Robust H2 nonlinear fuzzy decentralized control design for a VSC-HVDC link

A Robust $H_2$ Nonlinear Fuzzy Decentralized Controller ($H_2$ RNFDC) is proposed to improve the overall robustness and tracking ability of a VSC-HVDC link. The studied system is considered as composed by two overlapping nonlinear subsystems. The nonlinear interaction between the two subsystems is treated as a disturbance rejection problem by fuzzy control techniques. First, the Takagi Sugeno (TS) fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system. Next, new stability conditions for a generalized class of uncertain HVDC systems are derived from robust control techniques based on Linear Matrix Inequalities (LMIs). The design method employs the so-called Parallel Distributed Compensation (PDC) to obtain $H_2$ RNFDC gains based on LMIs.The efficiency and robustness of the proposed controllers are analytically proven and tested through validation simulations. The main contributions of this paper are: (i) resilience: in case of failure of one converter or loss of measures or controls, the control of the other converter is not affected; (ii) robustness is improved in order to provide good responses in case of network variations and HVDC line parameters changes; (iii) fuzzy techniques are adopted to handle nonlinearities and changes of operating conditions. The proposed $H_2$ RNFDC is compared with Fuzzy H${\hspace{0.17em}}_2$ Decentralized State Feedback Control ($H_2$ NFDC) and $H_{\infty }$ Linear Decentralized Control ($H_{\infty }$ LDC) in simulation to illustrate the control synthesis and its effectiveness.