Robust disturbance rejection

The problem of robust asymptotic disturbance rejection for systems involving parametric uncertainties is studied. A design method is proposed that is based on polynomial techniques. Various uncertainty structures are considered including single and multiple parameters as well as affine, polynomic and even non-polynomic cases. Both unmeasurable and measurable disturbances are considered. If the disturbance is not directly measurable, one must employ the standard internal model principle (“controller denominator should contain the dynamics of the disturbance”). When a direct measurement of the disturbance is available, however, a feedforward can be added that avoids the need to apply the principle. Therefore, a simpler controller (with two-degrees-of-freedom but of lower order) may be used. In addition, such a controller has no prespecified factors and hence it is more likely to be found robustly stabilizing. Transfer functions of the controller result from the solution of a couple of linear equations in polynomials with coefficients depending on the plant parameters. The first of the equations, that provides a robustly stabilizing feedback, is now frequently discussed in control literature. The second one: is the central theme of this paper. It gives rise to the feedforward part of the controller that guarantees the desired robust performance. Due to specific symmetry in appearance of the uncertain parameters, the feedforward equation is easier to handle. If the disturbance is not measurable or if, for some reason, its measurement is refused, the feedforward equation becomes trivial: a purely feedback controller results from a single equation-the modified feedback one