Iterative Learning Control Technique Research Articles

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

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.

Development of an ILC controller for the Droplet-on-Demand generation system

The droplet-on-demand systems have been increasingly attracting attention from many research groups. The droplet-on- demand system is a promising platform for many biochemical applications, especially for drug delivery applications, where the matter quantity requires very high accuracy, in microliter- scale or even in nanoliter-scale, for enhancing the efficiency, reducing the toxicity as well as the adverse effects of medicines. In order to generate microdroplets, microfluidic technology is emerged as one of the most effective methods. In this paper, we propose a droplet-on-demand generation system based on the Y-junction microfluidic structure with the generated droplet sizes are adjusted by iterative learning control (ILC) technique. The ILC controller can modify the current control input based on the error information measured during earlier experimental procedures, resulting in the desired droplet size in the proposed Y-junction microfluidic channel. The effectiveness of the ILC method was validated by experiments. The obtained results show that the proposed system can generate the required droplet size after 6 to 7 iterations. The results also prove the potential of integrating the ILC technique in the microdroplet generation system. The propose system can be extended to apply in the drug delivery systems for patients in hospitals or chemical mixing systems.

Performance evaluation of iterative learning control with different sliding mode algorithms for the slip‐ratio control of an electric vehicle

AbstractDeveloping a control strategy that can handle model uncertainties, external disturbances, and parameter fluctuations is essential for the desired operation of a nonlinear system. An attempt is made to develop such a control algorithm using the Learning Variable Structure Control technique. The proposed controllers have the advantages of both iterative learning control (ILC) and sliding mode control (SMC) such that they can compensate both structured and unstructured uncertainties. They are made comprised of modified‐twisting algorithm and super‐twisting algorithm respectively with the ILC technique. In this article, the performance of the two developed controllers is compared to a traditional SMC‐based ILC approach. Based on simulation results, the super‐twisting algorithm based ILC is found to be superior with reference to speed of convergence and tracking accuracy. This method is used to control the slip‐ratio of an electric vehicle as a specific application in this paper.

Control of batch pulping process using data-driven constrained iterative learning control

Kraft pulping uses steam and chemicals to convert wood chips to pulp, used for production of paper, textile fiber or other cellulosic materials, in large batch or continuous digesters. Batch digesters owe their widespread use to lower capex as well as flexibility of operation that can easily accommodate changes in feedstock or product grades. However, control of batch pulping process is challenging since wood is a naturally-occurring reactant. Moreover, lack of real-time measurements of key performance indicator such as Kappa number and lack of high-fidelity models make the batch control difficult to implement. One solution consists of using run-to-run control that uses offline laboratory measurements to provide a recipe for the upcoming batch. In this work, a first-principles dynamic model is developed for manufacture of dissolving pulp for textile fiber from wood. Subsequently, a data-driven constrained Iterative learning control (cILC) technique is explored for Kappa number control via manipulation of recirculation liquor temperature. Data-driven cILC uses a linear time varying model of the batch pulping process that is developed and updated from historical data. Constraints are imposed on batch-to-batch change in the inputs to prevent sharp fluctuations of the process state and output variables between batches. The data-driven cILC solves a multivariable linear regression followed by a quadratic program to generate a batch recipe for the next run. Three case studies are presented to evaluate performances for target Kappa tracking, and deterministic and stochastic uncertainty handling. The results demonstrate that data-driven cILC is effective in control of the pulp digester, even in presence of uncertainties, without the need for expensive real-time measurements.

Iterative learning algorithms for boundary tracing problems of nonlinear fractional diffusion equations

<abstract><p>In this paper, the iterative learning control technique is extended to distributed parameter systems governed by nonlinear fractional diffusion equations. Based on $ P $-type and $ PI^{\theta} $-type iterative learning control methods, sufficient conditions for the convergences of systems are given. Finally, numerical examples are presented to illustrate the efficiency of the proposed iterative schemes. The numerical results show that the closed-loop iterative learning control scheme converges faster than the open-loop iterative learning control scheme and the $ PI^{\theta} $-type iterative learning control scheme converges faster than the $ P $-type and the $ PI $-type iterative learning control scheme.</p></abstract>

A Novel Predefined Time PD-Type ILC Paradigm for Nonlinear Systems

Intelligent robotics has drawn a great deal of attention due to its high precision, stability, and reliability, which are the basic key factors for industrial automation. This paper proposes an iterative learning control (ILC) technique with predefined-time convergence as a solution to an applied engineering problem, namely, that local time cannot be preset when a second-order nonlinear system undertakes control of the accurate tracking of local time under any initial iterative value. A time-varying sliding surface with an initial value of zero was designed, and it was theoretically proven that the trajectory tracking error in the sliding surface could converge to zero within a predefined time. The iterative control problem of trajectory tracking was thus changed to an iterative control problem of time-varying sliding-mode surface tracing with a starting value of zero. A PD-type closed-loop ILC with a time-varying sliding mode surface was designed such that the trajectory tracking error converged and stabilized on the sliding mode surface after a finite number of learning iterations. The control goal for the system’s output was the ability to track the desired trajectory accurately within a predefined time interval, and it was achieved by combining this with the predefined time convergence characteristics of the time-varying sliding mode surface. Numerical simulation of trajectory tracking control of a repetitive motion manipulator was used to verify the effectiveness of the proposed controller and its robustness in the face of external disturbances.

