1. Instructor: Chen-Hsiung Yang
動態系統建模分析與控制
Lecture4 Transfer-function Approach to Modeling Dynamic Systems
Presentation slide for courses, classes, lectures et al.
Instructor: Chen-Hsiung Yang
Dynamic System Modeling Analysis and Control

2. Outline
4-1 Introduction 4-2 Block Diagrams 4-3 Partial-Fraction Expansion with MATLAB 4-4 Transient-Response Analysis with MATLAB
Beginning course details and/or books/materials needed for a class/project.

3. 4-1 Introduction

4. 4-2 Block Diagrams

5. 4-3 Partial-Fraction Expansion with MATLABIf
MATLAB Command
1. T.F. → Partial-Fraction
Type:
>>num=[1,8,16,9,6];
>>den=[1,6,11,6];
>>[r, p, k]=residue(num, den)
Display: r= p=
k=1 2
2. Partial-Fraction → T.F.
Type:
>>r=-6,-4,3
>>p=-3,-2,-1
>>k=1,2
>>[num, den]=residue(r, p, k)
Display:
num=
den=

6. 4-3 Partial-Fraction Expansion with MATLAB(Cont.)
sol:
By MATLAB
we obtain

7. 4-3 Partial-Fraction Expansion with MATLAB(Cont.)
sol:
By MATLAB
we obtain

8. 4-4 Transient-Response Analysis with MATLAB
Basic Command:
Transfer function：>>sys=tf(num,den)
Time interval ：>>t=0: Δt: T
MATLAB Command
1. For step response
Type:
>>num=[1,8,16,9,6];
>>den=[1,6,11,6];
>>sys=tf(num,den)
>>step(sys) or step(num,den)
>>y=step(sys) or [y,t]=step(sys,t)
2. For impulse response
Type:
>>num=[1,8,16,9,6];
>>den=[1,6,11,6];
>>sys=tf(num,den)
>>step(sys) or step(num,den)
>>y=step(sys) or [y,t]=step(sys,t)

9. 4-4 Transient-Response Analysis with MATLAB(Cont.)
Basic Command:
Transfer function：>>sys=tf(num,den)
Time interval ：>>t=0: Δt: T
MATLAB Command
3. For arbitary input
Type:
>>num=[1,8,16,9,6];
>>den=[1,6,11,6];
>>sys=tf(num,den)
>>t=0:0.01:4;
>>u=t
>>lsim(sys,u,t)
<Note>: lsim(sys1,sys2,…,u,t)
4. ramp response
Type:
>>num=[1,8,16,9,6];
>>den=[1,6,11,6];
>> sys=tf(num,den);
>> t=0:0.01:4;
>>u=t
>>lsim(sys, u, t)

10. 4-4 Transient-Response Analysis with MATLAB(Cont.)
sol:
By MATLAB