H-infinity design and multivariable delay margin. Application to the dynamical control of a four-wheeled vehicle

Abstract

One way of taking account of stability robustness to unmodelled dynamics, consists in the definition of delay margin. In the linear monovariable case, this delay margin, defined as the smallest additional delay in the loop, able to destabilize the closed-loop, is calculated by the way of phase margin and crossover frequency. In the multivariable case, the delay margin can be bounded by constraint on the upper principal gains on sensitivity and complementary sensitivity of the closed-loop. This constraint can be used in H-infinity mixed sensitivity design to achieve specified delay margin. An example is given on the control design of dynamical control of a four-wheeled vehicle, and has been developed in an industrial cooperation context.