Case Studies for Robust Control
The last chapter of this book is completely devoted to case studies for robust control. The first study continues the controller design for the lateral motion of an aircraft. We introduce different weightings as in Sect. 11.3.5 and obtain in this way a fe
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Case Studies for Robust Control
The last chapter of this book is completely devoted to case studies for robust control. The first study continues the controller design for the lateral motion of an aircraft. We introduce different weightings as in Sect. 11.3.5 and obtain in this way a feedback loop with good damping properties without prestabilization. Then a block which models multidimensional input-multiplicative uncertainty is defined and, by applying the D-K iteration, a J.l controller is synthesized which improves the robustness properties of the 1i ~ controller as weIl as that of the LQ controller. The next example is concerned with the rudder-roll stabilization of ships. As for aircraft, the roll motion of ships is badly damped and this property is particularly unfavorable if waves attack the ship with a frequency that is close to the eigenfrequency of the roll motion. The task is to improve the frequency response of the wave disturbance solely by the rudder and without severely degrading the course-keeping properties of the ship. This is actually achievable in a robust manner but at the price of a higher rudder dynamics in comparison to that in the case of a pure course controller. The uncertainty model comprises input-multiplicative uncertainty and two uncertain critical parameters related to the roll motion, which are only known to lie in a given interval. The design of a missile autopilot is another challenging control problem, which by now is already classical. For the missile under consideration here, due to its aerodynamical configuration, control of the lateral acceleration is essentially a second-order SISO system, but this has some properties which make the problem difficult. Above all, this is the strong nonlinearity of the missile dynamics. For a full acceleration command there is no valid linear model. Thus the controller must be capable of working for a set of linear models whose eigenvalues lie in a large region of the complex plane. We model the nonlinearity by a suitable parameter uncertainty. Besides this, the limited bandwidth of the actuator and the elastic behavior strongly influence the controller design. As we will see, J.l synthesis provides an efficient tool to design a controller which works very weIl under all these constraints. U. Mackenroth, Robust Control Systems © Springer-Verlag Berlin Heidelberg 2004
430 14 Case Studies far Robust Control Our last case study is concerned with the control of a distillation column, wh ich is again a MIMO problem. As in the previous examples, we make a considerable effort to derive the plant model, which is rather complicated in this case. After some simplifications, there remains a system with a 2 X 2 - state matrix and two inputs and two outputs as the very heart of the problem. This seems to be simple, but is not if high purity distillation is considered because in this case the plant is very ill-conditioned. We start our analysis by designing two different controllers by classical methods. It is shown that they do not lead to satisfactory
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