Performance of feedforward and feedback systems for active control

A consistent framework is presented for the calculation of the optimal performance of feedforward and feedback control systems in attenuating random disturbances. In both cases, the optimization problem is transformed into a quadratic form using an internal model of one part of the physical system under control. The resulting architecture for the feedback controller is known as internal model control (IMC) and is widely used in the H∞ control literature. With this controller architecture, the optimum performance of a multichannel feedback system can be readily calculated using the quadratic optimization techniques already developed in the sampled time domain for multichannel feedforward control. The robustness of the stability of such a feedback controller to changes in the plant response can be separately assessed using a generalization of the complementary sensitivity function, which has a particularly simple form when IMC is used. The stability robustness can be improved by incorporating various forms of effort weighting into the cost function being minimized, some of which are already used for adaptive feedforward controllers. By way of example, the performance is calculated of both feedforward and feedback controllers for the active attenuation of road noise in cars. The variation of performance with loop delay is calculated for both types of control, and it is found that in this example, the potential attenuation is greatest using feedback control but only if the loop delay is less than 1.5 ms.