Iterative learning-based adaptive disturbance rejection control method for the 3D overhead crane system with time-varying rope length

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.

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.

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, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

This paper addresses robust performance analysis and synthesis of lifted system iterative learning control (ILC). By applying the full block S-procedure, sufficient conditions for the robust performance of ILC with both unstructured and structured uncertainty are derived. In the synthesis problem, we consider the design of the learning filter Q for modelinversion based ILC. The problem is reformulated as a convex optimization problem such that the converged tracking error is minimized subject to the monotonic convergence condition. This synthesis approach enables full automation of the ILC design since neither an uncertainty model has to be identified nor a robustness filter has to be chosen. The advantages of this novel robust performance ILC technique are demonstrated on an experimental linear motor test setup.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

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.

Due to the nonlinearity, strong coupling, and uncertain parameters of autonomous underwater vehicle (AUV), it is difficult to build an accurate dynamic model, which makes precise control of AUV extremely challenging. To handle the precise heading-following problem of AUV, this paper proposes an iterative learning-based redefine model-free adaptive heading control (IL-RMFAC) method for the underactuated AUV with unknown disturbances based on data driven. The control scheme consists of a learning control algorithm, a parameter iterative update algorithm, and a parameter reset algorithm. It is designed using only the input and output (I/O) data of the controlled system and is a data-driven control method. The pseudo partial derivative (PPD) can be iteratively calculated through the parameter iterative update algorithm and reset algorithm to adjust the learning gain, solving the problem of strictly limited initial position of the traditional fixed learning gain iterative learning control (ILC). A linear combination of angle and angular velocity is introduced in the kinematic layer to avoid overshooting of the expected following target, and an iterative learning method is introduced in the dynamics to improve the accuracy. As the number of iterations increases, the steady-state error is gradually decreased. Finally, by comparing traditional proportional–integral–derivative (PID) simulations, the proposed algorithm’s effectiveness and outstanding performance for the AUV heading tracking are confirmed.

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

For batch processes with small time delays and actuator partial fault, the existing methods based on iterative learning control still have some limitations, including the conservative and computationally burdensome of stability conditions and the limited fault-tolerant control capabilities. For this background, an iterative learning robust predictive fault-tolerant control method is developed, which integrates the Lyapunov–Razumikhin function method and derives stability conditions based on robust positive definite invariant set and terminal constraint set. With small time delays, the stability conditions of the system deduced using the Lyapunov–Razumikhin function are solved at a lower computational cost, which is due to the fact that the dimensionality of the stabilization condition is directly related to the size of the time delay, and thus the small time delay implies a lower dimensionality. Especially, the computational effort for solving the stability conditions online is reduced, allowing real-time control law gains to be obtained and combined with historical batches of control inputs, reducing the learning cycles of the system, and realizing stable tracking of the setpoints within shorter operating batches. Moreover, the robust positive invariant set and the set of terminal constraints are able to constrain the state of the system within a safe range for all possible uncertainties, bounded disturbances, and faults. This makes the proposed methods based on them more robust and fault tolerant. Finally, a nonlinear batch reactor is used as an example to demonstrate the effectiveness and feasibility of the developed method.

An iterative learning control (ILC) framework based on two-degree-of-freedom control is presented for a linear plant with perturbations. A sufficient condition in the frequency domain is obtained for robust convergence with the bounded asymptotic error in the existence of input disturbance, output disturbance and errors in initial states. Based on the sufficient condition, the problem of designing ILC can be converted to a robust performance problem and a robust ILC against disturbances and initialization errors is derived by structured singular value and mu synthesis

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.

The adaptive iterative learning control method for electro-hydraulic shaking tables based on the complex optimization algorithm was proposed to overcome the potential stability problem of the traditional iteration control method. The system identification precision’s influence on convergence was analyzed. Based on the real optimization theory and the mapping relationship between real vector space and complex vector space, the complex Broyden optimization iterative algorithm was proposed, and its stability and convergence was analyzed. To improve the stability and accelerate the convergence of the proposed algorithm, the complex steepest descent algorithm was proposed to cooperate with the complex Broyden optimization algorithm, which can adaptively optimize the complex steepest gradient iterative gain and update the system impedance in real time during the control process. The shaking tables experiment system was designed, applying xPC target rapid prototype control technology, and a series of experimental tests were performed. The results indicated that the proposed control method can quickly and stably converge to the optimal solution no matter whether the system identification error is small or large, and, thus, verified that validity and feasibility of the proposed adaptive iterative learning method.

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.

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.