Indirect IMC-PID controller design

The internal model controller-proportional–integral–derivative (IMC-PID) is one of the simplest model based proportional–integral–derivative (PID) design methods available in the literature. In IMC-PID design, the three variable PID design problem is converted into the single variable design problem with the help of the internal model of the process and an internal model controller (IMC) filter. The IMC filter is used to control the robustness of the process and transient performance. The IMC filter, however, introduces additional phase lag in the process, due to which the stability of the process is compromised to maintain the transient response. In this study, a new indirect design approach of IMC-PID controller is proposed for first-order filter with dead time (FOPDT) and second-order filter with dead time (SOPDT) processes, in which the IMC-PID controller is designed for the pole-zero shifted process instead of original process and the process robustness is tuned with the help of the proposed shifting constant $\psi $ψ. The proposed design does not involve any IMC filter, which helps to achieve a better IAE and higher Phase Margin at desired Maximum Sensitivity. The proposed method is validated with the help of real-time experiment on water level control of Canonical Tank System and MATLAB simulation examples of the FOPDT and SOPDT processes.