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D1

x

D2

δ

x

x

D2/D1≧5~10倍

(1)在定理12-1的証明中,狀態回授真正要求的控制增益K,而非 Kc,而Kc=KcP^-1

(2)狀態回授設計能成立的前提是開路系統完全狀態可控制,而其設計的目標是設置閉迴路系統的極點(特性根)位置,因此,狀態回授設計又稱為極點位置設計(pole placement design)

det(SI-A+BK)=det(SI-P^-1AP+P^-1BKP)=det(P^-1(SI-A+BK)P)=DET(P^-1)det(SI-A+BK)det(P) ≒det(SI-A+BK)

1.檢查開路系統(受控系統)的控制性.若系統是完全狀態可控制,則進行狀態回授增益設計.

2.由開路系統的A矩陣求得閉迴路特性方程式

An-1 An-2 ….. 1

An-2 An-3 ….. 1 0

….

….

A1 1 ……. 0

1 0 …….. 0

det(SI-A)=S^n+a1S^n-1+a2S^n-2+……..+an=0

3.根據規格,決定希望的閉迴路特性方程式: αc(s)=(S-λ1)(S-λ2)………(S-λn)=S^n+δ1 S^n-1+……+ δn =0

4.決定可控制典型的轉換矩陣P:

P=[B AB ……… A^n-1B]*

5.求解狀態回授增益K:K=[δn-an δn-1-an-1…….. δ1-a1]P^-1