Order Iterative Learning Control Research Articles

Two-Dimensional Fractional Order Iterative Learning Control for Repetitive Processes

The convergence and robustness rejecting parameters variations and external disturbance of the system are crucial for repetitive processes. In this paper, a two-dimensional robust fractional-order iterative learning control (FOILC) is proposed for the repetitive motion process to enhance the convergence and robustness. A fractional-order proportional derivative function (FOPDF) is designed as the control variable to replace the tracking error of the integer-order iterative learning control (IOILC) algorithm. The required dynamic output fractional-order iterative learning controller is constructed by solving a set of linear matrix inequalities (LMI), and the control parameters are adjusted according to the given specifications. Simulation and experimental results in robot torque control are given to prove the effectiveness and feasibility of the proposed design method.

Iterative learning control for fractional order nonlinear system with initial shift

In this study, a closed-loop \({D^\alpha }\)-type iterative learning control (ILC) with a proportional D-type iterative learning updating law for the initial shift is applied to nonlinear conformable fractional order system. First, the system with the initial shift is introduced. Then, fractional order ILC (FOILC) frameworks that experience the initial shift problem for the path tracking of nonlinear conformable fractional order systems are addressed. Moreover, the sufficient condition for the convergence of tracking errors is obtained in the time domain by introducing \(\lambda \)-norm and Hölder’s inequality. Lastly, numerical examples are provided to illustrate the effectiveness of the proposed methods.

Consensus Control of Multi-agent Robot System with State Delay Based on Fractional-Order Iterative Learning Control Algorithm

This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.

Robust Model-Free Adaptive Iterative Learning Control for Vibration Suppression Based on Evidential Reasoning.

Through combining P-type iterative learning (IL) control, model-free adaptive (MFA) control and sliding mode (SM) control, a robust model-free adaptive iterative learning (MFA-IL) control approach is presented for the active vibration control of piezoelectric smart structures. Considering the uncertainty of the interaction among actuators in the learning control process, MFA control is adopted to adaptively adjust the learning gain of the P-type IL control in order to improve the convergence speed of feedback gain. In order to enhance the robustness of the system and achieve fast response for error tracking, the SM control is integrated with the MFA control to design the appropriate learning gain. Real-time feedback gains which are extracted from controllers construct the basic probability functions (BPFs). The evidence theory is adopted to the design and experimental investigations on a piezoelectric smart cantilever plate are performed to validate the proposed control algorithm. The results demonstrate that the robust MFA-IL control presents a faster learning speed, higher robustness and better control performance in vibration suppression when compared with the P-type IL control.

High order iterative learning control to solve the trajectory tracking problem for robot manipulators using Lyapunov theory

This paper deals with Iterative Learning Control (ILC) design to solve the trajectory tracking problem for rigid robot manipulators subject to external disturbances, and performing repetitive tasks. A high order ILC scheme is synthetized; this controller contains the information (errors) of several iterations and not only of one iteration. It has been shown that the closed loop system (robot plus controller) is asymptotically stable, over the whole finite time interval, when the iteration number tends to infinity. This proof is based upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed controller scheme. Finally, simulation results on two-link manipulator are provided to illustrate the effectiveness of the proposed controller.

Rectified fractional order iterative learning control for linear system with initial state shift

In this paper, a new rectifying action is combined into different proportional-α-order-derivative-type iterative learning control algorithms for a class of fractional order linear time-invariant systems. Unlike the existing fractional order iterative learning control techniques, the proposed algorithms allow the initial state value of a fractional order iterative learning control system at each iteration to shift randomly. By introducing the Lebesgue-p norm and using the method of fractional integration by parts and the generalized Young inequality of convolution integral, the tracking performances with respect to the initial state shift under the proposed algorithms are analyzed. These analyses show that the tracking errors are incurred by such a shift and improved by tuning the rectifying gain. Numerical simulations are performed to demonstrate the effectiveness of the proposed algorithms.

INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT

In this paper, iterative learning control (ILC) is combined with an optimal fractional order derivative (BBO-Da-type ILC) and optimal fractional and proportional-derivative (BBO-PDa-type ILC). In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO). Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC

Robust adaptive sliding mode control combination with iterative learning technique to output tracking of fractional-order systems

This paper develops a novel controller called adaptive iterative learning sliding mode (AILSM) to control linear and nonlinear fractional-order systems. This controller applies a hybrid structure of adaptive and iterative learning control in to sliding mode method. It can switch between both adaptive and iterative learning control in order to use the advantages of both controllers simultaneously and therefore achieve better control performance. This controller is designed in a way to be robust against the external disturbance. It also estimates unknown parameters of fractional-order system. The proposed controller, unlike the conventional iterative learning control, does not need to apply direct control input to output of the system. It is shown that the controller performs well in partial and complete observable conditions. Illustrative examples verify the performance of the proposed control in presence of unknown disturbances and model uncertainties.

Fractional order iterative learning control with randomly varying trial lengths

In this paper, we establish a uniform framework to deal with varying tracking problem in the finite time interval for fractional order system. In order to tracking the reference trajectory associated with nonlinear fractional differential systems with randomly varying trial lengths, we design a new type iterative learning control of the output equation with nonlinear input involving an integral term. As a result, convergence analysis results for several classes of learning laws with local average operator are given. Finally, some examples are given to illustrate our results.

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.

Resistance based iterative learning control of additive manufacturing with wire

This paper presents successful feed forward control of additive manufacturing of fully dense metallic components. The study is a refinement of former control solutions of the process, providing more robust and industrially acceptable measurement techniques. The system uses a solid state laser that melts metal wire, which in turn is deposited and solidified to build the desired solid feature on a substrate. The process is inherently subjected to disturbances that might hinder consecutive layers to be deposited appropriately. The control action is a modified wire feed rate depending on the surface of the deposited former layer, in this case measured as a resistance. The resistance of the wire stick-out and the weld pool has shown to give an accurate measure of the process stability, and a solution is proposed on how to measure it. By controlling the wire feed rate based on the resistance measure, the next layer surface can be made more even. A second order iterative learning control algorithm is used for determining the wire feed rate, and the solution is implemented and validated in an industrial setting for building a single bead wall in titanium alloy. A comparison is made between a controlled and an uncontrolled situation when a relevant disturbance is introduced throughout all layers. The controller proves to successfully mitigate these disturbances and maintain stable deposition while the uncontrolled deposition fails.

Physical layer privacy scheme for networked control systems

Control systems in general and networked controls systems in particular are vulnerable to harmful noise effect and malicious cyber-attacks that may have devastated outcomes on sensitive applications. One approach to address these threats is to introduce a stringent security and privacy schemes that able to protect the attacked systems. This paper addresses this issue by proposing a privacy scheme, for feedback signals, stemmed from the well-known spread spectrum principle and the information system theory. In order to confirm the efficiency of the proposed scheme in offering a good level of control system privacy, a theoretical analysis is provided and supported by a simulation example introduced to one of the relatively weak control systems to noise and malicious attacks namely Higher Order Iterative Learning Control (HOILC).

Robust second-order PD type iterative learning control for a class of uncertain fractional order singular systems

This paper presents a robust second-order feedback type iterative learning control (ILC) for a class of uncertain fractional-order singular systems. Sufficient conditions for the robust convergence of the proposed type of learning control algorithm, with respect to the bounded external disturbance and uncertainity, have been established and specified for time domain. Finally, simulation examples are presented to illustrate the performance of the proposed fractional order ILC.

Stability of first and high order iterative learning control with data dropouts

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to output measurement data dropouts. It is assumed that data dropout occurs during the data transfers from the plant to the ILC controller, resulting in what is called intermittent ILC. Using the super-vector approach for ILC, the expectation of output error is used to develop conditions for stability of the first order ILC and high order ILC processes. Through the theoretical analysis, it is shown that the convergence of the intermittent ILC is guaranteed although some measurements are missing. The analysis is also supported by numerical examples.

