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Select a system for the regulator design

Name	Notation	Description/Example
First-order system, PT1	Ty' + y = ku	First-order non-integrating system. E.g. speed control with DC motor, liquid level in a vessel with free outflow etc.
Second-order system, PT2	T²y'' + 2ξTy' + y = ku	Second-order non-integrating system. E.g. pendulum, two heat exchangers in series etc.
Two first-order systems in series, PT2	T1 T2 y'' + (T1 + T2 ) y' + y = ku	Two first-order non-integrating systems are connected in series. The result is one non-integrating second-order system. E.g. two heat exchangers in series etc.
First-order integrating system	Ty'=k u	First-order integrating system. E.g. liquid level control in a tank with a piston-pump on outflow.
Second-order integrating system	Ty'' + y' = ku	Second-order integrating system. E.g. position control with a DC motor.