Assignment Task: Numerical Integration Techniques for dynamic solutions
The word count for this assignment is indicative too: 2000 words
Learning outcomes:
1. Use and evaluate industry standard simulation methods to solve appropriate engineering problems
2. Assess the need for relevant modelling systems
3. Analyze how certain factors are affecting the accuracy of a simulation
4. Use engineering software effectively and compare exact solutions with simulation generated solutions and evaluate the differences and characteristics
5. Demonstrate effective research and report writing skills
The aim of this assignment is to use Numerical Integration techniques (Euler) within a spreadsheet (Excel) to produce simulations for 1st and 2nd order systems. You will then evaluate changes to the systems in response to different initial conditions. Graphical outputs from the system should help to describe how changes in initial conditions affect each system and what factors influence the accuracy of a simulation.
Problem 1 - 1st order system
Using the handout on 1st order systems and taking the spring damper as an example, produce a spreadsheet to simulate this system. Use the following as a guide.
1 Create a column for time using an appropriate time step that can be altered.
2 Create your own initial conditions for your system for:
Spring Stiffness (k)
Damping coefficient (c)
Let Static sensitivity (s) = 1
Let Initial input (u) = 5
Let Initial condition of y = 0
Time constant (Τ) = c/k
3 Create a column to determine dy/dt firstly based on the initial conditions using
dy/dt = su - y/Τ
4 Create a column to determine the next position of yn+1 = yn+ h(dy/dt) n
This should allow you to create a simulation of the 1st order system.
5 The exact solution for a 1st order system is given as
yt = su(1-e-1/Τ) + y0e-1/Τ
Use this to create a column to give an exact solution for the 1st order system\
6 Create a column to give the % error difference between the simulated and exact results
Problem 2 - 2ndOrder System
A spreadsheet will be given to you with a simulated response of a 2nd order system based on the mass-spring-damper system given in the handout
Based on the exact solution for the 2nd order system create an exact solution column and determine % error difference between the simulated and exact results
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