Initial-rectification iterative learning control approach of linear motor systems

In this work, path tracking control of autonomous vehicles (AVs) are studied under the framework of adaptive iterative learning control (AILC). In order to facilitate the controller design, the nonlinear vehicle dynamics are firstly transformed into a parametric form by utilizing proper variable transformations. Then a robust adaptive learning control approach is developed to achieve the path tracking tasks. Furthermore, to deal with the actuator constraints, an input-dependent auxiliary system is employed to work together with the proposed learning controller, which thus helps to reduce their influence to the control performance. The convergence analysis for the proposed method is also provided by virtue of the Lyapunov-like theory. It has been shown that with the proposed AILC approach, a good path tracking performance can be ensured in the presence of system uncertainties, exteranl disturbances and input constraints. A numerical example is illustrated to verify its effectiveness.

Air-fuel ratio control is a challenging control problem for port fuel injected and throttle body fuel injected spark ignition (SI) engines, since the dynamics of air manifold and fuel injection of the SI engines are highly nonlinear and often with unmodeled uncertainties and disturbance. This paper presents nonlinear control approaches for multi-input multi-output engine models, by developing adaptive control and learning control design methods. Theoretical proofs are established which ensure proposed controllers are able to give asymptotical tracking performance. Adaptive control and learning control approaches are capable of dealing with both constant uncertainty and time-varying periodic uncertainty. Simulation results illustrate the efficacy of the proposed controllers.

SummaryA new robust adaptive iterative learning control approach is proposed for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well‐designed dead‐zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function‐based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration‐varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single‐link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd.

An adaptive iterative learning control(ILC) approach is proposed for a class of uncertain nonlinear systems without prior knowledge about system control directions.The Nussbaum-type gain and the positive definite discrete matrix kernel are proposed for dealing with selection of the unknown control gain and learning of the repeatable uncertainties, respectively.Asymptotic convergence for a trajectory tracking within a finite time interval is achieved through repetitive tracking.Simulations are carried out to show the validity of the proposed control method.

This study explores the incorporation of time-varying sign gain into a parallel iterative learning control (ILC) architecture, augmented by an expert system, to enhance the performance and stability of a robotic arm system. The methodology involves iteratively tuning the learning control gains using time-varying sign gain guided by an expert system. Stability analysis, encompassing asymptotic and monotonic convergence, demonstrates promising results across multiple joints, affirming the effectiveness of the proposed control architecture. In comparison with traditional PID control, fixed gain ILC, and ILC with adaptive learning in the expert system, the analysis focuses on stability, precision, and adaptability, using root mean square error (RMSE) as a key metric. The results show that ILC with adaptive learning from the expert system consistently reduces RMSE, even in the presence of learning transients. This adaptability effectively controls the learning transients, ensuring improved performance in subsequent iterations. In conclusion, the integration of time-varying sign gain with expert system assistance in a parallel ILC architecture holds promise for advancing adaptive control in robotic systems. Positive outcomes in stability, precision, and adaptability suggest practical applications in real-world scenarios. This research provides valuable insights into the implementation of dynamic learning mechanisms for enhanced robotic system performance, laying the groundwork for future refinement in robotic manipulator control systems.

This paper presents a model-free adaptive iterative learning control (ILC) scheme called a proportional-type ILC scheme for non-linear systems. The obvious characteristic of the proposed ILC scheme is that we can easily finish the ILC task just utilising the Lipschitz constant of the system. In the proposed ILC scheme, the time-vary learning gain can be produced merely by input and output (I/O) measurements. Moreover, the convergence conclusion can be expressed by the ranges of the pseudo-partial derivative and the learning gain. In actual operation, a reasonable and useful convergence condition by a constant is also provided for selection. At last, the effectiveness of the proposed ILC scheme is shown by simulations.

