模糊自整定PID控制系統(tǒng)設(shè)計與仿真資料

1、模糊自整定PID控制系統(tǒng)設(shè)計與仿真 俯仰姿態(tài)保持模糊PID控制 姓名： 孫麗媛學(xué)號： 2010201393課程： 智能控制理論及應(yīng)用（095059）完成時間：2011年2月24日專業(yè)： 控制理論與控制工程指導(dǎo)老師：李愛軍一、設(shè)計內(nèi)容1、模型與設(shè)計要求（1） 某飛機(jī)縱向短周期運(yùn)動狀態(tài)方程為：。其中，；表示迎角，表示俯仰角速率，表示俯仰角，表示升降舵偏角。飛機(jī)在某狀態(tài)下的狀態(tài)參數(shù)矩陣為：，使用模糊PID控制器，設(shè)計跟蹤俯仰角的俯仰姿態(tài)保持閉環(huán)飛行控制系統(tǒng)，并對設(shè)計結(jié)果進(jìn)行分析，計算俯仰角的超調(diào)量和調(diào)節(jié)時間。（2）設(shè)計模糊控制規(guī)則。（3）在MATLAB下依據(jù)整定原理編寫仿真程序并調(diào)試。（4

2、）給定輸入為階躍信號，運(yùn)行程序，記錄仿真數(shù)據(jù)和曲線。（5）修改模糊控制規(guī)則，重復(fù)步驟4。（6）分析數(shù)據(jù)和控制曲線。2.報告要求（1）給出模糊控制器的設(shè)計過程和程序清單。（2）記錄仿真數(shù)據(jù)和曲線。（3）分析仿真結(jié)果。二、設(shè)計過程1.概述模糊PID控制器有多種結(jié)構(gòu)形式，但是工作原理基本一致，即運(yùn)用模糊數(shù)學(xué)的基本原理和方法，把規(guī)則的條件、操作用模糊集來表示，把這些模糊控制規(guī)則以及相關(guān)的信息作為知識存入計算機(jī)的知識庫中，然后計算機(jī)根據(jù)系統(tǒng)的實(shí)際響應(yīng)運(yùn)用模糊推理，可實(shí)現(xiàn)對PID參數(shù)的最佳調(diào)整。自適應(yīng)模糊PID控制器以誤差和誤差變化作為輸入，可以滿足不同時刻的和對PID參數(shù)自整定的要求。利用模糊控制規(guī)則在

3、線對PID參數(shù)進(jìn)行修改，便構(gòu)成了自適應(yīng)模糊PID控制器，其結(jié)構(gòu)如圖1所示。圖1 自適應(yīng)模糊控制器結(jié)構(gòu)PID參數(shù)模糊自整定是找出PID三個參數(shù)kp、ki、kd與e和ec之間的模糊關(guān)系，在運(yùn)行中通過不斷檢測和，根據(jù)模糊控制原理來對3個參數(shù)進(jìn)行在線修改，以滿足不同和時對控制參數(shù)的不同要求，而使被控對象有良好的動、靜態(tài)性能。2.控制原理PID參數(shù)的整定必須考慮到在不同時刻三個參數(shù)的作用以及相互之間的互連關(guān)系。而模糊自整定PID就是在PID控制算法的基礎(chǔ)上，通過計算當(dāng)前系統(tǒng)誤差和誤差變化率，利用模糊規(guī)則進(jìn)行模糊推理，查詢模糊矩陣表進(jìn)行參數(shù)調(diào)整。模糊控制設(shè)計的核心是總結(jié)工程技術(shù)人員的技術(shù)知識和實(shí)際操作經(jīng)驗

