系统模型频率响应分析与平衡降阶方法

# 系统模型频率响应分析与平衡降阶方法 ## 1. 结果绘图 ### 1.1 绘图代码概述 以下代码用于绘制包含所有 50 个模式的模型的频率响应，并叠加各个模式的贡献。同时，还会绘制采样频率响应，并与原始 50 模式模型响应进行比较。最后，绘制两个降阶模型，包括各个模式的贡献。工作区将保存为 act8_data.mat，供后续使用。 ```matlab magddb = 20*log10(magd); % start plotting % plot all modes included response loglog(f,mag(index_out,:),'k.-') title([headstr ', gap displacement, all ',num2str(num_modes_total),' modes included']) xlabel('Frequency, hz') ylabel('Magnitude, mm') axis([500 25000 -inf 1e-4]) grid off disp('execution paused to display figure, "enter" to continue'); pause hold on max_modes_plot = num_modes_total; for pcnt = 1:max_modes_plot index = 2*pcnt; amode = a(index-1:index,index-1:index); bmode = b(index-1:index); cmode = c_disp(7:8,index-1:index); dmode = [0]; sys_mode = ss(amode,bmode,cmode,dmode); [mag_mode,phs_mode]=bode(sys_mode,frad) ; mag_modedb = 20*log10(mag_mode); loglog(f,mag_mode(index_out,:),'k-') end axis([500 25000 -inf 1e-4]) disp('execution paused to display figure, "enter" to continue'); pause hold off loglog(f,mag(index_out,:),'k-',fd,magd(index_out,:),'k.-') title([headstr ', gap displacement, all ',num2str(num_modes_total), ... ' modes included, Nyquist frequency ',num2str(nyquist_freq),' hz']) xlabel('Frequency, hz') ylabel('Magnitude, mm') legend('continuous','discrete') axis([500 25000 1e-8 1e-4]) grid off disp('execution paused to display figure, "enter" to continue'); pause if num_modes_used < num_modes_total % calculate and plot reduced models % sorted modal truncation loglog(f,mag(index_out,:),'k-',f,mag_sort_red(index_out,:),'k.-') title([headstr ', sorted modal truncation: gap displacement, first ', ... num2str(num_modes_used),' modes included']) legend('all modes','sorted partial modes',3) xlabel('Frequency, hz') ylabel('Magnitude, mm') axis([500 25000 1e-8 1e-4]) grid off disp('execution paused to display figure, "enter" to continue'); pause hold on for pcnt = 1:max_modes_plot index = 2*pcnt; amode = a_sort(index-1:index,index-1:index); bmode = b_sort(index-1:index); cmode = cdisp_sort(7:8,index-1:index); dmode = [0]; sys_mode = ss(amode,bmode,cmode,dmode); [mag_mode,phs_mode]=bode(sys_mode,frad) ; loglog(f,mag_mode(index_out,:),'k-') end axis([500 25000 -inf 1e-4]) disp('execution paused to display figure, "enter" to continue'); pause hold off % modred using 'mdc' loglog(f,mag(index_out,:),'k-',f,mag_mdc(index_out,:),'k.-') title([headstr ', reduced matched dc gain: gap displacement, first ', ... num2str(num_modes_used),' sorted modes included']) legend('all modes','reduced mdc',3) xlabel('Frequency, hz') ylabel('Magnitude, mm') axis([500 25000 1e-8 1e-4]) grid off disp('execution paused to display figure, "enter" to continue'); pause hold on for pcnt = 1:max_modes_plot index = 2*pcnt; amode = a_sort(index-1:index,index-1:index); bmode = b_sort(index-1:index); cmode = cdisp_sort(7:8,index-1:index); dmode = [0]; sys_mode = ss(amode,bmode,cmode,dmode); [mag_mode,phs_mode]=bode(sys_mode,frad) ; loglog(f,mag_mode(index_out,:),'k-') end axis([500 25000 -inf 1e-4]) disp('execution paused to display figure, "enter" to continue'); pause hold off % modred using 'mdc' with unsorted modes loglog(f,mag(index_out,:),'k-',f,mag_mdc_nosort(index_out,:),'k.-') title([headstr ', reduced unsorted matched dc gain: gap displacement, first ', ... num2str(num_modes_used),' sorted modes included']) legend('all modes','reduced mdc',3) xlabel('Frequency, hz') ylabel('Magnitude, mm') axis([500 25000 1e-8 1e-4]) grid off disp('execution paused to display figure, "enter" to continue'); pause hold on for pcnt = 1:num_modes_used index = 2*pcnt; amode = a(index-1:index,index-1:index); bmode = b(index-1:index); cmode = c_disp(7:8,index-1:index); dmode = [0]; sys_mode = ss(amode,bmode,cmode,dmode); ```