de Theo J.A. Vries

Linear motor motion control using a learning feedforward controller

The design and realization of an online learning motion controller for a linear motor is presented, and its usefulness is evaluated. The controller consists of two components: (1) a model-based feedback component, and (2) a learning feedforward component. The feedback component is designed on the basis of a simple second-order linear model, which is known to have structural errors. In the design, an emphasis is placed on robustness. The learning feedforward component is a neural-network-based controller, comprised of a one-hidden-layer structure with second-order B-spline basis functions. Simulations and experimental evaluations show that, with little effort, a high-performance motion system can be obtained with this approach.

Pruning error minimization in least squares support vector machines

The support vector machine (SVM) is a method for classification and for function approximation. This method commonly makes use of an /spl epsi/-insensitive cost function, meaning that errors smaller than /spl epsi/ remain unpunished. As an alternative, a least squares support vector machine (LSSVM) uses a quadratic cost function. When the LSSVM method is used for function approximation, a nonsparse solution is obtained. The sparseness is imposed by pruning, i.e., recursively solving the approximation problem and subsequently omitting data that has a small error in the previous pass. However, omitting data with a small approximation error in the previous pass does not reliably predict what the error will be after the sample has been omitted. In this paper, a procedure is introduced that selects from a data set the training sample that will introduce the smallest approximation error when it will be omitted. It is shown that this pruning scheme outperforms the standard one.

Assessment of mechatronic system performance at an early design stage

For conceptual design of electromechanical motion systems, an assessment method is formulated that supports the design of a feasible reference path generator, control system, and electromechanical plant with appropriate sensor locations, in an integrated way. This method is based on a classification of standard transfer functions, plant models, and closed-loop systems. The assessment method can be applied in several ways, depending on the available knowledge about the design problem. In order to illustrate this method, an application to an industrial motion system is described. The assessment method quickly provides insight in the design problem. Furthermore, feasible goals and required design efforts can be estimated at an early stage.

On the use of noncausal LTI operators in iterative learning control

This paper demonstrates the use of noncausal operators in iterative learning control (ILC). First, it is shown that for a particular class of plants (having unstable zeros), perfect tracking can only be achieved by using noncausal operators. Then it is shown that with any converging algorithm (both causal and noncausal) we can associate a particular feedback controller. For causal algorithms this controller can be shown to be internally stabilizing. In the noncausal case, however, the associated controller is found to be generally destabilizing which implies that the existing notion of an equivalent controller for causal ILC does not extend to noncausal ILC.

Support-vector-based least squares for learning non-linear dynamics

A function approximator is introduced that is based on least squares support vector machines (LSSVM) and on least squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar to LSSVM. By selecting these as indicator functions the indicators for LS can be interpret in a support vector machine setting and the curse of dimensionality can be circumvented. The indicators are included by a forward selection scheme. This makes the computational load for the training phase small. As long as the function is not approximated good enough, and the function is not overfitting the data, a new indicator is included. To test the approximator the inverse nonlinear dynamics of a linear motor are learnt. This is done by including the approximator as learning mechanism in a learning feedforward controller.A function approximator is introduced that is based on least squares support vector machines (LSSVM) and on least squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar to LSSVM. By selecting these as indicator functions the indicators for LS can be interpret in a support vector machine setting and the curse of dimensionality can be circumvented. The indicators are included by a forward selection scheme. This makes the computational load for the training phase small. As long as the function is not approximated good enough, and the function is not overfitting the data, a new indicator is included. To test the approximator the inverse nonlinear dynamics of a linear motor are learnt. This is done by including the approximator as learning mechanism in a learning feedforward controller.

On using a support vector machine in learning feed-forward control

For mechatronic motion systems, the performance increases significantly if, besides feedback control, also feed-forward control is used. This feed-forward part should contain the (stable part of the) inverse of the plant. This inverse is difficult to obtain if non-linear dynamics are present. To overcome this problem, learning feed-forward control can be applied. The properties of the learning mechanism are of importance in this setting. In the paper, a support vector machine is proposed as the learning mechanism. It is shown that this mechanism has several advantages over other learning techniques when applied to learning feed-forward control. The method is tested with simulations.For mechatronic motion systems, the performance increases significantly if, besides feedback control, also feed-forward control is used. This feed-forward part should contain the (stable part of the) inverse of the plant. This inverse is difficult to obtain if non-linear dynamics are present. To overcome this problem, learning feed-forward control can be applied. The properties of the learning mechanism are of importance in this setting. In the paper, a support vector machine is proposed as the learning mechanism. It is shown that this mechanism has several advantages over other learning techniques when applied to learning feed-forward control. The method is tested with simulations.

On equivalence classes in iterative learning control

This paper advocates a new approach to study the relation between causal iterative learning control (ILC) and conventional feedback control. Central to this approach is the introduction of the set of admissible pairs (of operators) defined with respect to a family of iterations. Considered are two problem settings: standard ILC, which does not include a current cycle feedback (CCF) term and CCF-ILC, which does. By defining an equivalence relation on the set of admissible pairs, it is shown that in the standard ILC problem there exists a bijective map between the induced equivalence classes and the set of all stabilizing controllers. This yields the well-known Youla parameterization as a corollary. These results do not extend in full generality to the case of CCF-ILC; though gain every admissible pair defines a stabilizing equivalent controller, the converse is no longer true in general.

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.

A Comparison of the Performance Improvement by Collocated and Noncollocated Active Damping in Motion Systems

In this paper, both collocated and noncollocated active vibration control (AVC) of the vibrations in a motion system are considered. Pole-zero plots of both the AVC loop and the motion-control (MC) loop are used to analyze the effect of the applied active damping on the system dynamics. Using these plots and the simulated end-effector position of the actively damped plant, a comparison is made between the collocated AVC, using integral force feedback (IFF), and noncollocated AVC, by means of acceleration feedback. It is demonstrated that collocated AVC improves the performance of the plant by adding damping to both the resonance and antiresonance mode of the plant and making it possible to increase the MC bandwidth. The applied noncollocated AVC improves the performance by adding damping to the resonance mode. However, as opposed to the collocated AVC, for the applied noncollocated AVC, there is a tradeoff between various performance criteria, such as rise time and settling time, that is determined by the balance between the added damping and the increase of the bandwidth. This is true for all the AVC methods that do not increase the damping of the antiresonance mode.

On the Stability properties of P(I)D-controlled motion systems

For motion controller design, the reduced plant model is used in which high frequency dynamics are neglected. However, the maximum achievable closed-loop bandwidth is limited by the very same dynamics. The extent of their influence depends of the character of the high frequency modes. Another aspect that has an impact on the stability of the closed-loop system, is the damping present in the plant. The influence of the type of high frequency dynamics, the damping thereof, and the P(I)D controller bandwidth on the closed-loop stability is addressed in this paper. The results provide the reader with design rules of thumbs concerning the maximum achievable cross-over frequency.