AILC for Rigid-Flexible Coupled Manipulator System in Three-Dimensional Space with Time-Varying Disturbances and Input Constraints

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.

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.

This paper addresses the vibration control and the trajectory tracking control of a robotic arm system with input constraint. A hyperbolic tangent function and a saturation function are adopted to tackle the input constraint. By defining a composite energy function, a dual-loop iterative learning control (ILC) law is designed by integrating a restrained learning law and a saturated feedback law. For the closed-loop system, the angle displacements are asymptotically regulated to track a prescribed constant trajectory and the elastic displacements are asymptotically suppressed to zero along the iteration axis. Simulation and experimental results are provided to illustrate the effectiveness of the designed ILC law.

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.

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.

This article presents an iterative learning control (ILC) approach for linear parabolic distributed parameter systems with multiple actuators and multiple sensors. The distribution functions of actuators and sensors are chosen as delta function to produce pointwise control and pointwise measurement. A P‐type ILC law is proposed based on the iterative inputs and outputs to ensure the iterative process of the system is convergent under the ILC law. By utilizing integration by parts, triangle inequality, property of delta function, and Gronwall lemma, a sufficient condition based on an inequality constraint for the convergence analysis of the track error system is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.

This paper investigates the tracking control problem of high-speed trains in the presence of the input constraints caused by the distribution and output capacity of power systems. By virtue of the repetitive operation pattern of trains and the backstepping technique, an adaptive iterative learning control (ILC) strategy based on the multi-particle model is proposed to drive the train to track the given reference displacement and velocity, where the unknown time-varying parameters are learned and adjusted between successive operations, and an input-dependent auxiliary system is introduced to compensate the influence of input constraints. During the design of the controller, the Lyapunov function and composite energy function (CEF) are constructed to ensure the stability of the closed-loop system and the convergence of tracking errors for high-speed trains. Furthermore, numerical simulation is performed to confirm the effectiveness of the proposed scheme. The three main contributions of this work lie in: 1) Integrating the multi-particle model and ILC framework, which can more accurately reveal the dynamics of the train, and take full advantage of the repetitive operation pattern; 2) Following the backstepping procedure to devise the learning controller, where the parameter uncertainties and modeling inaccuracies are deliberately handled, and; 3) Solving the issues of distributed input constraints for the control system of high-speed trains.

In this paper, a new design of adaptive iterative learning control (ILC) for a class of uncertain nonlinear systems is proposed for the purpose of state tracking and improving convergence speed with both parametric and nonparametric uncertainties. The main feature of the design is that the controller signal is continuous due to the use of integral and employment of second-order sliding mode technique. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. In response to unknown bounded disturbances, a continuous sliding mode adaptive iterative learning control is more robust. By designing a suitable controller and composite energy function, the convergence of tracking error sequence within a small neighborhood of the origin is achieved in the iteration domain. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

An iterative learning-based adaptive disturbance rejection control (ADRC) method is proposed to tackle control issues for three-dimensional (3D) overhead crane. The tracking differentiator (TD) and extended state observer (ESO) are employed to extract desired displacement and estimate system disturbances. A robust iterative learning control (ILC) law is constructed by integrating sliding mode control (SMC) with ILC. The stability of the closed-loop system is proved through Lyapunov stability theory, and simulations are conducted to verify the effectiveness and robustness of the proposed method.

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

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 paper, an adaptive iterative learning control (AILC) method combined with sliding mode technique is proposed to improve the force control performance for repeating tasks of fluidic muscle (FM) driven parallel manipulators. Different from the traditional iterative learning control method, the proposed AILC is to learn the controller time-varying parameters rather than to learn the control signals. Since the AILC is sensitive to non-repetitive disturbances, the sliding mode technique is introduced to enhance the robustness. Since no model information involved in the controller design, the proposed method is a complete data-driven method. Hence, the difficulty of obtaining accurate model is avoided. Simulation studies are performed on a two degrees of freedom FM driven parallel manipulator. Simulation results demonstrate that the proposed method can achieve high force tracking performance and robustness.

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.

This paper deals with the problem of iterative learning control for large-scale interconnected linear systems in the presence of fixed initial shifts. According to the characteristics of the systems, iterative learning control laws are proposed for such large-scale interconnected linear systems based on the PD-type learning schemes. The proposed controller of each subsystem only relies on local output variables without any information exchanges with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of the system converges uniformly to the corresponding output limiting trajectory over the whole time interval along the iteration axis. Simulation examples illustrate 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.