Study On Stability Of PID Control System

In engineering practice, the most widely used control rule is PID control and the quality of all control systems is based on the stability of the controlled systems. Therefore, the study on stability of PID control system is of great significance in the industrial fields.In this thesis, the-state-of-the-art of stability of PID control systems is provided, most of which are seeking the stable region of kp, ki, kd and the applicable scope of controlled-object parameters. Based on this research situation, we focus on seeking the stability domain of PID controlling-period.First, a PID control model is established. Second, the stability affection on a PID control system with different controlling period is described by simulation. Third, this research provides some closed-loop character equations of PID control systems by Z-transform and Tustin transform. Fourth, starting with the closed-loop character equations, this thesis has proposed two options of seeking the stability domain of controlling periods.In the end, the stability domain of controlling period is obtained in solution.1. However, amount of computations are needed and the results are imprecise. The stability domain of controlling period can also be accessed through algorithm and programming in solution.2, finally, this algorithm is proved more simple, speed, accurate and practical.