Determining the parameters of PID-controller settings using the transient response of the controlled plant

Simple approximating formulas are proposed for determining the parameters of the settings of the controller used in a single-loop automatic control system with a PID-controller ; the transient response of the controlled plant is employed for this purpose. Formulas are obtained by generalizing the results from studies of automatic control systems with controlled plants whose transfer functions can be presented in the form of a network of single-capacitance elements having the same time constant and a time-delay element.