Transcript 重要!

CH 5 Reduction of Multiple Subsystems
5.1 Introduction
•實際系統複雜 由許多子系統組成 (1子系統 1方塊)
•分別求子系統的數學模型 連結各方塊呈現整體系
統
如何預測?
Tp , Ts , Tr , %OS
with step input
•系統表示法:
Frequency domain → Block diagrams
Time domain → Signal-flow graphs
• 本章目標
1. 化簡複雜 block diagrams
→
註1
2. 由Ge(s) →預測 Tp , Ts , Tr , %OS with step input
3. Find step response for Ge(s)
4. Design sys. gain → desired transient response
註:討論 Linear, Time-Invariant Systems
即 線性非時變系統
註2
註1: 化簡成單一方塊的理由
註2: 系統形態
Linear, Time-Invariant Systems
線性非時變系統
Linear, Time-varying Systems 線性時變系統
當a(t),b(t),k(t) 為變動的常數
Non-linear, Time-varying Systems 非線性時變系統
當a(t),b(t),k(t) 為變動的非線性函數
e.g. a(t) = sinωt
非線性非時變系統
5.2 Block Diagrams
• 符號介紹
加法器
撿取點
Figure 5.2
Components of a block diagram for a linear, time-invariant system
• Cascade Systems (分類1)
Figure 5.3a
Cascaded subsystems
Figure 5.3b equivalent transfer function
•兩子系統串連 要注意 Loading 問題
Figure 5.4
Loading in
cascaded
systems
• Parallel Systems (分類2)
Figure 5.5
a. Parallel subsystems; b. equivalent transfer function
• Feedback Systems (分類3)
Figure 5.6
a. Feedback control system; b. simplified model; c. equivalent transfer function
化簡
→
證明:
重要!
Block Diagram Algebra
重要
公式!
化簡
→
證明:
重要!
Block Diagram Algebra
重要
公式!
化簡
→
重要
公式!
化簡
→
化簡
→
G(s) H(s):
open-loop T.F.
loop gain
• Block Diagram Algebra
(for summing junctions )
Figure 5.7
Block diagram algebra for summing junctions — equivalent forms for moving a block
a. to the left past a summing junction; b. to the right past a summing junction
• Block Diagram Algebra
(for pickoff points )
Figure 5.8
Block diagram algebra for pickoff points—equivalent forms for moving a block
a. to the left past a pickoff point; b. to the right past a pickoff point
Example 5.1
方塊圖化簡
Figure 5.9
Figure 5.10 a. collapse summing junctions; b. form equivalent cascaded system in the forward
path and equivalent parallel system in the feedback path; c. form equivalent feedback system and
multiply by cascaded G1(s)
Example 5.2
P. 1/4
Figure 5.11
Example 5.2
P. 1/4
Figure 5.12 a
Example 5.2
P. 2/4
Figure 5.12 a
Figure 5.12 b
Example 5.2
P. 3/4
Figure 5.12 b
Figure 5.12 c
Example 5.2
P. 4/4
Figure 5.12 c
Figure 5.12 d
Figure 5.12 e
5.3 Analysis and Design of Feedback Systems
Figure 5.14
Second-order feedback
control system
K 為變數
↙
Example 5.3
Figure 5.15
Feedback system
求 Tp , Ts , %OS
Find ζ, ωn first
Example 5.4
Figure 5.16
求k=? Such that %OS=10%
gain design for transient response
H.W. 1 Skill-Assessment Exercise 5.2
H.W. 2 Problem 5 Fig. P5.5
H.W. 3 Problem 17 Fig. P5.17
Have a good time.