A new approach for designing a feedback controller of a wind tunnel model involving a delay

It is shown that linear time-invariant systems having a delay in the states can be transformed into a unique and exact alternative finite dimensional generalized state space model with no delay in the states. This model is capable of generalizing results previously restricted to the nondelay systems. The major feature of this new model is its application as a major tool in developing new qualitative properties of linear time-invariant state-delay systems. One of the most practical applications of the generalized model developed is the stabilization process of the wind tunnel model involving a delay in one state. It is shown that the transient response of such system can be improved by using only one feedback control law, which can be easily implemented in a manner analogous to those for standard state space systems, using the nondelay state variables. The results obtained are much more direct and the presence of time delay in the Mach number dynamics does not result in any problem in designing the controller compared with those given by other methods, mainly because the present design procedure allows possible updating of the controller´s parameters online with the change of the operating point without using any kind of numerical approximation