3723-lecture-18

3723-lecture-18 - ECEN/MAE 3723 Systems I MATLAB Lecture 3...

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ECEN/MAE 3723 – Systems I MATLAB Lecture 3
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Lecture Overview z Building Models for LTI System { Continuous Time Models { Discrete Time Models z Combining Models z Transient Response Analysis z Frequency Response Analysis z Stability Analysis Based on Frequency Response z Other Information
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Building Models for LTI System z Control System Toolbox supports continuous time models and discrete time models of the following types*: { Transfer Function { Zero-pole-gain { State Space * Material taken from http://techteach.no/publications/control_system_toolbox/#c1
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Continuous Time Transfer Function(1) Function: Use tf function create transfer function of following form: Example 2 3 1 2 ) ( 2 + + + = s s s s H >>num = [2 1]; >>den = [1 3 2]; >>H=tf(num,den) Transfer function: 2 s + 1 ------------- s^2 + 3 s + 2 Matlab Output
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Continuous Time Transfer Function(2) Include delay to continuous time Transfer Function Example 2 3 1 2 ) ( 2 2 + + + = s s s e s H s Transfer function: 2 s + 1 exp(-2*s) * ------------- s^2 + 3 s + 2 >>num = [2 1]; >>den = [1 3 2]; >>H= tf (num,den,’inputdelay’,2) Matlab Output
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Continuous Time Transfer Function(3) Function: Use zpk function to create transfer function of following form: Example () ( ) 2 1 5 . 0 2 2 3 1 2 ) ( 2 + + + = + + + = s s s s s s s H >>num = [-0.5]; >>den = [-1 -2]; >>k = 2; >>H=zpk(num,den,k) Zero/pole/gain: 2 (s+0.5) ----------- (s+1) (s+2) Matlab Output
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Continuous Time State Space Models(1) State Space Model for dynamic system Du Cx y Bu Ax x + = + = Matrices: A is state matrix; B is input matrix; C is output matrix; and D is direct transmission matrix Vectors: x is state vector; u is input vector; and y is output vector Note: Only apply to system that is linear and time invariant
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Continuous Time State Space Models(2) Function: Use ss function creates state space models. For example: [] [ ] 0 1 0 3 0 2 5 1 0 2 1 = = = = = D C B A x x x >>A = [0 1;-5 -2]; >>B = [0;3]; >>C = [0 1]; >>D = [0]; >>sys=ss(A,B,C,D) a = x1 x2 x1 0 1 x2 -5 -2 Matlab Output b = u1 x1 0 x2 3 c = x1 x2 y1 0 1 d = u1 y1 0
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Conversion between different models [z,p,k]=ss2zp(A,B,C,D) Zero-pole-gain State Space [num,den]=ss2tf(A,B,C,D) Transfer Function State Space [A,B,C,D]=zp2ss(z,p,k) State Space Zero-pole-gain [num,den]=zp2tf(z,p,k) Transfer Function Zero-pole-gain [A,B,C,D]=tf2ss(num,den) State Space Transfer Function [z,p,k]=tf2zp(num,den) Zero-pole-gain Transfer Function Matlab function Converting to Converting From
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Lecture Overview z Building Models for LTI System { Continuous Time Models { Discrete Time Models z Combining Models z Transient Response Analysis z Frequency Response Analysis z Stability Analysis Based on Frequency Response z Other Information
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Discrete Time Transfer Function(1) Function: Use tf function create transfer function of following form: Example: with sampling time 0.4
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This note was uploaded on 12/26/2010 for the course ECEN 3723 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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3723-lecture-18 - ECEN/MAE 3723 Systems I MATLAB Lecture 3...

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