Control synthesis for linear parametric time-varying systems

Abstract

Designing auto-pilots with classical controller design methods such as root-locus may be a laborious job and it requires a lot of experience to arrive at satisfactory controllers. The single loop closure techniques that are common practice for most aircraft manufacturers are mainly appreciated because of the vast amount of experience gained in this area. One of the great advantages of classical flight control laws is that the individual control mode structure is simple, which makes it conceptually easy to apply gain-scheduling to account for operating point changes (traversing through the flight envelope). However, the functional integration of all modes leads to conflicting control action due to lack of interaction. Moreover, serious problems occur during flight tests due to complexity of the overall control system; further difficulties arise when tuning the various modes. Finally, it is not always clear how uncertainties in the models on which the designs are based should be dealt with. Over the past decade several multivariable design techniques have emerged that provide controllers for a prespecified performance and uncertainty level. A promising approach is Hw /µ-synthesis, having the feature to incorporate both design specifications and knowledge about model uncertainty into the problem set-up. A disadvantage is that it is not straightforward to provide Hw"/µ-controllers with an appropriate gain-scheduling scheme. The reason for this is that deriving a stable multidimensional fit for the controller transfer functions in the various operating points is not trivial. Several approaches to schedule Hw/µ-controllers exist. These methods use ad hoc schemes and sometimes lack guaranteed stability margins. A method that does not suffer from these drawbacks, alles 'Gainscheduling via LFTs', is the main focus of this report. A complete discussion of the theoretical background is provided in order to appreciate the merits and limitations of the methods.