Sampled-data Iterative Learning Control Research Articles

Enhanced One Degree-of-Freedom ADRC with Sampled-Data Iterative Learning Controller for PMSM Uncertain Speed Fluctuations Suppression

Enhanced One Degree-of-Freedom ADRC with Sampled-Data Iterative Learning Controller for PMSM Uncertain Speed Fluctuations Suppression

Convergence Analysis of Sampled-Data ILC for Locally Lipschitz Continuous Nonlinear Nonaffine Systems With Nonrepetitive Uncertainties

This article investigates a challenging open problem of convergence analysis of sampled-data iterative learning control for locally Lipschitz continuous (LLC) nonlinear nonaffine continuous-time systems. The restrictive repetitive conditions are relaxed by taking the LLC nonlinear nonaffine systems with iteratively variant initial states, reference trajectories, and exogenous disturbances into consideration. A new convergence analysis method is proposed by incorporating the mathematical induction with the contraction mapping principle (MI-CMP) to prove the boundedness of system variables, and bounded convergence of tracking error for a finite iteration as the first step. Then, the mathematical proof by contradiction is utilized along with the MI-CMP to further prove the robust convergence of the tracking error in any iteration to an error bound related to the bounds of the iteration-varying uncertainties and the sampling period. It is also shown that the tracking error converges to a smaller bound if the iteration-varying uncertainties disappear, even to zero if the sampling period approaches zero. In addition, an algorithm is provided to optimize the learning operator under the convergence condition. Theoretical results are further verified by simulations.

On interval tracking performance evaluation and practical varying sampling ILC

ABSTRACTThis paperconsiders the evaluation of interval tracking error for sampled control performance and an associated sampling technique to enhance the tracking performance. The upper bounds of the tracking error profile of arbitrary sample interval for both the linear system and nonlinear system are first given. A practical sampled-data iterative learning control with varying sampling rates is proposed to ensure a prior given tolerant tracking error. In this control strategy, the inter-sample behaviour is checked to determine which intervals are not satisfactory when the given tracking performance at-sample time instants is satisfied, and then the sampling frequency for such intervals is increased. Both at-sample and inter-sample tracking performance are satisfied after enough learning iterations. Two examples are simulated to demonstrate the effectiveness of the proposed sampling strategy.

An extremum seeking approach to sampled-data iterative learning control of continuous-time nonlinear systems

Abstract: Iterative learning control (ILC) of continuous-time nonlinear plants with periodic sampled-data inputs is considered via an extremum seeking approach. ILC is performed without exploiting knowledge about any plant model, whereby the input signal is constructed recursively so that the corresponding plant output tracks a prescribed reference trajectory as closely as possible on a finite horizon. The ILC is formulated in terms of a non-model-based extremum seeking control problem, to which local optimisation methods such as gradient descent and Newton are applicable. Sufficient conditions on convergence to a neighbourhood of the reference trajectory are given.

On the current error based sampled-data iterative learning control with reduced memory capacity

The design of iterative learning controller (ILC) requires to store the system input, output or control parameters of previous trials for generating the input of the current trial. In order to apply the iterative learning controller for a real application and reduce the memory size for implementation, a current error based sampled-data proportional-derivative (PD) type iterative learning controller is proposed for control systems with initial resetting error, input disturbance and output measurement noise in this paper. The proposed iterative learning controller is simple and effective. The first contribution in this paper is to prove the learning error convergence via a rigorous technical analysis. It is shown that the learning error will converge to a residual set if a forgetting factor is introduced in the controller. All the theoretical results are also shown by computer simulations. The second main contribution is to realize the iterative learning controller by a digital circuit using a field programmable gate array (FPGA) chip applied to repetitive position tracking control of direct current (DC) motors. The feasibility and effectiveness of the proposed current error based sampled-data iterative learning controller are demonstrated by the experiment results. Finally, the relationship between learning performance and design parameters are also discussed extensively.

Varying-Order Sampled-Data Iterative Learning Control for MIMO Nonlinear Systems

In this paper,the problem of sampled-data iterative learning control is addressed for a class of nonlinear MIMO systems in the presence of perturbed initial conditions.In contrast to the fixed-order learning algorithms,a varying-order learning algorithm is proposed,for enhancing tracking performance against repositioning errors.Sufficient convergence conditions of the proposed varying-order learning algorithm are given,by which the learning gain can be chosen.The proposed learning algorithm is shown to be a unified one,because it is applicable to the systems with arbitrary but well-defined relative degree.Two implementation schemes,sampled-data direct division(DD) and division in phases(DIP) schemes,are presented,and numerical results are given to demonstrate effectiveness of the proposed schemes.

Extreme Precise Motion Tracking of Piezoelectric Positioning Stage Using Sampled-Data Iterative Learning Control

Positioning stages using piezoelectric stack actuators have been widely used in industrial applications. In this brief, we explore practical control algorithms that can achieve extreme precision motion tracking. Extreme precision is defined as the acquisition of tracking accuracy up to the hardware limit of a control system, for instance, the sensor resolution, the actuator resolution, the quantization limit of analog-to-digital converters (ADC), the limit of sampling interval, and the system repeatability. Sampled-data feedback control algorithms are unable to achieve such extreme precision tracking because of actuator saturation and stability margin. In this brief, we apply an iterative learning control (ILC) approach that can achieve the extreme precision for motion tracking tasks that repeat. ILC is essentially a feedforward control approach that fully utilizes the past control information, and hence is able to overcome the limit of feedback algorithms. The ILC algorithm used is simple in design and implementation, and fast in learning convergence. The sampled-data ILC is implemented on a piezoelectric positioning stage, in which the ADC device has a limited quantization of 49 nm. With only a few iterations of learning, the extreme precision motion tracking is achieved monotonically. Compared to well-tuned open-loop and proportional integral control algorithms, ILC can further reduce the tracking error by at least fourfold.

Sampled-data iterative learning control for nonlinear systems with arbitrary relative degree

In this paper, a sampled-daata iterative learning control method is proposed for nonlinear systems without restriction on system relative degree. The learning algorithm does not require numerical differentiations of any order from the tracking error. A sufficient condition is derived to guarantee the convergence of the system output at each sampling instant to the desired trajectory. Numerical simulation is conducted to demonstrate the theoretical result.

On D-type and P-type ILC designs and anticipatory approach

Many schemes of iterative learning control (ILC) have been developed for continuous-time, non-linear dynamic systems to improve tracking performance. Two schemes, D-type and P-type, have been the bases for many ILC designs. Recently, the anticipatory ILC scheme has been introduced, on the basis of a different approach (Wang 1998a, 1999). In this paper, these basic schemes are compared from both analysis and implementation view points. The anticipatory ILC scheme is designed on the basis of a causal pair of the action taken and its resulting state variables. This approach has the anticipatory characteristics of the D-type ILC and the simplicity for implementation of P-type ILCs. A sampled-data ILC scheme is presented as another form of this anticipatory ILC scheme. Furthermore, control device saturation is taken into account and tracking error convergence results are established, with proofs. The convergence results are also provided in the presence of uncertainties, disturbances and measurement noises. Experimental results are presented to show the effectiveness of this scheme.