Performance study of multi-rate output controllers under noise disturbances

This paper presents a comparative study of the performance of a multi-rate output controller (MROC) with a linear quadratic gaussian (LQG) controller in the presence of noise disturbances and anti-aliasing filters. The basis of comparison is to apply an LQG law with a one-step-ahead prediction-type Kalman filter (hereafter called LQG law I) and an LQG law with a current estimation-type Kalman filter (hereafter called LQG law II) to a linear time-invariant continuous-time plant model with a white gaussian process and measurement noise and compute a linear quadratic performance index for the discretized plant. Equivalent noise matrices for using the MROC law are derived and the same quadratic performance index computed. In order to have a fair comparison, the cut-off frequency of the anti-aliasing filter used to remove high frequency noise components prior to sampling is also kept the same when applying both laws. Application of both laws in typical situations shows that the performance of the MROC law is worse than either that of LQG law I or LQG law II.