Iterative learning control for linear parabolic distributed parameter systems with multiple point sensors

ABSTRACTIn this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.

A new iterative learning control (ILC) approach combined with an open-closed-loop PD scheme is presented for a flexible manipulator with a repeatable motion task in the case that only the endpoint pose of the flexible link is measurable. This approach takes advantage of the fact that the ILC performance is independent of the model used, thereby overcoming the drawback of the heavy reliance of PD controllers on the modeling accuracy. The open-closed-loop PD controller is mainly used to simultaneously reduce the effects of the modeling error and disturbances to enhance the controller's robustness. Meanwhile, an angular correction term is introduced by using the angular relationship of the system outputs to reward or penalize the ILC law. Specifically, when the current output tends toward the expected trajectory, the ILC law is enhanced accordingly; otherwise, it is penalized. The convergence conditions for the proposed approach are obtained through theoretical analysis, and experiments using a real flexible manipulator are presented. The results show that the proposed ILC scheme can overcome the impact of the endpoint error caused by link flexibility and has a good control effect.

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.

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.

The 2D state space system model is established with state delay and actuator faults, and what is more, the iterative learning control (ILC) law required by the batch process model is designed. Using the knowledge of 2D system theory and an iterative learning control law, the 2D state space model can be changed into an equivalent 2D-Roesser closed-loop system model. According to the optimized cost function and Lyapunov stability theory, sufficient conditions for the solvability of model predictive control (MPC) problems in the form of linear matrix inequalities (LMIs) are given. A new solution is proposed which depends on the bound of the state delay. At last, the effectiveness of the method is proved through simulation experiments.

In this paper, the control problem of semi-linear distributed parameter system (DPS) with sensors/actuators is considered using iterative learning control (ILC) method. During the learning process, the output signals of the system exist random data dropout which is described as a Bernoulli random variable. Then, a novel intermittent updating PD-type ILC algorithm is proposed on the basis of the available output information. In this kind ILC algorithm, the scheme only updates its control signal when the output signal is successfully transmitted. Hence, the intermittent updating PD-type ILC algorithm is presented for a semi-linear parabolic DPS based on single sensor and single actuator, and the convergence condition of the output error is obtained by using Bellman-Gronwall lemma and semigroup theory under some given assumptions. Secondly, this kind PD-type ILC law is extended to control the semi-linear DPS with multiple sensors and multiple actuators. Lastly, one example is given to demonstrate the effectiveness of the proposed scheme.

This article investigates the iterative learning control problem for a class of nonlinear heterogeneous multi-agent systems. The main contribution of this article is to apply iterative learning control algorithm to the multi-agent systems with multiple leaders, and solve the containment control problem of multi-agent systems in the sense of iterative learning control stability. Based on the framework of communication topologies, distributed iterative learning controllers are designed. And when the iterative learning control laws are applied to the systems, the containment errors between the followers’ states and the convex hull spanned by the leaders’ states over a finite-time interval are bounded, and furthermore, the containment errors can converge to zero as the iteration index approaches to infinity in the absence of initial errors. A simulation example is finally constructed to verify the effectiveness of the theoretical method.

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

In this paper, a modified learning gain for Iterative Learning Control (ILC) approach is proposed for linear Multi-Input-Multi-Output repetitive systems. The control law synthesis is based on the resolution of a quadratic criterion which minimizes the error between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem leads to a new gain which avoids matricial inversion problems appeared with classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The modified type ILC approach improves the learning convergence significantly compared to I-ILC and Q-ILC algorithms. Furthermore, a sufficient and necessary stability condition and convergence properties are established. Simulations with a MIMO Mass-spring damper system show the effectiveness of the proposed method.

This study first investigates robust iterative learning control (ILC) issue for a class of two‐dimensional linear discrete singular Fornasini–Marchesini systems (2‐D LDSFM) under iteration‐varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2‐D LDSFM is derived. A simple P‐type ILC law is proposed such that the ILC tracking error can be driven into a residual range, the bound of which is relevant to the bound parameters of boundary states. Specially, while the boundary states of 2‐D LDSFM satisfy iteration‐invariant boundary states, accurate tracking on 2‐D desired surface trajectory can be accomplished by using 2‐D linear inequality theory. In addition, extension to 2‐D LDSFM without direct transmission from inputs to outputs is presented. A numerical example is used to illustrate the effectiveness and feasibility of the designed ILC law.

Open-closed Loop ILC Corrected with Angle Relationship of Output Vectors for Tracking Control of Manipulator

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.

This paper presents an iterative learning control (ILC) approach for tracking problems with specified data points that are desired points at certain time instants. To design ILC systems for such problems, unlike traditional ILC approaches, an algorithm which updates not only the control signal but also the reference trajectory at each trial will be developed. The relationship between the reference trajectory and ILC control in tracking problems where there are specified data points through which the system should pass is investigated as the rate of convergence. In traditional ILC, the desired data is stored in a tracking profile file. Due to the huge size of the data file containing the target points, it is important to reduce the computational cost. Finally, simulation results of the presented technique are mentioned and compared to other related works to confirm the effectiveness of proposed scheme.

In this paper, an optimal iterative learning control (ILC) approach is proposed for a class of repetitive non-minimum phase (NMP) systems. The control law synthesis is based on the resolution of a quadratic criterion which minimises the errors between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem uses a new gain which avoids matricial inversion problems appearing in classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The new optimal ILC approach improves the learning convergence significantly compared to the previously mentioned algorithms. Furthermore, sufficient and necessary stability conditions are established with convergence properties. The effectiveness of the proposed method is proved by simulations with an NMP mass-spring damper system.

In this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law. With this new algorithm, monotonic convergence of the error to zero is guaranteed if the original system is a discrete-time LTI system and it satisfies a positivity condition. If the original system is not positive, two methods are derived to make the system positive. The effect of the choice of weighting parameters in the performance index on convergence rate is analysed. As a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm. A high-order version of the algorithm is also derived and its convergence analysed. The theoretical findings in this paper are highlighted with simulations.