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The University of Southampton

Research project: Robust control algorithms

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The control algorithms used in many applications of active control must be adaptive to changes in the disturbance, to ensure good performance, but be robust to changes in plant response, to ensure closed loop stability. This is an unusual requirement for a control system, which is normally either made robust to changes in the plant or is made adaptive to track these changes. The requirement in active control arises because the changes in the plant are relatively small and well bounded but they also occur rapidly compared with the plant's dynamic response. Such changes in the response between the secondary loudspeakers and the error microphones inside a car may be caused by the movement of people within the car, for example. If a conventional adaptive control system were used to track these changes in the plant, considerable levels of identification noise would need to be fed to the secondary actuators which would increase the sound level to such an extent that the effects of actively controlling the original disturbance would be lost.

Research in this area requires the study of a number of related topics: 

  • Characterisation of the changes in a single channel of the plant, or plant "uncertainty".

    For single channel systems this is usually quantified in terms of the multiplicative uncertainty at each frequency (Rafaely and Elliott, 1999).


  • Characterisation of the changes across the different channels of the plant.

    In multiple channel systems the changes in the response from one actuator to one sensor can be related to changes in the response from the other actuators to other sensors. An efficient method of describing these interactions at a single frequency has been found to be in terms of the changes in the matrix of singular values for the plant, which has a characteristic pattern for various kinds of uncertainty (Omoto and Elliott, 1999).


  • Ensuring robustness in adaptive feedforward control systems.

    This can often be achieved by including a leak in the adaptive algorithm which is equivalent to minimising a cost function which includes mean square error and sum of mean square controller coefficients (Elliott, 1998(a)).


  • Ensuring robustness in fixed feedback controllers.

    The problem can be formulated as that of designing a controller which minimises the mean square error while maintaining a given bound on the complementary sensitivity function. This is a classical control problem which can be solved either using H2 or H2/H¥ techniques, although the physical interpretation is much clearer if the Internal Model Control architecture is assumed for the feedback controller (Rafaely and Elliott, 1999; Tseng et al, 1998).

Related research groups

Signal Processing, Audio and Hearing Group
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