The modeling, analysis, and design of a control system for a distillation column illustrates the practical application of the tools implemented in Polynomial Control Systems. The case study starts with examining the stability of the open-loop system and its time-domain behavior. Then, some of the new analysis tools are demonstrated using the transformation of the original transfer-function matrix to the corresponding left and right matrix-fraction forms and the polynomial system matrix model. Next, as an example of controller synthesis, a new full-rank state-feedback pole assignment algorithm is applied to a state-space model of the system to speed up the slower open-loop system modes. Finally, after determining the relative gain array to ensure that the best individual inputs are being used to control the system outputs, the use of the Nyquist array as a design tool is demonstrated, and one of the new frequency-domain compensator design methods is applied to determine a simple controller that significantly reduces the interaction present in the system. Make sure the application is loaded. This is a transfer-function matrix representation of a distillation column, where output 1 is the change in the top temperature of the column in degrees C and output 2 is the change in the bottom temperature in degrees C. Input 1 is the change in reflux flow in kg/hr at the top of the column and input 2 is the change in steam flow into the reboiler in kg/hr at the bottom of the column. | Out[3]= |  |
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