A Method Study Of High-precision2-DOF-PID Control Stability

As a simple structure, strong robustness and high reliability of feedback controlimplementation, PID controller has been widely used in industrial fields since itsadvent. From different point of view, many PID tuning methods have been proposed inthe past decades, which either have a good suppression characteristic of loaddisturbance, or have a characteristic of following the set point well. However, it isimpossible for PID controller to optimize both of them simultaneously，which is thereason why we introduce the2-DOF-PID controller.Additionally, traditional PID controller have always been designed to give a finitegroup of PID parameters based on experience or some function optimizing, under theassumption that the feedback system is always stable and able to meet the requiredperformance. There is almost nothing about the existence of stability region and thecompatibility of performance regions to be discussed.The purpose of this dissertation is how to give robust2-DOF-PID parameterseffectively to meet the performance requirements. Based on the results of chapter2that the parametes of2-DOF-PID are separable and2-DOF-PID has the samecharacteristic polynomial with PID, the parametes of2-DOF-PID can be divided intotwo groups, and stability is only related to the first group parameters (traditional PID).For the design of the traditional PID parameters, first get the stability region and all thePID regions for individual performance constrains; then study the compatibility of allthese regions (if not compatible, then modify the relevant performance until themcompatibility); finally, some related knowledges of genetic algorithms and computational geometry are used to find the non-fragile PID parameters (theChebyshev center of the compatible region). After the PID parameters coming out, it istime for us to tune the additional parameters(α,β), using genetic algorithms andSIMULINK.Theoretical analysis and example simulations show that the2-DOF-PID tuningmethod presented here is effective. Moreover, we made some conclusions andinnovations as follows:1. The stability of the2-DOF-PID is only related to traditional PID parameters（K_pK_iK_d）.2. For non-time-delay system, the concept of generalized stability margin is proposedon the one hand; on the other hand, the ranges of amplitude margins of a systemare analyzed form the point of view of the existence of parameter region.3. For retarded-type time-delay system, a new method to construct the requiredparameter region is proposed based on a generalized Hermite-Biehler theorem.4. A principle of constructing sequence invariance is proposed to improvecomputational efficiency in the process of constructing parameter region.5. An error for testing the stability of line segment polynomial with complexcoefficients in some literature is corrected.6. A method for evaluating MCMC random sampling in3D region is proposed.7. A method of3D region reconstruction is given. And the spherical mutation andspherical crossover for genetic algorithm in3D region are presented to guaranteethat the offspring individuals are always in the3D region.8. On the basis of system stabilizing, the step response of a2-DOF-PID system isonly sensitive to the parameter (belonging to the additional parameters).