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

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.

4-1 Introduction

4-2 Block Diagrams

4-3 Partial-Fraction Expansion with MATLAB If 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=-6 -4 3 p=-3 -2 -1 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=1 8 16 9 6 den=1 6 11 6

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

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

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)

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)

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