Optimal Iterative Learning Control Algorithm Research Articles

An Optimal Iterative Learning Control Approach for Linear Systems With Nonuniform Trial Lengths Under Input Constraints

In practical applications of iterative learning control (ILC), the repetitive process may end up early by accident during the performance improvement along the trial axis, which yields the nonuniform trial length problem. For such practical systems, input signals are usually constrained because of some certain physical limitations. This article proposes an optimal ILC algorithm for linear time-invariant multiple-input–multiple-output (MIMO) systems with nonuniform trial lengths under input constraints. The optimal ILC framework is specifically modified for the nonuniform trial length problem, where the primal–dual interior point method is introduced to deal with the input constraints. Hence, the constraint handling capability are improved compared with the conventional counterparts for nonuniform trial lengths. Also, the monotonic convergence property of the proposed optimal ILC algorithm is obtained in the sense of mathematical expectation. Finally, the effectiveness of the proposed algorithm is verified on the numerical simulation of a mobile robot.

Data-driven Norm Optimal Iterative Learning Control for Point-to-Point Tasks

Iterative learning control (ILC) is suitable for high-performance repetitive tasks since it learns from past trials to improve the tracking performance. Existing ILC designs often require a model, which can be difficult or expensive to obtain in practice. To address this problem, we recently developed a data-driven norm optimal ILC using the latest developments from data-driven control, namely, the Willems’ fundamental lemma. In this paper, we show that the idea can also be extended to point-to-point ILC tasks that focus on tracking some intermediate points of the whole trial. We propose a novel data-driven point-to-point norm optimal ILC algorithm that can achieve the same performance as the model-based algorithm but without using an analytical model. The design requires the available data to be persistently exciting of a sufficiently high order. To relax this requirement, a receding horizon based algorithm and a trial partition based algorithm are further developed with well-defined, but different convergence properties. Numerical examples are given to illustrate the proposed algorithms’ effectiveness.

Fast-Update Iterative Learning Control for Performance Enhancement With Application to Motion Systems

Iterative learning control (ILC) algorithms are typically used to improve the performance of repetitive processes. Numerous successful applications of ILC, such as computer numerical control (CNC) machining processes, robot manipulation, and lithography processes, have been reported. However, ILC often exhibits less than satisfactory performance since the control unit operates at a limited sampling rate in consideration of cost. In this study, the multiloop, multirate structure of servo motor control systems is taken advantage of and a fast-update multirate ILC (FILC) scheme is proposed for high-accuracy trajectory tracking, where compensation is updated at a rate faster than that of the original position loop without the need for redesigning the feedback controller. The key difficulty related to the design of the FILC lies in the extremely complex and time-varying dynamics inherent in multirate systems. To address this problem, a novel equivalent single-rate parametric model description of the multirate system is derived, which enables the use of the efficient norm optimal ILC algorithm. Consequently, a computationally efficient FILC is obtained to improve the performance. Subsequently, the proposed FILC is applied to the position control of the CNC motion stage. Simulation and experimental results are used to verify the effectiveness of the proposed method.

Robust monotonic convergent iterative learning control design: An LMI‐based method

AbstractThis work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of l2 norm of error signals is derived. First, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities. Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

Iterative learning control with forgetting factor (ILCFF) is widely used in control engineering. However, choosing the optimal parameters of ILCFF to improve system-output characteristics has been a challenging issue for controller designers. This paper proposes an iterative learning control (ILC) algorithm that involves a variable forgetting factor based on optimal gains for a class of discrete linear time-invariant systems with aperiodic disturbances. The convergence of the algorithm is analyzed, and the necessary and sufficient condition for its convergence is derived in terms of proportional–integral–derivative coefficients. A design method based on optimal gains is established to determine the algorithm coefficients and to accelerate system convergence. Furthermore, the influence of the forgetting factor on both the system-output error and the scope of the proposed algorithm is analyzed. Additionally, the most suitable system type for the application of the forgetting factor is determined. The effectiveness of the algorithm is verified by performing a theoretical analysis and a case-based simulation. The proposed iteration-varying optimal forgetting-factor-based ILC algorithm undergoes fast convergence with a small system-output error. The findings disrupt the conventional view that the use of the forgetting factor increases system-output error. In fact, in a system with small trajectory and increased disturbances, the error induced by the forgetting factor may be smaller than that of the traditional optimal ILC algorithm.

