an iterative learning control law with an adaptive iteration-varying fuzzy system to overcome all the uncertainties and achieve the learning control objective. Furthermore, we present a sufficient condition for designing adaptive gains and prove the convergence of the learning error to a small value as the trial number is large enough. Finally, we use two simulation examples to demonstrate all the theoretical results.

A Novel Fast Iterative Learning Control for Linear Discrete Systems with Parametric Disturbance and Measurement Noise

Precise industrial control technology is constantly in need of accurate and strong control. Error convergence for a typical linear system is very minimal when using a conventional iterative learning control strategy. This study develops a quick iterative learning control law to address this issue. We have presented a new PD iterative learning control approach which is basically grounded on backward error and control parameter rectification for a class of linear discrete time-invariant (LDTI) systems. We have deliberated the repetitive system, which has constraint disturbance and measurement noise. First, we have developed a form of the faster learning law along with a full explanation of the algorithm’s control factor generation process. And then, using the vector method in conjunction with the theory of spectral radius, sufficient conditions for the algorithm’s convergence are introduced for parameter estimation with no noise, parameter uncertainty but excluding the noise, parameter uncertainty with small perturbations, and noise in four different scenarios. Eventually, results show that convergence depends on the control law’s learning factor, the correction term, the factor of association, and the learning interval. Ultimately, the simulation results indicate that suggested approach has a faster error convergence as compared with classical PD algorithm.

Data-driven adaptive tuning of iterative learning control

In this paper, we propose two data-driven adaptive tuning (DDAT) approaches of iterative learning control (ILC) for nonlinear non-affine systems. First, a compact-form iterative dynamic linearization (CFIDL) method is introduced to transfer the original nonlinear system into a linear data model. Then, we design an objective function for the tuning of the learning gains of a PD-type ILC law. By optimizing the designed cost function subjected to the linear data model, a CFIDL-based DDAT method is proposed, where only the real I/O data are used without requiring any mechanistic model information. Furthermore, the results are extended by introducing a partial-form iterative dynamic linearization (PFIDL) method for the purpose of utilizing more additional control information. Following the similar steps, a PFIDL-based DDAT method is developed for learning gain tuning of the PD-type ILC scheme. Both the proposed DDAT methods can help the PD-type ILC have a better robustness against to the uncertainties since they can use the real I/O data to iteratively tune the learning gains. The convergence of the DDAT-based PD-type ILC methods has been proved rigorously. The effectiveness of the two proposed DDAT-based ILC methods are further verified through simulations.