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A numerical simulation, using the MATLAB program, is obtained to show the time-history response, the effect of the parameters on the system and the controller. The effects of system parameters on the performance of the primary system and the controller are investigated. A comparison between all the obtained solutions made to confirm the results. Validation curves are provided to show how closely the perturbation and numerical solutions are related. A comparison is made with recently released papers.In the chemical industry, the ethylene