PID參數(shù)對控制系統(tǒng)穩(wěn)定性影響的研究

摘 要
PID控制是在工程實際中，應(yīng)用最為廣泛的控制規(guī)律。系統(tǒng)穩(wěn)定性是控制品質(zhì)的好壞的重要指標(biāo)。因此對PID控制系統(tǒng)的穩(wěn)定性研究工作在工控領(lǐng)域有重要意義。
本文分析了PID控制系統(tǒng)的穩(wěn)定性研究現(xiàn)狀。目前的穩(wěn)定性研究工作主要集中在求取參數(shù)kp,ki,kd穩(wěn)定域和控制對象的參數(shù)適用范圍上。針對這種現(xiàn)狀，本文將研究工作放在確定PID控制周期Ts的穩(wěn)定域上。
本文先建立PID控制系統(tǒng)的模型，通過仿真直觀描述了控制周期Ts對系統(tǒng)穩(wěn)定性的影響關(guān)系。接著用Z變換法和雙線性變換法得到系統(tǒng)的閉環(huán)特征方程。然后從閉環(huán)特征方程入手，提出兩種求取Ts穩(wěn)定域的方法。
方法一雖然能求出Ts的穩(wěn)定范圍，但是計算量大，而且存在誤差。而方法二提出的Ts穩(wěn)定域求取算法，經(jīng)過實例仿真驗證，被證明即簡單快捷又精確實用。

關(guān)鍵詞：PID ；一階時滯系統(tǒng)穩(wěn)定性；控制周期；離散化

ABSTRACT

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.
Keywords：PID; first order system with time delay; stability; controlling; period discretization

目 錄

1 緒論 1
1.1選題背景和意義 1
1.2本文工作 4
2 PID控制原理 5
2.1 PID控制的原理和特點 5
2.2 PID參數(shù)整定 6
2．2．1　用經(jīng)驗數(shù)據(jù)法確定PID控制器參數(shù) 6
2．2．2用試湊法確定P ID控制器參數(shù) 6
2．2．3　比例部分整定 6
2．2．4　積分部分整定 6
2．2．5　微分部分整定 7
3 連續(xù)PID調(diào)節(jié)器與數(shù)字PID控制器 8
3.1連續(xù)型PID調(diào)節(jié)器 8
3.2 理想PID控制算法 9
4 數(shù)學(xué)模型的建立 12
4.1連續(xù)系統(tǒng)的數(shù)學(xué)模型的建立 12
4.2離散系統(tǒng)數(shù)學(xué)模型的建立 12
4.2.1“等價離散化設(shè)計”方法下的簡化模型 13
4.2.2計算機控制系統(tǒng)典型結(jié)構(gòu) 14
5 PID控制系統(tǒng)的穩(wěn)定性研究現(xiàn)狀 16
5.1連續(xù)PID穩(wěn)定域分析 16
5.2 連續(xù)系統(tǒng)對象參數(shù)的穩(wěn)定域的求取 17
5.3 離散系統(tǒng)的穩(wěn)定性分析 17
6 離散PID系統(tǒng)控制周期Ts的確定 19
6.1控制周期對系統(tǒng)穩(wěn)定性的影響 19
6.2 控制周期、被控對象延遲時間與閉環(huán)特征方程 22
6.3 通過穩(wěn)定性判據(jù)確定控制周期的方法 24
6.3.1雙線性變換的勞斯穩(wěn)定判據(jù) 24
6.3.2 z變換法的朱利穩(wěn)定判據(jù) 25
論文總結(jié) 27
參考文獻 28
致謝 31
英文原文及中文翻譯