Sensitivity properties of multirate feedback control systems, based on eigenstructure assignment

Some sampled-data systems, e.g., fly-by-wire control schemes, have a necessarily multirate structure, various input and/or outputs sampled at different rates. When considering a multirate system which has parameter uncertainty, it is important to examine ways in which the full freedom of the multivariable design can be utilized to minimize the sensitivity to parameter variations. Given the accompanying problems induced by intersample ripple disturbance. This note examines the design capabilities of a class of multirate systems with multiple input and fixed state sampling rates (MIFS), based on eigenstructure assignment. Although the use of eigenstructure assignment for continuous and single rate discrete systems is well understood, the eigenstructure assignment for the design of multirate feedback systems is an open topic of research. Accepting that the problems of intersample ripple are often magnified through multirate control, there are advantages in terms of increased freedom for minimizing sensitivity and optimizing robustness to parameter variations. A special feature of the MIFS class of multirate systems is the ability to introduce extra design freedom in the eigenproblem by a suitable choice of eigenstructure assignment and sample rates. The criteria for the selection of minimum sample rates to produce this extra freedom, and the implication that this has on the eigenstructure assignment problem, are outlined. The improved insensitivity properties are demonstrated using an example comparing the performance of multirate and corresponding single rate designs