Design and experimental validation of adaptive iterative learning control for nonlinear vehicular platoons

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.

In this study, a two‐dimensional (2D) H ∞ ‐based method is presented for the iterative learning control (ILC) design problem of a class of linear discrete‐time systems with iteratively periodic factors, including initial states, parametric uncertainties, disturbances, measurement noises, and reference trajectories. First, the ILC design problem of the linear systems is described as a controller design problem of 2D uncertain Roesser models. Second, the H ∞ performance of 2D Roesser models is studied under a general boundary condition. Third, an ILC design criterion is presented to achieve the perfect tracking and specified H ∞ performance by using linear matrix inequality approaches. Finally, a numerical example is given to illustrate the efficiency of the proposed ILC design method.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

In this paper, we study the design of iterative learning controllers for nonaffine nonlinear interconnected systems with repeatable control tasks. The interaction between each subsystem can be a general type of unknown nonlinear function if a bounding condition is satisfied. An error model is derived such that only local subsystem information is required for the controller design. An adaptive iterative learning controller for each subsystem is constructed based on a fuzzy neural learning component and a robust learning component. The fuzzy neural learning component designed by an output recurrent fuzzy neural network is utilized as an approximator to approximate the system nonaffine nonlinearities and interconnections. The approximation error due to the fuzzy neural learning component will be then compensated by a robust learning component. Stable adaptive laws are derived to update the control parameters in order to guarantee the stability and convergence. We show that the internal signals are bounded during the learning process and the state tracking errors of each subsystem converge asymptotically along the iteration axis to a tunable residual set.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

This paper aims at iterative learning control (ILC) design and analysis for a class of linear distributed parameter systems (DPSs) that may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the linear characteristic of systems, the system equations are first cast into a matrix form in the Laplace transform domain. Then, through determination of a fundamental matrix, the system transfer function is precisely evaluated in a closed form. The derived transfer function clearly demonstrates the input-output relationship of system, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and makes full use of the process repetition, while avoids any simplification or discretization for the 3D dynamics of distributed parameter systems in the time, space, and iteration domains. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

In this paper, we consider the design of adaptive iterative learning control for a class of uncertain nonlinear discrete-time systems with unknown control direction. A new design methodology using two fuzzy systems is presented to deal with the problem of unknown sign and upper bound of the input gain function. The fuzzy systems are used as approximators to compensate for the system unknown nonlinearities. In order to solve the uncertainties from fuzzy approximation errors and random input disturbance, a dead zone like auxiliary error with a time-varying boundary layer is introduced. The auxiliary error is utilized for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. Based on a Lyapunov like analysis, we show that the closed-loop is stable and the internal signals are bounded for all the iterations. The learning performance is guaranteed in the sense that the norm of output tracking error vector will asymptotically converge to a residual set which is bounded by the width of boundary layer. Finally, an illustrative example is conducted to verify effectiveness of the proposed fuzzy AILC.

SummaryBatch process, working as a best choice for low‐volume and high‐value products in manufacturing, has been widely used in chemical industries. The actuator faults and time delays often occur in practical production. This paper develops an iterative learning control (ILC) design for a batch process described by two‐dimensional (2D) Roesser system with packet dropouts and time‐varying delays. The phenomenon of actuator faults is regarded as an arbitrary stochastic sequence satisfying the Bernoulli random binary distribution. Firstly, the ILC design for a batch process is transformed into stability analysis for a 2D stochastic system with time‐varying delays. Secondly, for analyzing the stability of 2D stochastic systems, we derive the stability condition in terms of linear matrix inequality. Then, we give a procedure to get the control gain for the ILC design. An injection modeling process as an example with simulations in different cases of data dropout is given to demonstrate the validity of the proposed method. Furthermore, the proposed method has a better result by comparing the existing methods.

In this note, we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems. It is shown that if a Lyapunov based adaptive control law is available for the system under consideration and the Lyapunov function satisfies certain conditions, it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval. According to the value of a certain parameter γ, the parametric adaptation law can be a pure time-domain adaptation, a pure iteration-domain adaptation or a combination of both.A pure iteration-domain adaptation is described by a difference equation, a pure time-domain adaptation is described by a differential equation, and a combination of both is described by a differential-difference equation. The advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given.

Among the existing adaptive iterative learning control (ILC) work concerning unknown control direction problem, no result is available for the two-dimensional (2-D) dynamical systems. In this paper, an adaptive ILC is developed for a class of 2-D dynamical systems described by the Fornasini-Marchesini model (FMM). Notably, the 2-D FMM system under investigation possesses not only random uncertainties in boundary condition and reference trajectory, but also unknown control direction. Even so, the constructed adaptive ILC combining with a modification mechanism can still guarantee the precise tracking of iteration-variant reference trajectory and the boundedness of all the system signals, as iteration number k tends to infinity. Theoretical analysis and simulation study are given to demonstrate the effectiveness of the developed adaptive ILC.

This work studies the initial-rectification adaptive iterative learning control design for the linear motor systems with unknown input deadzone. For overcoming the nonzero initial error of iterative leaning control, an initial-rectification trajectory is constructed. By making the system state follow the initial-rectification trajectory along the iteration axis, we can get the necessary accurate tracking during the presented time interval. Robust adaptive learning control approach is employed to compensate for complicated uncertainties and disturbances.

Passivity-Based Iterative Learning Control for Spacecraft Attitude Tracking on SO(3)

Angular vibration turntable is an important device in the performance test of inertial device. First, the mathematical model of the three-axis angular vibration turntable is established in this paper; second, the iterative learning control algorithm based on the mathematical model is designed; and considering the situations of parameter uncertainty and parameter time-varying, in order to improve the precision during the period of tracking periodic anticipant input, the method of parameter adaptive is introduced based on the traditional PID iterative learning control; third, the convergence analysis of the adaptive parameter iterative learning control algorithm is carried out; finally, the experiments are carried out on the three-axis angular vibration turntable in order to verify the control algorithm proposed in this paper. The results of the experiments show that the parameter adaptive iterative learning control, compared to traditional PID control, can improve the precision of the system during tracking the periodic input, and the design is of benefit to reducing the periodic disturbance too.

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.

A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Theoretical background

In this article, an adaptive robust iterative learning control is developed to solve the trajectory tracking problem of a parallel Delta robot performing repetitive tasks and subjected to external disturbances. The proposed control scheme is composed of an adaptive proportional–derivative controller to increase the convergence rate, a proportional–derivative-type iterative learning control to enhance the tracking performances through the repetitive trajectory as well as a robust term to compensate the repetitive and nonrepetitive disturbances. The practical assumption of alignment condition is introduced instead of the classical assumption of resetting conditions. The asymptotic convergence is proved using Lyaponuv analysis, and it is shown that the tracking error decreases through the iterations. Simulation and experiments are performed on a Delta robot to demonstrate the effectiveness and the superiority of the proposed controller over the traditional iterative learning control.