Iterative learning control with initial rectifying action for nonlinear continuous systems

An iterative learning control algorithm within prescribed input-output subspace

Since they were first introduced by Arimoto, iterative learning control (ILC) methods have received lots of attention because of their effectiveness and briefness. In this paper, an open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common, as in other ILC research papers on the convergence problem, sufficient conditions for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for a similar ILC scheme.

The feedback control based on the model and method of iterative learning control, which in turn is based on the macroscopic fundamental diagram (MFD), mostly belongs to the classification of single-layer boundary control method. However, the feedback control method has the problem of time delay. Therefore, a feedforward feedback iterative learning control (FFILC) method based on MFD of the multi-layer boundary of single-area oversaturated intersections is proposed. The FFILC method can improve the effectiveness of boundary control and avoid the time-delay problem of feedback control. Firstly, MFD theory is used to determine the MFD of the control area; the congestion zone and the transition zone of the control area are identified; and the two-layer boundary of the control area is determined. Then, the FFILC controllers are established at the two-layer boundary of the control area. When the control area enters into a congestion state, the control ratio of traffic flow in and out of the two-layer boundary is adjusted. The cumulative number of vehicles in the control area continues to approach the optimal cumulative number of vehicles, and it maintains high traffic efficiency with high flow rates. Finally, The actual road network is taken as the experimental area, and the road network simulation platform is built. The controller of the feedforward iterative learning control (FILC) is selected as the comparative controller and used to analyse the iterative effect of FFILC. Improvements in the use of traffic signal control indicators for the control area are analysed after the implementation of the FFILC method. Results show that the FFILC method considerably reduces the number of iterations, and it can effectively improve convergence speed and the use of traffic signal evaluation indicators for the control area.

This work presents a two-dimensional (2-D) system theory based iterative learning control (ILC) method for linear continuous-time multivariable systems. We demonstrate that a 2-D continuous-discrete model can be successfully applied to describe both the dynamics of the control system and the behavior of the learning process. We successfully exploited the 2-D continuous-discrete Roesser's linear model by extending the ILC technique from discrete control systems to continuous control systems. Three learning rules for ILC are derived. Necessary and sufficient conditions are given for convergence of the proposed learning rules. Compared to the learning rule suggested by Arimoto et al. (1984), our developed learning rules are less restrictive and have wider applications. The third learning rule proposed ensures the reference output trajectory can be accurately tracked after only one learning trial. Three numerical examples are used to illustrate the proposed control procedures.

In this brief, a novel spatial iterative learning control (ILC) method is proposed for a class of high-order nonlinear motion systems in the presence of both parametric and nonparametric uncertainties. Since the system performs the tracking task iteratively in the spatial domain and the uncertainties are functions of spatial coordinates, the traditional ILC that updates the control signals in the time domain is not applicable. The proposed spatial ILC aims at improving the system tracking performance by making full use of the spatial periodicity. First, the dynamics of the motion systems are converted from the temporal domain to the spatial domain via feedback linearization. Then, the learning law is designed to tackle the system uncertainties. By utilizing a newly defined space-based barrier composite energy function, the boundedness and the convergence of state tracking error are ensured rigorously. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC scheme.

A Multi-Input Single-Output iterative learning control for improved material placement in extrusion-based additive manufacturing

The repetitive processing and large quantity of single product represented by 3C products are urgently needed. However, for current processing operations, previous processing data have not been used in the optimization of control input. In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise, the idea of iterative learning was introduced to improve the accuracy of machining. On the control level, since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories, an open-loop iterative learning controller and a position loop feedback controller were introduced, which worked fast with good convergence effects. Aiming at reducing the influence of accidental error, step type iterative learning was put forward. The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity, store the current iterative part of the control input, and make constant value compensation. However, in simulation and experiment, it was found that after superposition of the iterative learning controller, the phenomenon of partial divergence of the system tracking error occurred. Therefore, the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed. High-frequency noise was introduced in frequency domain, which was found to be the cause of the abovementioned phenomenon, and high-frequency components were filtered to solve the problem. To further improve the accuracy of convergence and avoid filtering effective high-frequency information in some area, a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed. Through SIMULINK simulation and dSPACE experimental verification, it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

The injection stretch blow moulding (ISBM) process is widely used to manufacture plastic bottles for the beverage and consumer goods industry. The majority of the production processes are open-loop systems, often suffering from high raw material and energy waste. In this paper, a heuristic based norm-optimal terminal iterative learning control (ILC) method is proposed to control the preform temperature profiles in the reheating process. The reheating process is a batch process, and ILC can achieve improved tracking performance in a fixed time interval. The terminal ILC (TILC) is a useful strategy when only the terminal temperature profile can be measured in a batch process like the preform reheating in ISBM. To balance the control performance and energy cost, a norm-optimal method is applied, leading to a proposal of the new norm-optimal TILC method in this paper. Heuristic methods including the swarm optimisation (PSO), differential evolution (DE) and teaching-learning based optimization (TLBO) are used to calculate the sequence of norm-optimal control inputs for this non-linear batch process. Simulation results confirm the efficacy of the proposed control strategy.

Soft robots have recently received much attention with their infinite degrees of freedoms and continuously deformable structures, which allow them to adapt well to the unstructured environment. A new type of soft actuator, namely, dielectric elastomer actuator (DEA) which has several excellent properties such as large deformation and high energy density is investigated in this study. Furthermore, a DEA-based soft robot is designed and developed. Due to the difficulty of accurate modeling caused by nonlinear electromechanical coupling and viscoelasticity, the iterative learning control (ILC) method is employed for the motion trajectory tracking with an uncertain model of the DEA. A D2 type ILC algorithm is proposed for the task. Furthermore, a knowledge-based model framework with kinematic analysis is explored to prove the convergence of the proposed ILC. Finally, both simulations and experiments are conducted to demonstrate the effectiveness of the ILC, which results show that excellent tracking performance can be achieved by the soft crawling robot.

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.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

In this paper, a new iterative learning algorithm is proposed for repetitive nonlinear systems. The control system employs a combination of state feedback and iterative learning control (ILC) in which the coefficients of states are learned similar to ILC methods. The control system is in a closed loop format both in iteration domain (because of ILC) and in time domain (because of feedback control) which improves the robustness of the conventional ILC. The convergence of the control algorithm is also proved. Finally, simulation results for a 5-DOF manipulator have been presented to illustrate that the proposed algorithm is more robust than a first order P type ILC method at the presence of white Gaussian noise as a nonrepeating disturbance.

In order to improve the pulp quality and to reduce the energy consumption, the fiber length distribution (FLD) is generally employed as one of the important technological indexes in the refining process. Considering that the traditional mean and variance of fiber length are unable to adequately characterize the non-Gaussian distribution properties, this paper proposes a novel geometric analysis based double closed-loop iterative learning control (ILC) method for probability density function (PDF) shaping of output FLD in the refining process. Primarily, a radial basis function (RBF) neural network with Gaussian-type is utilized to approximate the square root PDF in the inner loop, where the RBF basis function parameters (center and width) are tuned between any two adjacent batches by using an ILC law, and the subspace identification method can be applied to establish the state-space model of weight vector. Then, for the sake of accelerating the convergence rate of the closed-loop system, a geometric analysis based ILC method is adopted in the outer loop. Finally, both simulation and experiments demonstrate the effectiveness and practicability of the proposed approach.

Newton-method based iterative learning control method for nonlinear systems