4、，建立合適的模糊規(guī)則表，得到針對、三個參數(shù)分別整定的模糊控制表如表1至表3所示。表1 的模糊控制規(guī)則表ecKpeNBNMNSZOPSPMPBNBPBPBPMPMPSZOZONMPBPBPMPSPSZONSNSPMPMPMPSZONSNSZOPMPMPSZONSNMNMPSPSPSZONSNSNMNMPMPSZONSNMNMNMNBPBZOZONMNMNMNBNB表2 的模糊控制規(guī)則表ecKieNBNMNSZOPSPMPBNBPSNSNBNBNBNMPSNMPSNSNBNMNMNSZONSZONSNMNMNSNSZOZOZONSNSNSNSNSZOPSZOZOZOZOZOZOZOPMPBNSPS

5、PSPSPSPBPBPBPMPMPMPSPSPB表3 的模糊控制規(guī)則表ecKdeNBNMNSZOPSPMPBNBNBNBNMNMNSZOZONMNBNBNMNSNSZOZONSNBNMNSNSZOPSPSZONMNMNSZOPSPMPMPSNMNSZOPSPSPMPBPMZOZOPSPSPMPBPBPBZOZOPSPMPMPBPB將系統(tǒng)誤差和誤差變化率的變化范圍定義為模糊集上的論域。其模糊子集為，子集中元素分別代表負(fù)大、負(fù)中、負(fù)小、零、正小、正中、正大。設(shè)、和、均服從正態(tài)分部，因此可得出各模糊子集的隸屬度，根據(jù)各模糊子集的隸屬度賦值表和各參數(shù)的模糊調(diào)整規(guī)則模型，運(yùn)用模糊合成推理設(shè)計出的PID參

6、數(shù)模糊調(diào)整矩陣表，查出修正參數(shù)代入下式計算式中、是PID控制器的參數(shù)，、是、的初始參數(shù)，它們通過常規(guī)方法獲得，在線運(yùn)行過程中，通過微機(jī)測控系統(tǒng)不斷的檢測系統(tǒng)的輸出響應(yīng)值，并實(shí)時的計算出偏差和偏差變化率，然后將它們模糊化得到 和，通過查詢模糊調(diào)整矩陣即可得到、三個參數(shù)的調(diào)整量完成整定過程。3.工作流程圖在線運(yùn)行的過程中，控制系統(tǒng)通過對模糊邏輯規(guī)則的結(jié)果處理、查表和運(yùn)算，完成對PID參數(shù)的在線自校正。其工作流程圖如圖2所示。開始對當(dāng)前值進(jìn)行采樣計算e、ece、ec量化、模糊化模糊整定,計算當(dāng)前,PID控制器輸出返回圖2 在線自校正工作流程圖4. 應(yīng)用模糊控制工具箱設(shè)計模糊控制器（1）首先，選擇兩輸

7、入，三輸出的模糊控制器。輸入信號為偏差信號和偏差信號的微分信號。輸出信號分別為、信號。在Matlab模糊工具箱中建立的模糊模型如圖3所示。圖3 模糊工具箱（2）測出偏差信號和誤差信號的微分信號的實(shí)際變化范圍。并根據(jù)實(shí)際情況，選擇所有的論域均為，適當(dāng)?shù)倪x擇比例因子。（3）考慮到高斯曲線叫符合人的思維，選擇使用一部分高斯曲線，設(shè)計、隸屬函數(shù)分別如圖4.1、4.2、4.3 4.4所示：圖4.1 e,ec的隸屬函數(shù)圖4.2 kp的隸屬函數(shù)圖4.3 ki的隸屬函數(shù)圖4.4 kd的隸屬函數(shù)（4）根據(jù)表1至表3中總結(jié)的實(shí)際經(jīng)驗，選擇49條模糊規(guī)則如下：<1> If (e is NB) and (

8、ec is NB) then (kp is PB)(ki is NB)(kd is PS) <2> If (e is NB) and (ec is NM) then (kp is PB)(ki is NB)(kd is NS) <3> If (e is NB) and (ec is NS) then (kp is PM)(ki is NM)(kd is NB)<4> If (e is NB) and (ec is Z) then (kp is PM)(ki is NM)(kd is NB) <5> If (e is NB) and (ec is

