Linearized PID control in a nonlinear model of an active hydromagnetic journal bearing

A proportional-integral-derivative (PID) control model of an active hydromagnetic journal bearing (AHJB) is presented here and its design guidelines are explicitly described. The nonlinear rotor equations of motion, is introduced. Then, the linearization of these equations in the bearing specific equilibrium point is performed and presented along with the appropriate PID gains. Consequentially, the linear equation is transformed via Laplace method and the control model of the AHJB is finally developed. The multiphysics module of Ansys is used to calculate the forces that the hydrodynamic lubrication applies to the rotor, in every position of the rotor, during its movement inside the bearing. This has been done, in order not to have linear equations of the hydrodynamic forces, but the real, nonlinear equations. The nonlinear equations are used for the electromagnetic forces too. The Matlab software is used to simulate the components that the AHJB is consisted of. The P, I, and D gains are the obtained results of this simulations, which are produced via robust control method, in single-input-single-output tool module. Finally, the Simulink module of Matlab is energized to check the control characteristics of the developed AHJB system, taking into account the nonlinear equations of motion of the system, in combination with the rotor unbalance and gyroscopic effects and the saturation of the coils. The rotor response, the overshoot, the rotor center vibration are controlled using the above produced P, I, and D gains. Several plots are constructed and presented, such as the rotor orbits, to show the possibility of the AHJB control.