基于MATLAB实现的悬臂梁振动主动控制，包括悬臂梁振动动力学模型，悬臂梁振动力学分析，悬臂梁的PID控制仿真+使用说明文档

clc,clear E=70*10^9;%弹性模量 de=2700;% 密度 l=0.8;% 长 b=50*10^(-3);% 宽 h=3*10^(-3);% 高 I=b*h^3/12;% 惯性矩 A0=b*h;%横截面积 b11=1.875; b21=4.694; b31=7.855; b41=10.996; b1=b11/l; b2=b21/l; b3=b31/l; b4=b41/l; %前4阶固有频率 w1=b1^2*sqrt(E*1/(de*A0)); w2=b2^2*sqrt(E*I/(de*A0)); w3=b3^2*sqrt(E*I/(de*A0)); w4=b4^2*sqrt(E*I/(de*A0)); w=[w1,w2,w3,w4];%角频率(rad) f=w/2/pi;%频率(Hz) rl=-(cos(b11)+cosh(b11))/(sin(b11)+sinh(b11)); r2=-(cos(b21)+cosh(b21))/(sin(b21)+sinh(b21)); r3=-(cos(b31)+cosh(b31))/(sin(b31)+sinh(b31)); r4=-(cos(b41)+cosh(b41))/(sin(b41)+sinh(b41)); syms x Y01=cos(b1*x)-cosh(b1*x)+rl*(sin(b1*x)-sinh(b1*x)); Y02=cos(b2*x)-cosh(b2*x)+r2*(sin(b2*x)-sinh(b2*x)); Y03=cos(b3*x)-cosh(b3*x)+r3*(sin(b3*x)-sinh(b3*x)); Y04=cos(b4*x)-cosh(b4*x)+r4*(sin(b4*x)-sinh(b4*x)); C1=double(sqrt(l/int(de*A0*Y01^2,x,0,l))); C2=double(sqrt(l/int(de*A0*Y02^2,x,0,l))); C3=double(sqrt(l/int(de*A0*Y03^2,x,0,l))); C4=double(sqrt(l/int(de*A0*Y04^2,x,0,l))); x=0:0.001:l; Yl=C1*(cos(b1*x)-cosh(b1*x)+rl*(sin(b1*x)-sinh(b1*x))); Y2=C2*(cos(b2*x)-cosh(b2*x)+r2*(sin(b2*x)-sinh(b2*x))); Y3=C3*(cos(b3*x)-cosh(b3*x)+r3*(sin(b3*x)-sinh(b3*x))); Y4=C4*(cos(b4*x)-cosh(b4*x)+r4*(sin(b4*x)-sinh(b4*x))); hf=figure('units','normalized','position',[0.4 0.4 0.5 0.4]); % [x,y,宽，高] plot(x,zeros(1,length(x)),'.') hold on plot(x,Yl,'-') plot(x,Y2,'--') plot(x,Y3,':') plot(x,Y4,'-.') legend('参考位置','一阶主振型','二阶主振型','三阶主振型','四阶主振型') web('http://www.ilovematlab.cn/forum-235-1.html','-browser')