Pid Parameters Of The Three-dimensional Stability Domain, With Typical Nonlinear Components

The PID control is one of the earliest developed control strategy, it is widely used in motion control and process control for its simple algorithm, high reliability and good robustness. In real life, ideal linear system does not exist. Strictly speaking, dynamic and static characteristics of various elements composing the control system will come out with varying degrees of non-linear. And in actual system, a great deal of common non-linear will have a bad effect on system performance. Therefore, determinating the PID parameters of three-dimensional stability region with typical segments of the nonlinear system, and finding PID controller parameters meeting closed-loop control in the stability region by setting parameters, is of great significance and application value.This paper focuses on three kinds of common typical non-linear in actual control system: saturation, saturation nonlinearity with dead-zone and dead-zone, and studies and discusses how to determine the three-dimensional stability region of PID parameters of system with typical nonlinear process. When the control system has a typical nonlinearity, by using the describing function method, the nonlinear part of the system can be represented by the describing function of N(A). A set of N(A) can be established by taking different value A by law. Based on the set of N(A), the nonlinear system can be described as a linear system cluster. Then according to the inverse nyquist plot, by means of the Hermite-Biehler theorem and its generalization and by using "Counterclockwise " law, through intersecting the parameter stability region of the linear system cluster, the whole stabilizing region of PID controller parameters with typical segments of the nonlinear system is given. At the same time, the anti-interference of the control system under the income parameters of PID parameters in three-dimensional region stability has been discussed briefly.Finally, introducing the stability performance index, based on the stability margin constraint, the whole stabilizing region of PID controller parameters with typical segments of the nonlinear system has been discussed in the frequency domain. By treating the amplitude constraint or the angle constraint as the proportional gain of the complex field, using the intersection approach, the whole stabilizing region of PID controller parameters with typical segments of the nonlinear system is given. The simulation examples have proved the algorithm's simplicity and effectiveness.