Active damping in precision equipment using piezo

In this paper, the rotational vibration in the linearly actuated precision machines with low damping is discussed. This so called Rocking mode is e.g. caused by the compliance in the guiding system of a linear actuator and leads to a long settling time of the end-effector. Another problem occurs when a feedback motion controller is applied to the plant. Complex poles present in the loop transfer that are close to the imaginary axis due to low damping, are destabilized by a relatively small gain. A possible solution is actively damping the resonance frequencies. By flattening the resonance peaks, the bandwidth of the system can increase without the danger of instability. In turn, this allows for higher integral gain in the motion control algorithm

On-line nonparametric regression to learn state-dependent disturbances

A combination of recursive least squares and weighted least squares is made which can adapt its structure such that a relation between in- and output can he approximated, even when the structure of this relation is unknown beforehand.\ud This method can adapt its structure on-line while it preserves information offered by previous samples, making it applicable in a control setting. This method has been tested with compntergenerated data, and it b used in a simulation to learn the non-linear state-dependent effects, both with good success

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

Phase correction for Learning Feedforward Control

Intelligent mechatronics makes it possible to compensate for effects that are difficult to compensate for by construction or by linear control, by including some intelligence into the system. The compensation of state dependent effects, e.g. friction, cogging and mass deviation, can be realised by learning feedforward control. This method identifies these disturbing effects as function of their states and compensates for these, before they introduce an error. Because the effects are learnt as function of their states, this method can be used for non-repetitive motions. The learning of state dependent effects relies on the update signal that is used. In previous work, the feedback control signal was used as an error measure between the approximation and the true state dependent effect. If the effects introduce a signal that contains frequencies near the bandwidth, the phase shift between this signal and the feedback signal might seriously degenerate the performance of the approximation. The use of phase correction overcomes this problem. This is validated by a set of simulations and experiments that show the necessity of the phase corrected scheme

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 simulation

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

Self-tuning integral force feedback

A self-tuning procedure is proposed for an active structural element with collocated sensing and actuation (a so-called ‘Smart Disc’). The procedure aims at optimal active damping by means of Integral Force Feedback control. In case the behavior of the structure to be damped may be described by a single dominant vibration mode, self-tuning is realized in two fairly simple steps: (1) recursive estimation of three system parameters and (2) determination of the optimal controller parameters. However, if the assumption concerning a single dominant vibration mode does not hold, both steps in the selftuning procedure may easily fail