Robust Control Based On Loop Shaping

The algorithm of H_∞loop shaping is studied in this thesis.It is one of robust control paradigms design robust controller design methodlogy.H_∞loop shaping is one of H_∞robust controller designing approachs, which is one synthesis algorithm combining the standard H_∞control problem with the traditional loop shaping theory. The plant. To improve the frequency characteristics of the open loop singular function, the approach shape the nominal plant with selected weighting function according to the desired behavior. After that, getting the robust stability controller through the algorithm of the standard H_∞control problem. Substantially, H_∞loop shaping achieve the desired close loop performance through shaping the frequency characteristics of the open loop, and make a compromise between the robust stability and the rubust performance.The second chapter introduce some basic mathematics applied in the H_∞loop shaping methodology, which consist of norm thoery, the singular decompoaition and the singular function, the state space description of control system, and the linear fraction transformation.Chapter three describe the basic theory of H_∞control methodology, which include the performance and the stability of the feedback system, the coprime factorization on RH_∞, the robustness and the uncertainty of the system, the standard problem of H_∞control.Chapter four introduce the fundamental theory of H_∞loop shaping, which cover the discussion of the selection of weight function, the robust stabilization of the system based on the coprime factorization turpertation, H_∞loop shaping designing procedure.Chapter five is about the simulation, the system simulated include one SISO system and one MIMO system.