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 attenuatin g random disturbances. In both cases, the optimization problem is tran sformed into a quadratic form using an internal model of one part of t he physical system under control. The resulting architecture for the f eedback controller is known as internal model control (IMC) and is wid ely used in the H-infinity control literature. With this controller ar chitecture, 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 feedforw ard control. The robustness of the stability of such a feedback contro ller 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 in to the cost function being minimized, some of which are already used f or adaptive feedforward controllers. By way of example, the performanc e is calculated of both feedforward and feedback controllers for the a ctive attenuation of road noise in cars. The variation of performance with loop delay is calculated for both types of control, and it is fou nd that in this example, the potential attenuation is greatest using f eedback control but only if the loop delay is less than 1.5 ms.