Delay Pid Parameters Of Three-dimensional Stability Region

Because of its simple structure and high performance, PID controller is widely used in various industrial control. Determine the three-dimensional PID control parameters stability regions has gradually become a hot field; Delay system is very common in practical applications, resulting in extensive engineering background of delay systems, so the research has very important theoretical significance and application value. However, practical industrial processes are complex, low-order delay systems are often not precise enough, while high-order delay system can more accurately describe the actual industrial process. Therefore, the research on PID control of high-order delay system stability region has very important theoretical significance and application value.Based on generalized Hermite-Biehler theorem, use the reverse curve to determine the stability range of the proportional gain; In the integral and differential gain plane, propose a "counterclockwise law" for boundary line of the stability region that may quickly determine the possible parameter stable regions in this two-dimensional plane, judging by the deduction of two stability criterion of time-delay systems, two-dimensional plane parameters can be determined. Simulation examples show the effectiveness of the algorithm. In condition of the time-delay systems closed-loop stability, introduce the frequency stability margin:gain margin and phase margin. Gain and phase margin specification are treated as a complex proportional gain:eJY/h, equivalently replace the open-loop frequency of time-delay system according to a certain step at the range of this gain, each two-dimensional plane parameters of this proportional can be determined, then 22 for intersection. Through traverse all values of proportional gain, three-dimensional PID control parameters stability regions under the section of gain and phase margin can be determined. Simulation examples show the effectiveness of the algorithm.Finally, apply the above theory with an interactive software using MATLAB GUI. With this interactive GUI interface, three-dimensional PID control parameters stability regions can be drawd by giving transfer function of time dealy systems and the section of gain and phase margin, it provides a convenient method to adjust online and design based on performance in practice. And this software also allows users to research stability characteristics of integral and differential plane for a fixed proportional gain, which provides a convenient method to research stability characteristics in three-dimensional PID control parameters stability regions.