20210808 滑模中常见趋近率
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20210808 滑模中常见趋近率
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(1) 等速趨近律 s˙=?εsgn?(s)ε>0\dot{s}=-\varepsilon \operatorname{sgn}(s) \quad \varepsilon>0s˙=?εsgn(s)ε>0
(2) 指數趨近律 s˙=?εsgn?(s)?ksε>0,k>0\dot{s}=-\varepsilon \operatorname{sgn}(s)-k s \quad \varepsilon>0, k>0s˙=?εsgn(s)?ksε>0,k>0
(3) 冪次趨近律 s˙=?k∣s∣αsgn?(s)0<α<1\dot{s}=-k|s|^{\alpha} \operatorname{sgn}(s) \quad 0<\alpha<1s˙=?k∣s∣αsgn(s)0<α<1
Matlab代碼
close all;% Isokinetic Reaching Law clear; clc; T=10; step=0.1; epsilon = 1; s=5; s_re = [0;s]; for t=0+step:step:Ts = s + step * (-epsilon*sign(s));s_re = [s_re [t;s]]; end figure plot(s_re(1,:),s_re(2,:))% Exponential Reaching Law clear; clc; T=10; step=0.1; epsilon = 1; k=1; s=5; s_re = [0;s]; for t=0+step:step:Ts = s + step * (-epsilon*sign(s)-k*s);s_re = [s_re [t;s]]; end figure plot(s_re(1,:),s_re(2,:))% Power Reaching Law clear; clc; T=10; step=0.1; alpha = 0.5; k=1; s=5; s_re = [0;s]; for t=0+step:step:Ts = s + step * (-k*(abs(s))^alpha*sign(s));s_re = [s_re [t;s]]; end figure plot(s_re(1,:),s_re(2,:))總結
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