WEEK 1 CHALLENGE - (SIMULINK BASICS)

PROJECT NAME – SIMULINK BASICS

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

Here, we have stop time for 10 seconds so we get 10 values of x. that is why we have 10 divisions on x – axis. The y axis shows the values of calculated y(x).

Run Simulink example “Suspension System Comparison” and answer the following:

1. What is the objective of the simulation? What are the similarities and differences between the three systems understudy?
2. What are your observations from the results?
3. How the oscillating velocity source is created?

1. What is the objective of the simulation? What are the similarities and differences between the three systems understudy?

Simulink is the block diagram environment for model based design and for multi domain simulation. It supports automated code generation, simulation, system code design, continuous test and verification of embedded systems. Simulink also provides modelling solvers, dynamic system simulation, customizable block libraries, graphical editor, it is integrated with MATLAB and also provides incorporation of MATLAB algorithms into exporting simulation & incorporation of MATLAB algorithms into models to MATLAB for further analysis.

Simulink acts as a visual tool for doing computational simulations. It uses drag and drop system for simulation components that can be connected to each other with the help of lines also we can configure the components and we can use components that allow mathematical operations.

It is mostly used in engineering where you can represent your system as a set of variables and model it mathematically. Some examples are electrical systems, mechanical components, hydroelectric drives, thermal systems, Simscape models etc. which can be controlled and its applications are Robotics, Cars, Aeroplanes, Chemical industry pipelines, Valves & Switches.

It is the great way to model your systems as it is very visual and suited for many applications that are not very specific. The disadvantage is that this system is very expensive and proprietary and used by industries.

Simulink is a graphical modelling & simulation environment for dynamic system. You can create block diagrams, where block represents part of the system. A block can represent part of the system, a physical component, a small system or a function and the input/ output system fully characterizes the block.

Simulink data handling is divided into three categories-

Signals – Blocks input and outputs, computed during simulation.

States- internal values, representing the dynamics of the blocks, controlled by the user.

Parameters- Values that effect the behaviour of the block, controlled by the user.

At each step Simulink computes new values for signals and states. By contrast you specify parameters when you build the model and can change them when simulation is running.

This is the Home screen of Simulink

This is the library where we can use tools as per our need and application.

Suspension System Comparison-

This system shows the three sets of springs and dampers excited by same oscillating velocity source.

In above suspension system there are 3 different suspensions are used to compare and study the suspension system.

1. Non – Linear Spring - it has a nonlinear relationship between displacement and force. A graph showing force vs. displacement for a nonlinear spring will be more complicated than a straight line, with changing slope.
2. Linear spring – A linear spring has a nonlinear relationship between force and displacement are directly proportional to each other. A graph showing force vs. displacement for a linear spring will be a straight line with a constant slope.
3. Shock Absorber – A spring mass damper system consists of discrete mass modes distributed throughout an object & interconnected via a network of spring and damper.
4. Variable spring – In this pitch varies but diameter of the coil remains the same.
5. Damper – it resists the motion via viscous friction, in physical systems, damping is produced by the processes that dissipate the energy stored in the oscillation.
6. Stiffness - the stiffness (K) of a body is a measure of the resistance offered by the elastic body to deformation.
7. Sprung & Unsprung mass – In an automobile the sprung mass act as a very important role which refers to the part which is dependent on the spring is called as sprung mass. The parts which are independent to the suspension is called unsprung mass.
8. Natural Frequency - Natural frequency is the rate at which object vibrates when it is not disturbed by an outside force.

The above model also includes scope block, spectrum analyser, sensor block, spring block, stiffness block, damper block, mass block, velocity source block, solver configuration block etc……….

Why Suspension is important?

The main function of the suspension is to keep the road wheel in contact with the road surface as much as possible because all the road or ground forces acting on the vehicle and keep the vehicle on the road surface through contact patches of tyres. The suspension also protects the vehicle itself and any cargo or luggage from damage and wear. Also keeps passengers comfortable.

Suspension System Comparison-

The spring constant is varied during the velocity simulation using open loop control and damping coefficient adjusts to ensure critical damping is achieved. Closed loop control can be added to simulate an adaptive suspension system.

Oscillating velocity source –

Oscillating Velocity Source is created by the flow chart as shown.

Pulse generator and sine wave combined to produce new velocity (x) and again those are combined twice to produce two more velocity values.

The above model is input velocity for all the suspension systems. the Simulink PS- Converter block used to convert block value to physical system value to the model. The value is used to velocity source which is common for all the suspension system. The block represents an ideal source of velocity that generates the velocity differential at its terminals proportional to the input physical signal and the source is powerful enough to maintain specified velocity regardless of the force exerted on the system. The velocity refers to suspension movement which is indirectly the vehicle moving on uneven road surface which creates vibration, the three different systems are used to study the variation of the wheel w.r.t time and displacement. In variable system the spring used is linear spring and the only difference is the patch rate and damping system which is used to connect parallel. When vibrates the spring is compressed and damper resists the motion of the spring. In nonlinear spring the spring coil diameter is varying by using nonlinear damping system. The spring mass damper system connected in a series way which reduces oscillations more when compared to other two suspension system.

Values for amplitude and frequency for the sine waves and amplitude, period and pulse width have been inputted for the sine waves and pulse generators and these graphs are multiplied using product block finally all the three products have been added to show the final plot of all three road conditions.

Common inputs have been given to the 3 suspension systems. it is basically different road conditions – one is bumpy, last one is even road still with slight minute bumps. If we zoom in on the graph of the third case, we can still see some light pulse widths below is the zoomed in plot of the third case.

Similarities and differences-

Velocity source applied to all systems which is considers as the input.

The stiffness, sprung mass & unsprung mass are also similar for all the systems.

The differences in the characteristics of absorbers used is explained above.

Results and Conclusion –

Block diagram for the given function [y (x)] was done successfully and the graph was plotted for the time vs. y(x).

The second study has helped us to understand the application of shock absorbers in real-life applications. Therefore, we could see variable shock absorber displays the best characteristics because it comes fastest to a straight line (in the graph) when the velocity is removed whereas the other two take some time to dampen to a straight line.

The yellow line represents the variable shock absorber therefore, we can see as compared to other 2. The variable has almost no or little variations when the velocity has removed.

The variable system has sudden increasing and decreasing nature with respect to the displacement and time. But the nonlinear and the spring mass damper system the variation fluctuates according to the damping system.