Robust stability analysis of a boost pressure PID controller

There are many uncertain errors during the A/D and the D/A processes, and also in the fixed-point calculation when proportional-integral-derivative (PID) controller was employed in the engine control module. These will cause the perturbations of the parameters of PID controller. The robust stability performance of PID controller should be taken into account. It must be guaranteed that the uncertainties of the coefficients of the plant and the controller will not result in the feedback system unstable. The PID controller for the boost pressure control of a turbocharged diesel engine was designed based on the identified third order plant model. The parameters stability space of the PID controller was analyzed according to Hurwitz stability criterion. Using nonlinear programming method, the radius of the maximum stability ball of the parameters of Kp, Ki and Kd, which was centered at the tuned values calculated according to ISTE criterion, was computed. The permitted maximum uncertainty of the coefficients of the plant model denoted by the infinite norm was also analyzed based on the Edge Theorem. The results indicate that the tuned PID controller has good time domain performance, at the same time, the robust stability could satisfy the requirements.