SIMULINK: 3 ASSIGNMENT SERIES

ASSIGNMENT 1:

AIM: To determine the work done as the tool moves through a distance of 100 mm.

The force on a cutting tool of a shaping machine varies over the length of cut as follows:

Distance (mm) 0 20 40 60 80 100

Force (kN) 60 72 65 53 44 50

THEORY:

Work done=`int F.ds`

Which is, effectively area under the graph F vs displacement. Since the displacement of the object is only along one direction the distance covered is equal to the displacement of the object at any given point of time.

The F vs displacement graph plotted using 'signal builder block' is

SIMULINK MODEL TO CALCULATE THE AREA:

We feed in the above graph generated by the signal builder block to an integrator block and connect it to the display block to show us the final result.

The final result i.e Work done is 5780 Joules.

ASSIGNMENT 2(a):

AIM:To create two array data sets x = [22 3 55.6 9 12 10] and y = [5 31 95 56.3 77 61] from the command window and develop a Simulink model to implement equation z=3x²-5y+18

The results are to be stored using the To File block.

MODEL:

We first generate two arrays named X and Y in the command window.

This results in the creation of these two variables in the workspace

We use GAIN block and SQUARE block to implement equation z=3x²-5y+18 in simulink

SIMULINK MODEL:

Since we input an array of values for X and Y we get the output result also in the form of an array that is displayed using a display block.

And as stated in the aim we are required to export this data to the same MATLAB workspace. For this, we use TO FILE block where we create a new challenge.mat file which is to be stored in the same current folder as this Simulink model that can be accessed from the same MATLAB workspace where we defined the X and Y values.

We note that the challenges.mat has been created in the same current and can be accessed from the same MATLAB workspace where we defined the X and Y values.

ASSIGNMENT 2(b):

AIM:

To plot a function `y(x)=(x-1)*(x-3)^2*(x-9)^2` using basic Simulink blocks.

Basic blocks used here are:

• Ramp is used in place of x(because it is set with a slope of 1 for 10 seconds)

• Display is used to display the final value of the function.

• Scope is used to display the function variation with time in the form of a graph

• Product multiplies the inputs

• Divide operator is used for division operations to the inputs

The arrangement for the plot is:

The plot is run for 10 seconds which means the input x has a domain of 0 to 10 with an increment of 1 each time.

The graphical plot:

RESULT:

The graph is plotted.

ASSIGNMENT 3:

AIM:To read and analyze the inbuilt model named Mass-Spring-Damper which is designed both in Simulink and Simscape

OVERALL MODEL AND EXPLANATION:

This example shows two models of a mass-spring-damper

1.A model with Simulink input/output blocks

This model uses signal connections, which define how data flows from one block to another.

2.Another using Simscape physical networks.

The Simscape model uses physical connections, which permit a bidirectional flow of energy between components.

Physical connections using the Simscape physical networks make it possible to add further stages to the mass-spring-damper simply by using copy and paste but, Input/output connections in the simulink model require rederiving and reimplementing the equations.

The initial deflection for the spring is 1 meter.

This is given as input in the block parameters for the Spring in the simscape model.

and for the Simulink model we define it as an initial condition in one of the Integrator blocks.

THE GOVERNING EQUATION OF THE MASS SPRING DAMPER SYSTEM:

`mddot(x)+bdot(x)+kx=0`

THE GRAPH FOR VELOCITY OF MASS WITH RESPECT TO TIME:

This graph is for the default value of the variables b,k,m i.e

b=100 N/(m/s)

k=1000 N/m

m=1Kg

Now we try changing the initial displacement to the simulink model alone to x=2 m

Now we change the values of k,m and adjust b to ensure critical damping takes place.

Let us take k=5000 N/m and m=2Kgs

to ensure critical damping `b=sqrt(k.m)`therefore we adjust b=200 N/(m/s).

For these values and the same initial displacement of the spring, we get the graph to look like this

We note that there is no oscillation and the mass comes to rest <0.5 seconds.

Now we change the values of k,m and adjust b to ensure over damping takes place.

Let us take k=5000 N/m and m=2Kgs

to ensure over damping our b value should be greater than 200N/(m/s)

therefore we take a value of b=300N/(m/s)

For these values and the same initial displacement of the spring, we get the graph to look like this

We note that the mass does not come to rest even at 1.5 seconds.

Therefore we infer that for perfect damping it is not good to act greedy and increase the gaming coefficient. WE NEED TO CALCULATE THE CRITICAL DAMPING FACTOR ACCORDING TO spring stiffness coefficient and mass values and act wisely to place a damper with a damping factor of `b=sqrt(k.m)`.