Quantitative synthesis for a 3×3 distillation column to achieve performance robustness

In this paper, quantitative synthesis of a multivariable two-matrix-degree-of-freedom feedback system for a 3×3 distillation column with sidestreams example having significant plant parameter uncertainty, is performed. The synthesis procedure is that of multi-input multi-output (MIMO) quantitative feedback theory (QFT). From the given MIMO problem, equivalent single-loop problems are derived whose solution guarantees the solution of the original problem. Using the basic single-input single-output (SISO) QFT procedure, the single-loop problems are then solved to satisfy the frequency domain specifications on the tracking and disturbance-rejection properties. The design is verified in both frequency and time domains for 81 plants picked randomly from the set of uncertain plants. The results show that the performance specifications are successfully achieved for the range of parameter uncertainty considered