Analyzing PID algorithms


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I'm new to control. i'm trying to use numerical integration method to obtain several discrete pid algorithms. I've just discretized the continuous time pid algorithm using euler forward integration, euler backward integration, trapezoidal and simpson methods. i now want to do a comparative performance analysis of the discrete pid algorithms obtained.

please i need several case studies to analyze these discrete algorithm. please where can i get some direct and simple case studies?? i've gone through several text but the things there are so complicated and confusing. thank you.