H°°-design and the improvement of helicopter handling qualities

This thesis presents the results of a study into the use of Hꝏ-optimization for the design of feedback control laws for improving the handling qualities of a Lynx helicopter. An important improvement to the Hꝏ-optimization procedure is the reduction in the number of iterative steps in the γ-iteration before convergence to the optimal γ. Some new algorithms are derived which significantly reduce the computation time for the γ-iteration. Both 2-block and 4-block cases are considered. Control laws are designed for precise control of pitch and roll attitude, yaw rate and heave velocity. Analysis of the raw helicopter showed the need for a stability augmentation system as the dynamic characteristics of the unaugmented helicopter do not comply with military helicopter handling qualities requirements. Results from current research on helicopter handling qualities were used as guidelines in order to define the required dynamic characteristics. A six-degree of freedom nonlinear simulation was used to analyse the helicopter dynamic time histories. A possible solution to the problem of incorporating helicopter handling qualities in the design of robust controllers is to use a two-degree of freedom controller structure. This is illustrated using both H2 and Hꝏ-optimization. A piloted simulation study to assess the effectiveness of advanced control laws was initiated at RAE, Bedford.The trials were carried out in the single seat cockpit flight simulator, at the Flight Research Division and represent the first ever real-time piloted simulation using a Hꝏ-controller.</p

Robustness of multivariable feedback systems

The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H∞-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution.</p