Batch-to-Batch Adaptive Iterative Learning Control-Explicit Model Predictive Control Two-Tier Framework for the Control of Batch Transesterification Process.

To harness energy security and reduce carbon emissions, humankind is trying to switch toward renewable energy resources. To this extent, fatty acid methyl esters, also known as biodiesel, are popularly used as a green fuel. Fatty acid methyl esters can be produced by a batch transesterification reaction between vegetable oil and alcohol. Being a batch process, fatty acid methyl esters production is beset with issues such as uncertainties and unsteady state behavior, and therefore, adequate process control measures are necessitated. In this study, we have proposed a novel two-tier framework for the control of the fatty acid methyl esters production process. The proposed approach combines the constrained batch-to-batch iterative learning control technique and explicit model predictive control to obtain the desired concentration of the fatty acid methyl esters. In particular, the batch-to-batch iterative learning control technique is used to generate reactor temperature set-points, which is further utilized to obtain an optimal coolant flow rate by solving a quadratic objective cost function, with the help of explicit model predictive control. Our simulation results indicate that the fatty acid methyl esters concentration trajectory converges to the desired batch trajectory within four batches for uncertainty in activation energy and six batches for uncertainty in both inlet concentration of triglyceride and in activation energy even in the presence of process disturbances. The proposed approach was compared to the heuristic-based approach and constraint iterative learning control approach to showcase its efficacy.

A Robust Iterative Learning Control Technique to Efficiently Mitigate Disturbances for Three-Phase Standalone Inverters

This article investigates a robust iterative learning control (ILC) technique that effectively rejects the influence of periodic and nonperiodic disturbances for a three-phase constant-voltage constant-frequency standalone voltage source inverter (VSI) with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter under variable initial states. In conventional ILC, the learning dynamics are more complex when the initial iterative state is different at each iteration due to the fixed initial state value. Unlike conventional ILC, the proposed ILC follows a transformed dynamic model for robust learning rule convergence that is less restricted under varying initial states and significantly eliminates the impact of periodic and nonperiodic disturbances. Moreover, a simplified stability analysis is provided, and the conditions required for robust learning rule convergence are discussed. A comparative verification with the results of conventional ILC using a TI TMS320F28335 digital signal processor based prototype standalone VSI proves that the proposed ILC technique offers robust and effective steady-state performance, with benefits such as reduced steady-state errors and low total harmonic distortion under periodic disturbances. Finally, its improved robustness and fast transient-state performance are validated under nonperiodic disturbances due to the existence of tough load conditions, i.e., step-changes of linear, unbalanced, and nonlinear loads with significantly distorted model parameters.

가속센서 데이터 기반 반복 학습 제어 적용 디스플레이 패널 이송 로봇 경로 오차 보상에 대한 연구

Transfer robots for large-sized panels used in the display industry need to compensate for path error and reduce vibration. The iterative learning control (ILC) technique can simply compensate for the uncertainty of a control system in a repetitive motion. This study introduces an ILC compensation system applied with an accelerometer to a display panel transfer robot control system. The ILC technique was used to reduce the path error and vibration induced the flexibility of the large size robot. This method was applied to a robot system without the system model of the mechanical and measurement elements. To improve the iterative learning performance through the accelerometer, the ILC is configured by applying an acceleration element and time shift method to the PD-Offline ILC algorithm. In addition, based on the characteristics of repetitive motion, the ILC derives an acceleration data-based position estimation value. In this study, the ILC system and a large-sized panel transfer robot were implemented in MATLAB-Simulink with RECURDYN. The path errors and vibration level of the robot with a suggested ILC of 20 repeated learnings were reduced by more than 90%.

