Robust Synthesis of Discrete PID Controllers for Objects with Interval Parameters

Abstract

The main aim of this paper is the robust control synthesis of the cascade system with discrete proportional integral (PI) controllers. The PI and proportional integral derivative (PID) controllers are employed for the control of the various, in particular, high order plants with structural and parametric uncertainties. But with PI controllers, only the low order plants can be correctly controlled. Consequently, the synthesis must be completed with the first order models of the plant in the control loops. Hence, the problem is to calculate the PI controller parameters in order to offer the dynamics quality in conditions of structural and parametric uncertainties of it he plant. The proposed parametric synthesis is based on the time scale approach and roots location on the complex plane. The small constant ε is denoted as a spectral value of the slow mode as percentage to the fast one. The nominal dynamics of each loop must be similar to the second order model dynamics. For the second order subsystems the regions of the admissible eigenevalues is denoted with limitations of real root boundary, bandwidth and damping. The analysis of the roots deviation on the complex plane with plant parameters variations allow to establish the conditions of dominant roots location in the denoted area. The values of small constant ε < 0,25 get the linear system with calculated discrete PI controllers and the valid (not reduced) plant similar to the chosen second order model dynamics. The proposed synthesis method is helpful for the system with the fast and slow components; in particular, the electrical drives control system. The numerical example of synthesis is presented with simulation results, which illustrate the application of the method