H-2 and H-infinity-optimal control for the tracking problem with zero variation

The problem of signal tracking, in the presence of a disturbance signal in the plant, is solved using a zero-variation methodology. A state feedback controller is designed in order to minimise the H-2-norm of the closed-loop system, such that the effect of the disturbance is attenuated. Then, a state estimator is designed and the modification of the zeros is used to minimise the H-infinity-norm from the reference input signal to the error signal. The error is taken to be the difference between the reference and the output signals, thereby making it a tracking problem. The design is formulated in a linear matrix inequality framework, such that the optimal solution of the stated control problem is obtained. Practical examples illustrate the effectiveness of the proposed method.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.