It is a challenge to design a satisfactory controller for a complex multivariable industrial\nsystem with minimal offsetting and a slow response. An internal model control method is proposed\nfor rank-deficient systems with a time delay based on a damped pseudo-inverse. An internal model\ncontrol was designed to obtain the desired dynamic characteristics of the system by transforming the\ntime-delay system into a system without a time delay, following the Pade approximation approach.\nBy introducing a damping factor, the internal model controller was designed based on a damped\npseudo-inverse, since the inverse matrix of the rank-deficient system does not exist. Furthermore,\na singular value decomposition was used to analyze the steady-state performance of the system.\nThe selection of the damping factor was also presented, and a micro m analysis was made to evaluate the stability of the system. To demonstrate the effectiveness of the proposed method, a crude distillation\nprocess with five inputs and four outputs was considered as an example. The simulation results\nillustrate that not only can the proposed strategy guarantee the systemâ??s stability, but it also has a\nrelatively good dynamic performance.
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