Barrier Adaptive Iterative Learning Control for Tank Gun Control Systems Under Nonzero Initial Error Condition

In this paper, a barrier adaptive iterative learning control scheme is proposed to solve the trajectory-tracking problem for tank gun control systems under nonzero initial error condition. A novel construction method of rectified reference trajectory is presented for dealing with the initial position problem of iterative learning control for tank gun control systems. With a quadratic form barrier Lyapunov function adopted to controller design, the quadratic form of system error is constrained within the preset range during each iteration. Adaptive iterative learning control technique and robust control technique are jointly used to compensate for the parametric/nonparametric uncertainties and nonsymmetric deadzone nonlinearity. As the iteration number increases, the system state of tank gun control systems may accurately track the rectified reference trajectory, which leads to a excellent tracking performance during the part operation interval of tank gun control systems. Simulation results are presented to verify the effectiveness of the proposed barrier adaptive iterative control scheme.

Application of a modified iterative learning control algorithm for superconducting radio-frequency cavities

Transient beam loading, which causes cavity gradient fluctuation, is becoming a major concern for the stable operation of the high current superconducting radio-frequency (SRF) accelerators. Iterative learning control (ILC) is an effective algorithm aiming to improve systems operated in repetitive mode. This ILC technique was successfully introduced to the low-level radio-frequency (LLRF) control in accelerators to compensate for the field fluctuation caused by repetitively pulsed beam. The modern LLRF system prefers to use the FPGA-based hardware platform to realize a real-time control framework. However, considering the algorithm complexity and the hardware cost, the ILC algorithm is usually implemented outside FPGA. This practice would decrease the real-time ability of the control system. In this paper, we present a modified ILC algorithm that can be implemented inside FPGA. The key idea of our method is to simplify the beam profile using a rectangular pulse. The method was demonstrated in the SRF cavities at Chinese Accelerator driven system Front-end demo SRF linac (CAFe). The experimental results in the CAFe beam-commissioning confirmed that the beam-induced gradient fluctuation is successfully suppressed.

Iterative learning control with discrete‐time nonlinear nonminimum phase models via stable inversion

AbstractOutput reference tracking can be improved by iteratively learning from past data to inform the design of feedforward control inputs for subsequent tracking attempts. This process is called iterative learning control (ILC). This article develops a method to apply ILC to systems with nonlinear discrete‐time dynamical models with unstable inverses (i.e., discrete‐time nonlinear nonminimum phase models). This class of systems includes piezoactuators, electric power converters, and manipulators with flexible links, which may be found in nanopositioning stages, rolling mills, and robotic arms, respectively. As these devices may be required to execute fine transient reference tracking tasks repetitively in contexts such as manufacturing, they may benefit from ILC. Specifically, this article facilitates ILC of such systems by presenting a new ILC synthesis framework that allows combination of the principles of Newton's root finding algorithm with stable inversion, a technique for generating stable trajectories from unstable models. The new framework, called invert‐linearize ILC (ILILC), is validated in simulation on a cart‐and‐pendulum system with model error, process noise, and measurement noise. Where preexisting Newton‐based ILC diverges, ILILC with stable inversion converges, and does so in less than one third the number of trials necessary for the convergence of a gradient‐descent‐based ILC technique used as a benchmark.

Support vector machine and its difficulties from control field of view

The application of the support vector machine (SVM) classification algorithm to large-scale datasets is limited due to its use of a large number of support vectors and dependency of its performance on its kernel parameter. In this paper, SVM is redefined as a control system and iterative learning control (ILC) method is used to optimize SVM’s kernel parameter. The ILC technique first defines an error equation and then iteratively updates the kernel function and its regularization parameter using the training error and the previous state of the system. The closed loop structure of the proposed algorithm increases the robustness of the technique to uncertainty and improves its convergence speed. Experimental results were generated using nine standard benchmark datasets covering a wide range of applications. Experimental results show that the proposed method generates superior or very competitive results in term of accuracy than those of classical and state-of-the-art SVM based techniques while using a significantly smaller number of support vectors.

Decomposition-Learning-Based Output Tracking to Simultaneous Hysteresis and Dynamics Control: High-Speed Large-Range Nanopositioning Example

In this brief, a decomposition-learning-based output tracking approach is proposed to compensate for both hysteresis and dynamics effects on output tracking of hysteresis systems such as smart actuators. Simultaneous hysteresis and dynamics control (SHDC) is needed to fully exploit smart or soft actuators/sensors for high-speed, large-range positioning/tracking. It remains still, however, as a challenge to achieve SHDC with both precision (performance) and robustness in general output tracking (i.e., not restricted to periodic/repeated operations), and without complicity in modeling and controller design and/or online implementation. The proposed approach aims to address these challenges, by utilizing libraries of input–output elements constructed offline to online decompose the partially known (i.e., previewed) desired output trajectory and synthesize the control input. Iterative learning control techniques are used a priori to obtain the input elements each tracking the corresponding output elements accurately, and the Preisach modeling of hysteresis is employed to obtain the combination coefficients of the synthesized control input. An experimental implementation to high-speed, large-range nanopositioning using piezoelectric actuator is presented to demonstrate the efficiency and efficacy of the proposed approach in achieving SHDC.

