Simple PID tuning using D-stability and parameter plane of PI controller

Parameter space and D stability are used in this paper to propose a simple PID tuning method and give some insight into the tuning point selection process. Parameter space is reduced to two parameters: the proportional and the integral coefficient of the PID regulator. The differential component is embedded in the plant as an internal feedback. The reduction of the parameter space to the parameter plane makes possible to find appropriate region in parameter plane without a need to use sophisticated mathematical methods. The presented technique may be applied to any linear plant. The time delay treatment does not require any approximations. The method allows a very quick way to find if a plant is tunable at all with a PID controller. Also it is easy to find robust tuning and check robustness for all relevant plant parameters. The influence of the shape of the D-stability region and the particular choice of the tuning point on the unit step response of the system is addressed as well.