科学计算科学计算 (54).pdf

《科学计算科学计算 (54).pdf》由会员分享，可在线阅读，更多相关《科学计算科学计算 (54).pdf（16页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、9.4 Example of Simulink Simulation 9.4 Example of Simulink Simulation ApplicationApplicationSystems analysis Simulation modelSimulation results and analysisModel and simulate the bungee jumping systemAnalyze bungee jumping system through Simulink.The requirements are as follows:Build the Simulink si

2、mulation model of the bungee jumping systemAnalyze the security of the system，include：When the elasticity of the elastic rope is fixed,find out the safe weight for bungee jumpers.When the bungee jumpers weigh a certain amount,find out the minimum coefficient of elasticity of the elastic rope.1 1Syst

3、ems Systems A AnalysisnalysisThe bungee jumpers descend from the jumping platform freely.The height between the platform and the water surface is h.The length of the elastic rope is s.Take the bungee jumper as research object,and according to Newtons law of motion,F is equal to ma.We can get the dif

4、ferential equations that describe the system.The forces that bungee jumpers are subjected to include their own gravity,tension of the elastic rope and resistance of the air.Let k be the elasticity coefficient of the elastic rope.At the same time,when man stands on the jumping platform.let the lower

5、end of the elastic rope be the coordinate origin O.y is the distance of the bungee jumpers from the coordinate origin.b(y)indicates the tension of the elastic rope.The mathematical expression for this is:b yky yy(),00,0=Let m be the mass of the bungee jumper and g be the gravitational acceleration.a

6、1 and a2 are air resistance coefficients.And then the system equation can be expressed as:of which items 3 and 4 indicate the resistance of the air.The initial condition of the equation is that y(0)=-s,y(0)is the initial velocity 0.+=mgb ya y a y ymy12()|the jumping platformwater surface2 2Simulatio

7、n Simulation MModelodelLaunch Simulink.Open the model editing window.Since this differential equation contains a derivative of up to 2nd order,two integrators are needed in the simulation model.From the continuous system blockset of Simulink,an integral block can be added to the model editing window

8、 and connect.After the integration link,the second-order derivative of y yields first-order derivative of y.After the integration link,the first-order derivative of y yields y.There are two types of air resistance,both of which are related to the first-order derivative of y,the velocity.Use the gain

9、 block in the math operations blockset to indicate air resistance ratio coefficient.Use function block in the user-defined function blockset to indicate the non-linear part of air resistance.At the same time,flip the gain block and function block 180 degrees and determine their parameters.Add the ad

10、dition block to the math operations blockset,and set the parameters.And a gain block,its output is the second-order derivative of y.Back to the bungee jump system.Perform block connection for elastic rope tension.Use switch block for the tension of the elastic rope.And gain and constant blocks are r

11、equired.After setting the parameters and connecting the blocks,get the simulation model.Finally add the gravity block and the output block to get the complete simulation model.Add constant block in the signal source block to indicate the gravity of the bungee jumpers.Add an oscilloscope block in the

12、 output blockset to output the distance the bungee thrower ejects.It also outputs the bungee jumpers distance from the water surface.That is,the distance of the coordinate origin from the water surface and it is exactly h minus s and minus the distance y the bungee jumpers bounce.If the value is les

13、s than zero,it indicates the person will touch the water during the bungee,which is not safe.Add constant block addition block and oscilloscope block.Set block parameters and make connections.So,the system simulation model is built.3 3Simulation Simulation R Results and esults and A Analysisnalysis

14、m=75;g=9.8;k=20;a1=1;a2=1;h=100;s=40;m=65;Now change the weight of the bungee jumpers to 65kg.and other parameters remain the same.Check the curve at this time.The distance between the jumper and the water surface is greater than 0,so the system is safe.Therefore,when the other system parameters are

15、 determined,there is a weight requirement for bungee jumpers.(1)Calculate the maximum weight for bungee safetyfor m=100:-0.5:20t,x,y_w=sim(bengji,0:0.01:100);if min(y_w)1.5break;endenddisp(The maximum safe weight is,num2str(m)dis=min(y_w);disp(The minimum safe distance is,num2str(dis)plot(t,y_w)grid

16、 onRun the program,and get the results:The maximum safe weight is 67.5The minimum safe distance is 1.6803That is,when the elasticity of the elastic rope is 20,the safe weight is 67.5kg,and the safe distance is 1.68m.The curve of human-to-water distance change is shown.(2)Find out the minimum coeffic

17、ient m=65;for k=10:0.1:50t,x,y_w=sim(bengji,0:0.01:100);if min(y_w)1.5break;end enddisp(The minimum elasticity coefficient k is,num2str(k)dis=min(y_w);disp(The minimum safe distance is,num2str(dis)plot(t,y_w)grid onRun the program,and get the results:The minimum elasticity coefficient k is is 18.9The minimum safe distance is 1.5521The minimum safety elasticity coefficient is 18.9and the minimum distance between the bungee jumpers and the ground is 1.55m.Under the minimum safety elasticity coefficient,the simulation results of the system are shown here.