Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation

An application of a finite spectrum assignment method for time-delay systems to a feedback control of Mach number in a wind tunnel is presented. The linearized model of Mach number control is a system of three state equations with a delay in one of the state variables. The proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay. The spectrum of the closed-loop system is finite and consists of three eigenvalues that can be placed arbitrarily. Four possible variants of the feedback control law are presented. The calculation of feedback coefficients is very simple, which makes it possible to update the controller´s parameters on-line with the changes of the operating point. An extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions. In particular, a very good settling time under problem constraints has been obtained, and several nice features of the proposed feedback controller have been demonstrated.