Nghiên cứu bài toán giảm bậc mô hình cho hệ tuyến tính theo phương pháp cân bằng nội

Dao Huy Du vd cs Tap chi KHOA HOC & CONG NGHE 75(13): 97- 102

NGHIEN Ctru BAI TOAN GIAM BAG MO HINH CHO HE TUYEN TINH THEO

PHUOTVG PHAP CAN BANG NOI

Dao Huy Du'", Vu Ngoc Kien', Ngo Cuong", Vii Van Dam-

' Trudng Dgi hgc Ky thudl Cdng nghiep - Dgi hgc Thdi Nguyen

'Trudng Cao ddng Kinh le Ky thudl - Dgi hgc Thdi Nguyen

TOMTAT

De thiet ke he thong dieu khien trong linh vuc dien- dien tu va co khi ta thudng phai biet dugc mo

hinh doi tugng. Khi md hinh phuc tap, cac phuong phap thiet ke hien nay se gap kho khan. VI vay

viec don gian hoa mo hinh ma van dam bao sai so cho phep co mot y nghia Idn. Bai bao dua ra bai

toan giam bac mo hinh tong quat, cac phuong phap giam bac mo hinh co ban doi vdi he dgng hgc

tuyen tinh. Gidi thieu phuong phap can bang noi do Moore de xuat va cac vi du cung cac ket qua

mo phong di kem the hien tinh dung dan ciia phuong phap.

Til' khoa: md hinh gldm bde, he ddng hoc tuyen tinh, phuong phdp cdn bdng ndi

DAT VAN DE

Tai sao can phai giam bac mo hinh

Hau het cac phuong phap dieu khien deu dua

tren co' sd md hinh toan hpc cua ddi tupng

dieu khien (cdn gpi la he ddng hpc can dieu

khien). Tuy nhien trong thuc tien thudng gap

nhung he ddng hpc md ta bdi md hinh toan

hpc phiic tap, cd bac rat cao dan tdi viec nam

bat trang thai boat ddng ciia he phuc vu cho

muc tieu phan tich he gap khdng it khd khan

va cang khd khan khi mudn tdng hpp va dieu

khien he. Nhung viec dd hien nhien se trd nen

de dang hon khi sir dung mdt md hinh don

gian hon, bac thap ban dupe chpn sao cho cd

cac dac diem quan trpng cua md hinh bac cao.

Do vay van de giam bac md hinh dupe dat ra

la rat can thiet va int huu ich trong viec thiet

ke he thdng dieu khien ddi tupng.

Trong thuc te, hau het cac he ddng hpc cd

ddng hpc la phi tuyen, tuy nhien da sd cac he

nay cd the dua ve dang md hinh ddng hpc

tuyen tinh vdi nhiing gia thiet nhat djnh. Vi

vay, hau het nhung cdng trinh lien quan den

giam bac md hinh da dugc cdng bd tren cac

tap chi khoa hpc trong nude va qudc te deu ap

dung cho ddi tupng cd ddng hpc tuyen tinh.

Tir day, chimg tdi dua ra bai toan giam bac

md hinh cho he tuyen tinh nhu sau:

' Tel: 0912347222

Phat bieu bai toan giam bac mo hinh

Cho mdt he tuyen tinh, lien tuc, tham sd bat

bien theo thdi gian, cd nhieu dau vao, nhieu

dau ra, md ta trong khdng gian trang thai bdi

he phuong trinh sau:

x = Ax-\- Bit

(1.1)

y = Cx + Du

trong dd. X G R", u e RP, y e R", A e R'"^", B

e R"'", C e R^"\ D e R''^^

Muc tieu ciia bai toan giam bac ddi vdi md

hinh md ta bdi he phuong trinh da cho trong

(1.1) la tim md hinh md ta bdi he cac

phuong trinh:

A^x,. -F B.u

(1.2)

y,- - Cr^r D..U

trong do, X, e R', u G R". y^GR'', A^ G R'" . B,-

G R"P, C, G R^", D, G R"" vdi r < n:

Sao cho md hinh md ta bdi phuong trinh (1.2)

cd the thay the md hinh md ta bdi phuong

trinh trong (1.1) irng dung trong phan tich,

thiet ke, dieu khien he thdng.

Cac phu-o-ng phap giam bac mo hinh

Hon 40 nam qua, da cd hang tram cdng trinh

nghien ciru de giai quyet bai toan giam bac

ciia md hinh bac cao dupe cdng bd va de xuat

cac phuang phap tiep can khac nhau. Tuy

nhien. theo quan diem ciia tac gia, ddi vdi mdt

md hinh bac cao cho trudc, cac phuong phap

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