Model and experience‐based initial input construction for iterative learning control

AbstractThe initial choice of input in iterative learning control (ILC) generally has a significant effect on the error incurred over subsequent trials. In this paper, techniques are developed that use experimental data gathered over previous applications of ILC in order to generate an initial input signal for the tracking of a new reference trajectory. A model‐based approach is then incorporated to overcome the limitation of insufficient previous experimental data, and a robust design procedure is developed. Experimental evaluation results are obtained using a gantry robot facility. Copyright © 2010 John Wiley & Sons, Ltd.

Designing PI Controller Based on Iterative Learning Control using Adaptive Technique

This paper presents a technique that can be used in designing an equivalent PI controller to different classes of the known Iterative Learning Control (ILC) namely P-type and high order ILCs. The equivalent PI controller can be explicitly represented in the z domain in contrast to the time domain based ILC, which gives another potential for stability analysis. Moreover, the derived PI controller combines the ease of tuning with the learning feature from past processes, which is the base of Iterative Learning Control (ILC). The results show that the ability of proposed approach to provide an equivalent PI controller that provides similar performances to the ILC when applied to various systems with no restrictions on the system order or type.

Decentralized Iterative Learning Control to Large-Scale Industrial Processes for Nonrepetitive Trajectory Tracking

In the procedure of steady-state hierarchical optimization with feedback for a large-scale industrial process, it is usual that a sequence of step set-point changes is carried out and used by the decision-making units while searching the eventual optimum. In this case, the real process experiences a form of disturbances around its operating set-point. In order to improve the dynamic performance of transient responses for such a large-scale system driven by the set-point changes, an open-loop proportional integral derivative-type iterative learning control (ILC) strategy is explored in this paper by considering the different magnitudes of the controller's step set-point change sequence. Utilizing the Hausdorff-Young inequality of convolution integral, the convergence of the algorithm is derived in the sense of Lebesgue-P norm. Furthermore, the extended higher order ILC rule is developed, and the convergence is analyzed. Simulation results illustrate that the proposed ILC strategies can remarkably improve the dynamic performance such as decreasing the overshoot, accelerating the transient response, shortening the settling time, etc.

PI CONTROLLER DESIGN BASED ON ITERATIVE LEARNING CONTROL

This paper presents a technique that can be used in designing an equivalent PI controller to different classes of the known Iterative Learning Control (ILC) namely P-type and high order ILCs. The equivalent PI controller can be explicitly represented in the z domain in contrast to the time domain based ILC, which gives better potential for stability analysis. Moreover, the derived PI controller combines the ease of tuning with the learning feature from past processes, which is the base of Iterative Learning Control (ILC). The results show that the ability of proposed approach to provide an equivalent PI controller that provides similar performances to the ILC when applied to various systems with no restrictions on the system order or type.

On the disturbance properties of high order iterative learning control algorithms

The disturbance properties of high order iterative learning control (ILC) algorithms are considered. An error equation is formulated, and using statistical models of the load and measurement disturbances an equation for the covariance matrix of the control error vector is derived. The results are exemplified by analytic derivation of the covariance matrix for a second order ILC algorithm.

Optimality of First-Order ILC Among Higher Order ILC

Higher order iterative learning control (HO-ILC) algorithms use past system control information from more than one past iterative cycle. This class of ILC algorithms have been proposed aiming at improving the learning efficiency and performance. This paper addresses the optimality of HO-ILC in the sense of minimizing the trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances. It is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero. That is, an optimal HO-ILC does not add to the optimality of standard first-order ILC in the sense of minimizing the trace of the control error covariance matrix. The system under consideration is a linear discrete-time varying systems with different relative degree between the input and each output