Closed loop l1 scaling for fixed-point digital control implementation

In fixed-point implementation of digital controllers, the effects of quantisation can be reduced by proper scaling of the controller parameters. Commonly, controllers are scaled using l₁ norm based calculations, i.e. determining the worst case impulse response of the controller. However, this is only possible if the controller is asymptotically stable. If this is not the case, a solution is to calculate the scaling transformation on the basis of the closed-loop impulse responses. From the experience with actual implementation on a compact disc system, frequency weighting reflecting the disturbance spectrum has to be applied as well in order to obtain good experimental results.