Robust Learning Control for a Class of Uncertain Linear Motor Systems

The tracking problem for a class of linear motor systems with unknown input deadzone is addressed in this paper. Alignment condition is adopted to solve the initial position problem for iterative learning control systems, with the control law and learning laws being developed according to Lyapunov method. Iterative learning control technique and robust control technique are together adopted to compensate uncertainties and disturbances. The position state and velocity state can accurately track the desired trajectories over the whole interval, as the iteration number increases. In the end, a simulation example is presented to demonstrate the effectiveness of the designed control scheme.

Consensus Tracking for Second-Order Multi-Agent System with Pure Delay Using the Delay Exponential Matrices

In this paper, the consensus tracking of second-order multi-agent systems with pure delay is studied by two kinds of delayed exponential matrices and iterative learning control technique. Theoretical analysis is easier with the help of delay exponential matrices, and it is simpler to design the control strategies. Further, sufficient conditions are put forward via delay exponential matrices, which can guarantee the asymptotic convergence of the consensus tracking error. Finally, a numerical example is given to verify the theoretical results.

Analog Predistorter Averaged Digital Predistortion for Power Amplifiers in Hybrid Beam-Forming Multi-Input Multi-Output Transmitter

For higher data throughput, the Massive Multi-input Multi-output (MIMO) system has been widely used in modern communication systems. Due to the circuit size and power consumption, it is difficult to integrate one Radio Frequency (RF) chain for each power amplifier (PA). As a result, MIMO transmitters with hybrid beam-forming don't have enough RF chains, and this demands the digital predistortion (DPD) block to deal with several power amplifiers (PA) simultaneously, which causes a shared DPD problem. This article presents an Analog Predistorter Averaged DPD (A 2 -DPD) for hybrid beam-forming massive MIMO transmitters. To linearize more than one PAs with one shared digital predistortion unit, continuously tunable Analog Predistortion (APD) modules are employed to uniform the nonlinear behavior of PAs in each channel. Based on iterative learning control (ILC) technique, crossed normalized mean square error (CNMSE) is derived to judge the uniformity of PAs. By comparing the CNMSE of each PAs, the best similarity state of PAs can be found. The nonlinear behavior of PAs can be adjusted to a similar state by tuning the APD control voltage. The adjustment makes PAs easier to be linearized by a shared DPD. Furthermore, an averaged DPD algorithm is proposed to improve the total linearity performance for each PA. Simulations are performed to study the relationship between CNMSE and PA uniformity and further simulations show the ability of A 2 -DPD to deal with a multi-PA scenario. In the end, to verify the feasibility of the proposed A 2 -DPD, two class-AB PAs with operating frequency at 3.5 GHz with the same type transistor and similar design are tested. Experimental results show the proposed A 2 -DPD can significantly improve the uniformity of PAs and the Adjacent Channel Power Ratio (ACPR) can be improved by 8 dB compared with using the DPD parameter of the other PA.

An Improved Approach to Iterative Learning Control for Uncertain Systems

For iterative learning control (ILC) algorithms to date, there is a fundamental tradeoff between plant model knowledge and convergence rate in the iteration domain. This article presents a new fast ILC (FILC) method that uses a novel error term in the ILC learning law based on techniques from sliding mode control (SMC). The input signal is guaranteed to remain bounded in the time and iteration domains and is insensitive to noise due to the unique structure of the FILC learning algorithm. Moreover, the FILC approach does not require end-user tuning of arbitrary gains, which is useful for uncertain systems with significant uncertainty. The stability and convergence properties for the FILC system are presented using the Lyapunov analysis techniques. Simulation and experimental system results on a manufacturing system compare FILC with the existing ILC techniques and demonstrate that FILC achieves improved iteration convergence while retaining stability when plant uncertainty is high.

Distributed Control of Multiple Flexible Manipulators With Unknown Disturbances and Dead-Zone Input

Multiple flexible manipulators can be used to complete some repeatable missions. Each flexible manipulator can be described as an underactuated Lagrangian system based on the assumed modes method. Also, the actuator nonlinearity may deteriorate the system performance. Hence, this article aims to develop a distributed controller to solve the leader–follower consensus of multiple flexible manipulators with uncertain parameters, unknown disturbances, and actuator dead zones. The disturbances are classified as repeatable and nonrepeatable ones. The adaptive, iterative learning, and sliding-mode control techniques are used to handle uncertain parameters, repeatable, and nonrepeatable disturbances, respectively. Based on a dead-zone inverse and a finite-time observer, a distributed controller is developed to drive the flexible manipulators to track a moving leader and keep the flexible vibrations bounded simultaneously. Experimental results are presented to verify the effectiveness of the proposed controller.