The multiple reference principle component least mean squares algorithm: a projection based approach

The principal component least mean squares algorithm (PCLMS) is an elegant adaptive control algorithm for cancelling a tonal disturbance signal in active control applications, such as active noise control and active vibration isolation control. The algorithm removes the spatial correlation between the actuator inputs and the error sensor outputs to enable fast convergence of the adaptive controller. However, a drawback of the PCLMS algorithm is that it can only suppress a disturbance signal which contains a single frequency component. The contribution of this paper is that we present a numerically robust projection based approach in which the PCLMS is extended with the ability to suppress a disturbance signal which contains multiple frequency components. The potential of the algorithm is demonstrated by multi-tonal control on a realistic model of a real-time vibration isolation set-up. The algorithm is shown to outperform the traditional filtered-x least mean squares algorithm

Flexible multibody modelling for exact constraint design of compliant mechanisms

In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system’s degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly

A robust subspace based approach to feedforward control of broadband disturbances on a six-degrees-of-freedom vibration isolation set-up

The contribution of this paper is twofold. First, the paper introduces a novel hybrid vibration isolation approach which uses a combination of passive and active vibration control techniques to provide additional design freedom. The approach can be used to meet higher design requirements with respect to vibration isolation. To illustrate the feasibility of the approach, a stiff hybrid sixdegrees-of-freedom vibration isolation set-up will be presented. The objective of the set-up is to investigate if the receiver structure can be isolated from the source structure by six hybrid vibration isolation mounts, such that disturbances induced by the source structure are isolated from the receiver structure. Vibration isolation is established by minimizing signals from six acceleration sensor outputs and by steering six piezo-electric actuator inputs. Our second contribution is that a state space based fixed gain H2 controller is designed, implemented and validated. Real-time broadband feedforward control results are presented (between 0 - 1 kHz) which show that an average reduction of 8.0 dB is achieved in the error sensor outputs in real-time