9、PS) then (kp is PS)(ki is NS)(kd is NB) <6> If (e is NB) and (ec is PM) then (kp is Z)(ki is Z)(kd is NM) <7> If (e is NB) and (ec is PB) then (kp is Z)(ki is Z)(kd is PS) <8> If (e is NM) and (ec is NB) then (kp is PB)(ki is NB)(kd is PS) <9> If (e is NM) and (ec is NM) then

10、 (kp is PB)(ki is NB)(kd is NS)<10> If (e is NM) and (ec is NS) then (kp is PM)(ki is NM)(kd is NB) <11> If (e is NM) and (ec is Z) then (kp is PS)(ki is NS)(kd is NM) <12> If (e is NM) and (ec is PS) then (kp is PS)(ki is NS)(kd is NM) <13> If (e is NM) and (ec is PM) then (

11、kp is Z)(ki is Z)(kd is NS) <14> If (e is NM) and (ec is PB) then (kp is NS)(ki is Z)(kd is Z)<15> If (e is NS) and (ec is NB) then (kp is PM)(ki is NB)(kd is Z) <16> If (e is NS) and (ec is NM) then (kp is PM)(ki is NM)(kd is NS) <17> If (e is NS) and (ec is NS) then (kp is

12、PM)(ki is NS)(kd is NM) <18> If (e is NS) and (ec is Z) then (kp is PS)(ki is NS)(kd is NM) <19> If (e is NS) and (ec is PS) then (kp is Z)(ki is Z)(kd is NS) <20> If (e is NS) and (ec is PM) then (kp is NS)(ki is PS)(kd is NS) <21> If (e is NS) and (ec is PB) then (kp is NS)

13、(ki is PS)(kd is Z) <22> If (e is Z) and (ec is NB) then (kp is PM)(ki is NM)(kd is Z) <23> If (e is Z) and (ec is NM) then (kp is PM)(ki is NM)(kd is NS) <24> If (e is Z) and (ec is NS) then (kp is PS)(ki is NS)(kd is NS) <25> If (e is Z) and (ec is Z) then (kp is Z)(ki is Z

14、)(kd is NS)<26> If (e is Z) and (ec is PS) then (kp is NS)(ki is PS)(kd is NS)<27> If (e is Z) and (ec is PM) then (kp is NM)(ki is PM)(kd is NS)<28> If (e is Z) and (ec is PB) then (kp is NM)(ki is PM)(kd is Z) <29> If (e is PS) and (ec is NB) then (kp is PS)(ki is NM)(kd is

15、 Z) <30> If (e is PS) and (ec is NM) then (kp is PS)(ki is NS)(kd is Z) <31> If (e is PS) and (ec is NS) then (kp is Z)(ki is Z)(kd is Z) <32> If (e is PS) and (ec is Z) then (kp is NS)(ki is PS)(kd is Z) <33> If (e is PS) and (ec is PS) then (kp is NS)(ki is PS)(kd is Z) <

16、;34> If (e is PS) and (ec is PM) then (kp is NM)(ki is PM)(kd is Z) <35> If (e is PS) and (ec is PB) then (kp is NM)(ki is PB)(kd is Z)<36> If (e is PM) and (ec is NB) then (kp is PS)(ki is Z)(kd is PB) <37> If (e is PM) and (ec is NM) then (kp is Z)(ki is Z)(kd is PS) <38>

17、; If (e is PM) and (ec is NS) then (kp is NS)(ki is PS)(kd is PS) <39> If (e is PM) and (ec is Z) then (kp is NM)(ki is PS)(kd is PS)<40> If (e is PM) and (ec is PS) then (kp is NM)(ki is PM)(kd is PS)<41> If (e is PM) and (ec is PM) then (kp is NM)(ki is PB)(kd is PS) <42> I