The linear motor tool feed system is an important part in noncircular turning. In this paper, the compact form dynamic linearization based model-free adaptive iterative control scheme (CFDL-MFAILC) and the full form dynamic linearization based model-free adaptive iterative control method scheme (FFDL-MFAILC) are designed for a complex nonlinear tool feed system. Theoretical analysis shows that the proposed scheme guarantees the output tracking error monotonic convergence along the iteration axis, and the FFDL-MFAILC is a complement and improvement to the CFDL-MFAILC. The designed control schemes are compared with PID and iterative learning feedforward and model-free adaptive predictive control feedback combination scheme (ILC-MFAPC) by simulations and experiments. Simulation results show that the proposed scheme can greatly decrease linear motor position error as iteration time increase, and has better position control advantages then other algorithms, the FFDL-MFAILC has faster convergence speed and smaller steady-state error than the CFDL-MFAILC. Experiment results prove that the proposed scheme is effective in linear motor tool feed system position control.

This chapter presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of dead-zone nonlinearity is presented. The assumption of identical initial condition for iterative learning control (ILC) is removed by introducing boundary layer function. The uncertainties with time-varying delays are compensated for by using appropriate Lyapunov-Krasovskii functional and Young0s inequality. Radial basis function neural networks are used to model the time-varying uncertainties. The hyperbolic tangent function is employed to avoid the problem of singularity. According to the property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, simulation examples are presented to verify the effectiveness of the proposed approach.

This article presents an innovative enhanced model-free adaptive iterative learning control approach suited for autonomous bus trajectory tracking systems that may experience measurement disruptions and random data dropouts. Data loss can occur independently and randomly at different times and in different iterations with varying probabilities, leading to successive data dropouts on both the time and iteration axes. The proposed enhanced model-free adaptive iterative learning control controller incorporates a data compensation mechanism to compensate for missing data, ensuring excellent control performance. This data-driven control strategy requires only input/output data for controller design. The convergence and effectiveness of the proposed approach are verified through rigorous mathematical analysis and simulation outcomes.

Reference trajectory learning based adaptive iterative impedance control for a lower limb rehabilitation exoskeleton with actuator saturation

This work focuses on the model-free iterative learning control (ILC) design with good transient performance and fast convergence rate that is employed for precision control of a wafter stage. First, the experimental setup, the mathematical model, and the desired reference are introduced. Notice that the desired reference and its internal model (IM) are known in advance. Then, based on the internal model principle (IMP), a new ILC scheme, named as 1M-based ILC, is proposed by incorporating the 1M of the reference. The proposed 1M-based ILC is model-free, that is, independent on the system model of the controlled plant. The 1M -based ILC is carefully constructed to track the reference along the time axis while tracking/rejecting repetitive variations along the iteration axis. Precisely because of the tracking capability along the time axis in every iteration, the 1M-based ILC can achieve satisfactory performance even in the 0th iteration and improve the transient performance and the convergence speed. In addition, the 2-D $H_{\infty}$ theory is used to establish the design criterion for the 1M-based ILC. Finally, in the experiments, the efficiency of the 1M-based ILC is illustrated by comparing with a P-type ILC and a model-based one.

A pseudo-downsampled iterative learning control (ILC) scheme with a time shift along iteration axis is proposed. In this scheme, there are two sampling rates: a system with a fast sampling rate and an ILC scheme with a downsampled slow sampling rate. After one cycle, the input update points of ILC are shifted one sampling period w.r.t. fast system sampling rate. That is, there is always a time shift for ILC input updates points along iteration axis for two successive cycles. This process is repeated so that the input on every point w.r.t. fast system sampling rate can be updated once every several cycles. Theoretical basis and the design of the proposed ILC are given. The advantages include that it can guarantee the good learning transient; it can track high frequency trajectory; it needs not a filter design; and it can deal with initial position offset. Experimental results are presented to verify the proposed scheme

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

An adaptive robust fault tolerant control approach is proposed for a class of uncertain nonlinear systems with unknown signs of high‐frequency gain and unmeasured states. In the recursive design, neural networks are employed to approximate the unknown nonlinear functions, K‐filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unknown sign of the virtual control direction. By incorporating the switching function σ algorithm, the adaptive backstepping scheme developed in this paper does not require the real value of the actuator failure. It is mathematically proved that the proposed adaptive robust fault tolerant control approach can guarantee that all the signals of the closed‐loop system are bounded, and the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.

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.