Robustness with respect to disturbance model uncertainty: Theory and application to autopilot performance analysis (Q5950077)

When designing controllers, the disturbances usually are assumed to belong to a given class of signals (for example, stochastic process with given power spectral density), although there is often considerable uncertainty as to whether or not the disturbance is, in fact, in this class. In the paper, the disturbance is modeled as an output of the first-order filter \(F(s)=K\sqrt{2\omega_b}/(s+\omega_b)\), where uncertain positive constants \(\omega_b\) and \(K\) corresponds to the disturbance bandwidth and the disturbance root-mean-square value. The main analysis tool, the \(V\)-transform, is defined; \(V\)-transforms give explicit expressions for the signal variance as a function of \(K\) and \(\omega_b\). Then two robustness margins, the disturbance gain and bandwidth margins, are defined in terms of \(V\)-transforms to quantify how much uncertainty in \(K\) and \(\omega_b\) can be tolerated before the performance becomes unacceptable. These tools are applied to an altitude-hold autopilot in the presence of uncertain turbulence. It is shown that a seemingly good controller design lacks the extra robustness with respect to uncertainty in the turbulence scale.