18、f (e is PM) and (ec is PB) then (kp is NB)(ki is PB)(kd is PB) <43> If (e is PB) and (ec is NB) then (kp is Z)(ki is Z)(kd is PB) <44> If (e is PB) and (ec is NM) then (kp is Z)(ki is Z)(kd is PM) <45> If (e is PB) and (ec is NS) then (kp is NM)(ki is PS)(kd is PM) <46> If (e

19、 is PB) and (ec is Z) then (kp is NM)(ki is PM)(kd is PM) <47> If (e is PB) and (ec is PS) then (kp is NM)(ki is PM)(kd is PS) <48> If (e is PB) and (ec is PM) then (kp is NB)(ki is PB)(kd is PS) <49> If (e is PB) and (ec is PB) then (kp is NB)(ki is PB)(kd is PB) 圖4 控制規(guī)則觀察窗口圖5 kp

20、、kd 、ki輸出量曲面如此設(shè)計的模糊控制器的部分推理規(guī)則如圖4所示，輸入與輸出的關(guān)系曲線如圖5所示，顯然模糊控制是一種非線性控制。在控制曲面上，檢查其期望值是否在模糊控制輸出結(jié)論空間的中心附近，若超過20%，則需重新調(diào)整規(guī)則、隸屬度函數(shù)或模糊運(yùn)算，對模糊控制器進(jìn)行優(yōu)化。5、搭建simulink仿真結(jié)構(gòu)圖圖6 控制系統(tǒng)仿真結(jié)構(gòu)圖其中，模糊控制子系統(tǒng)fuzzy的內(nèi)部結(jié)構(gòu)如圖7所示。圖7 模糊控制器的子系統(tǒng)結(jié)構(gòu)圖輸入信號為階躍信號：r=10 rad。6、 仿真結(jié)果曲線及分析俯仰角的超調(diào)量為13.9%調(diào)節(jié)時間ts=1.04skp、ki、kd的值為13、5、2.29 圖8 kp、ki、kd的自整定曲線

21、圖9 俯仰角的給定和輸出響應(yīng)曲線 圖10 迎角的響應(yīng)曲線 圖11 俯仰角速率q的響應(yīng)曲線 圖12 誤差變化率ec的響應(yīng)曲線圖13 誤差e的響應(yīng)曲線 俯仰角的單位階躍響應(yīng)的調(diào)節(jié)時間和超調(diào)量有大幅度減小，過渡過程平穩(wěn)。俯仰角速率的峰值也有所減小，改善了飛機(jī)的性能。在運(yùn)行過程中，模糊PID的參數(shù)是不斷在線自動調(diào)整的。模糊規(guī)則對系統(tǒng)的影響較大，合適的模糊規(guī)則可以得到良好的動態(tài)特性。模糊規(guī)則的制定是根據(jù)一定的工程經(jīng)驗。模糊PID適用于非線性系統(tǒng)，具有方便簡潔、調(diào)整靈活、實(shí)用性強(qiáng)的特點(diǎn)，同時在抗干擾方面模糊PID也具有很好的效果，參數(shù)在線自調(diào)整能力強(qiáng)，對一直干擾和噪聲是很有效的，能提高控制系統(tǒng)的品質(zhì)，具有較強(qiáng)的自適應(yīng)能力和較好的魯棒性。三、思考題1不同的解模糊方法對控制效果有什么影響？答： 1. 重心法 所謂重心法就是取模糊隸屬函數(shù)曲線與橫坐標(biāo)軸圍成面積的重心作為代表點(diǎn)。理論上應(yīng)該計算輸出范圍內(nèi)一系列連續(xù)點(diǎn)的重心，即但實(shí)際上是計算輸出范圍內(nèi)整個采樣點(diǎn)（即若干離散值）的重心。這樣，在不花太多時間的情況下，用足夠小的取樣間隔來提供所需要的精度，這是一種最好的折衷方案。2. 最大隸屬度法 這種方法最簡單，只要在推理結(jié)論的模糊集合中取隸屬度最大的那個元素