tailieunhanh - Analysis and Control of Linear Systems - Chapter 15

Chapter 15 Robust H∞/LMI Control Các tổng hợp của một đạo luật điều khiển đi qua việc sử dụng các mô hình là không có gì khác hơn là một đại diện không hoàn hảo của thực tại: bên cạnh thực tế là các định luật vật lý cung cấp chỉ có một đại diện toàn cầu của các hiện tượng, chỉ có giá trị trong một phạm vi nhất định, luôn có các không chắc chắn của mô hình thành lập bởi vì các hành vi của các quá trình vật lý không thể được chính xác được mô tả bằng. | Chapter 15 Robust H LMI Control The synthesis of a control law passes through the utilization of patterns which are nothing other than an imperfect representation of reality besides the fact that the laws of physics provide only a global representation of phenomena valid only in a certain range there are always the uncertainties of pattern establishment because the behavior of the physical process cannot be exactly described using a mathematical pattern. Even if we work with patterns whose validity is limited we have to take into account the robustness of the control law . we have to be able to guarantee not only the stability but also certain performances related to incertitude patterns. This last issue requires completing the pattern establishment work with a precise description of pattern uncertainties to include them in a general formalism enabling us to take them into account and to reach certain conclusions. The synthesis of a control law is hence articulated around two stages which are being alternatively repeated until the designer reaches satisfactory results - controller calculation during this stage only certain performance objectives and certain robustness objectives can be taken into account - analysis of the controlled system properties from the perspective of its performances as well as their robustness. Chapter written by Gilles DUC. 480 Analysis and Control of Linear Systems The approaches presented in this chapter are articulated around these two concepts. . The Hm approach The preoccupation for robustness which is inherent among the methods used by traditional automatic control engineering reappears around the end of the 1970s after having been so widely obscured due to the development of state methods. It is at the root of the development of HTO approaches. . The H standard problem Within this approach the designer considers a synthesis scheme whose general form is presented in Figure vector u represents the controls and vector