W.J.R. Velthuis

Brief Stability analysis of learning feed-forward control

In this paper, a learning control system is considered for motion systems that are subject to two types of disturbances; reproducible disturbances, that re-occur each run in the same way, and random disturbances. In motion systems, a large part of the disturbances appear to be reproducible. In the control system considered, the reproducible disturbances are compensated by a learning component consisting of a B-spline neural network that is operated in feed-forward. The paper presents an analysis of stability properties of the configuration in case of a linear process and second-order B-splines. The outcomes of the analysis are quantitative criteria for selection of the width of the B-splines, and of the learning rate, for which the system is guaranteed to be stable. These criteria facilitate the design of a learning feed-forward controller.

Learning Feed-Forward Control: A Survey and Historical Note

Abstract From a mechatronic point of view, the performance of electro-mechanical motion systems can be improved by changing both the mechanical design and the controller. The design of a controller is generally based on a model of the plant. Thus, to improve the controller, a more accurate model of the plant is required. When the structure is not known or when many parameters cannot be determined, learning control may be considered. A simple yet powerful learning control scheme that is suitable for electro-mechanical motion systems is Learning Feed-Forward Control. In this paper an overview is given of applications that have been reported concerning this scheme. Also, relations are listed with alternative learning control schemes that are in some sense alike.

Learning feedforward control of a flexible beam

Servo control is usually done by means of model-based feedback controllers, which has two difficulties: 1) the design of a well performing feedback controller requires extensive and time consuming modelling of the process; and 2) by applying feedback control a compromise has to be made between performance and robust stability. The learning feedforward controller (LFFC) may help to overcome these difficulties. The LFFC consists of a feedback and a feedforward controller. The feedback controller is designed such that robust stability is guaranteed, while the performance is obtained by the feedforward controller. The feedforward controller is a function approximator that is adapted on the basis of the feedback signal. The LFFC is applied to a flexible robot arm, which has complex dynamics and unknown properties, such as friction. A stability analysis of the (idealised) LFFC is presented. Simulation experiments (with a non-idealised LFFC) confirm the results of this analysis and show that without extensive modelling a good performance can be obtained.

Experimental verification of the stability analysis of learning feed-forward control

In this paper the learning feedforward control (LFFC) scheme is considered. This type of controller is used for processes that repeatedly perform a specific task. LFFC compensates both for reproducible disturbances that depend on the state of the process, and for remaining random disturbances. The random disturbances are compensated by a feedback controller. The reproducible disturbances are compensated by a learning component consisting of a B-spline neural network that is operated in feedforward. In previous research, the stability properties LFFC were analyzed. From this analysis, quantitative criteria were obtained for selection of the support of the B-splines, and of the learning rate, for which the system is guaranteed to be stable. In this research the validity of the criteria is verified by means of experiments on a linear motor motion system.

Design Procedure for a Learning Feed-Forward Controller

Abstract When a process is subject to reproducible disturbances, Learning Feed-Forward Control (LFFC) can be used to obtain accurate tracking. Until recently, LFFCs were designed by means of trial and error. This paper formulates a design procedure, according to which an LFFC can be designed in a structured way. The design is based on qualitative knowledge of the process and the disturbances. This design procedure results in a shorter design phase and better performing LFFC. As an example, the design procedure is used to construct an LFFC for a linear motor. Simulations show that the resulting LFFC is able to obtain accurate control.

Performance Optimisation of Learning Feed Forward Control

The performance of sub-optimal feedback controllers can be improved in several ways. In this paper a learning control strategy is considered. The learning control system consists of the feedback and a feed forward controller. The feed forward controller is implemented as a neural network that is trained during control in order to minimise the tracking error. The type of neural network is a single layer network, in which B-spline basis functions are used to store the input-output mapping. The distribution of the Bsplines on the domain of the input(s) is of influence on the performance of the learning controller. Until recently, the basis functions were distributed by rule of thumb. In this paper fuzzy clustering techniques are used to obtain the distribution in a systematic way. In experiments the learning controller has been used to control a linear motor. Also when the B-splines are chosen by rule of thumb, the learning controller was able to improve the performance of the feedback controller considerably. The tracking error could be reduced further by determining the distribution of the basis functions using fuzzy clustering.