Application of Norm Optimal Iterative Learning Control to Quadrotor Unmanned Aerial Vehicle for Monitoring Overhead Power System

Wind disturbances and noise severely affect Unmanned Aerial Vehicles (UAV) when monitoring and finding faults in overhead power lines. Accordingly, we propose repetitive learning as a new solution for the problem. In particular, the performance of Iterative Learning Control (ILC) that are based on optimal approaches are examined, namely (i) Gradient-based ILC and (ii) Norm Optimal ILC. When considering the repetitive nature of fault-finding tasks for electrical overhead power lines, this study develops, implements and evaluates optimal ILC algorithms for a UAV model. Moreover, we suggest attempting a learning gain variation on the standard optimal algorithms instead of heuristically selecting from the previous range. The results of both simulations and experiments of gradient-based norm optimal control reveal that the proposed ILC algorithm has not only contributed to good trajectory tracking, but also good convergence speed and the ability to cope with exogenous disturbances such as wind gusts.

A Nonlinear Optimal Iterative Learning Control Algorithm Based on RBF Neural Network and Clonal Selection Algorithm

Improved clonal selection algorithms and RBF neural network are used for solving nonlinear optimization problems and modeling respectively in iterative learning control, and a nonlinear optimal iterative learning control algorithm (NOILCA) is proposed. In this method, an improved clonal selection algorithm is used for solving the optimum input for the next iteration; another one is used to update the RBF neural network model of real plant. Compared with GA-ILC, NOILCA has faster convergence speed, and is able to deal with the problem of inaccurate plant model, can obtain satisfactory tracking through the few several iterations.

Active control of repetitive impulsive noise in a non-minimum phase system using an optimal iterative learning control algorithm

In this paper, active control of repetitive impulsive noise is studied. An optimal iterative learning control (ILC) algorithm is developed for an active noise control (ANC) system with a non-minimum phase secondary path. A non-causal transversal finite impulse response (FIR) filter is used as the ILC learning filter, and the impulse response coefficients of the FIR filter are designed according to the asymptotically stable and monotonically convergent criterion in time domain. Computer simulations have been carried out to suggest that the proposed algorithm is effective for attenuating repetitive impulsive noise, and then the proposed algorithm has been implemented in an experimental ANC system. Experimental results show that the proposed scheme has good performance for repetitive impulsive noise attenuation in a non-minimum phase ANC system.

Clonal Selection Algorithm Based Iterative Learning Control with Random Disturbance

Clonal selection algorithm is improved and proposed as a method to solve optimization problems in iterative learning control. And a clonal selection algorithm based optimal iterative learning control algorithm with random disturbance is proposed. In the algorithm, at the same time, the size of the search space is decreased and the convergence speed of the algorithm is increased. In addition a model modifying device is used in the algorithm to cope with the uncertainty in the plant model. In addition a model is used in the algorithm cope with the uncertainty in the plant model. Simulations show that the convergence speed is satisfactory regardless of whether or not the plant model is precise nonlinear plants. The simulation test verify the controlled system with random disturbance can reached to stability by using improved iterative learning control law but not the traditional control law. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.1921

A Clonal Selection Algorithm Based Fuzzy Optimal Iterative Learning Control Algorithm

In order to realize effective tracking of output of non-linear plants with model uncertainty in specified time domain, a clonal selection algorithm based fuzzy optimal iterative learning control algorithm is proposed. In the algorithm, a clonal selection algorithm is employed to search optimal input for next iteration, and another clonal selection algorithm is used to update the parameters of Takagi-Sugeno-Kang fuzzy system model of the plant. Simulations show that the proposed method converges faster than GA-ILC in iterative domain，and is able to deal with model uncertainty well

A Clonal Selection Algorithm Based Optimal Iterative Learning Control with Random Disturbance

Clonal selection algorithm is improved and proposed as a method to solve optimization problems in iterative learning control. And a clonal selection algorithm based optimal iterative learning control algorithm with random disturbance is proposed. In the algorithm, at the same time, the size of the search space is decreased and the convergence speed of the algorithm is increased. In addition a model modifying device is used in the algorithm to cope with the uncertainty in the plant model. In addition a model is used in the algorithm cope with the uncertainty in the plant model. Simulations show that the convergence speed is satisfactory regardless of whether or not the plant model is precise nonlinear plants. The simulation test verify the controlled system with random disturbance can reached to stability by using improved iterative learning control law but not the traditional control law.

Practical implementation of a model inverse optimal iterative learning controller

In this paper, a new model inverse optimal iterative learning control algorithm is practically implemented on an industrial gantry robot. The algorithm has only one tuning parameter which can be adjusted to provide a balance between convergence speed and robustness. Results show that the algorithm is capable of learning the required trajectory in very few iterations. However at this convergence rate the lack of robustness is a major issue. Appropriate use of the tuning parameter is shown to greatly increase the algorithm robustness as demonstrated by tests which successfully reach 600 iterations.