PI2D-Controllers Synthesis for Nonlinear Nonstationary Plants

PID controller modification by adding an additional differentiation channel is presented in the paper. The resulting linear controller is proposed to be called the PI2D controller. It is proposed to move the differential channel in the feedback to eliminate the undesirable effects from differentiation. It is shown that such controller division into two components entails the appearance of two control loops in the system. In accordance with this fact, it is proposed to calculate the PI2D controller coefficients in the two stages. At the first stage, it is recommended to use the basic relation of the localization method for calculating the inner contour. It is proposed to apply a modal approach in the outer control loop synthesis. It is shown that the calculated PI2D controller provides the stabilization of the second order nonlinear non-stationary plants. The results of numerical simulation of the system in the MatLab are presented. They illustrate the PI2D controller main properties.