Aim :
- To plot a function yx=(x-1)*(x-3)^2*(x-9)^2 using basic Simulink blocks.
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Run Simulink example “Suspension System Comparison” and answer the following:
- What is the objective of the simulation? What are the similarities and differences between the three systems understudy?
- What are your observations from the results?
- How the oscillating velocity source is created?
1) Plotting function yx=(x-1)*(x-3)^2*(x-9)^2 using simulink
Time spanned = 10 sec
Ramp : outputs a ramp signal starting at a specified time.
Constant : Outputs the constant specified by the user.
Subtract : addition or subtraction operator.
Square : mathematical functions including logarithemic , exponential , power and modulus functions.when the function has more than 1 argument,the first argument corresponds to the top.
Product : multiply or divide inputs.
Display : displays the output of the input values fo the function.
Scope : displays the graph for the output.
Explanation:
first ramp is set up with value of 1 , the ramp is connected to the three constants with values 1,3 and 9 .now the constants are connected to the -ve terminal and the ramp is connected to the +ve terminal. The outputs from subtract is sent to the product operator , output from subtract 1 and 2 are sent to the suare operator and then to the product operator , here is the product operator all the inputs are multiplied and sent to the display and scope operator to display the final output and graph.
output graph for the function :
2) Suspension System Comparison
Theory and Objective:
Suspension system :
Suspension is the system of tires, tire air, springs, shock absorbers and linkages that connects a vehicle to its wheels and allows relative motion between the two. Suspension systems must support both road holding/handling and ride quality, which are at odds with each other.
In this project we are studying about three types of suspension system :
- The first uses the Shock Absorber block and includes linear stiffness and damping. Optional friction and hard stops are not used.
- The second shock absorber uses a Nonlinear Translational Spring and a Nonlinear Translational Damper specified by symmetric polynomials.
- The third uses a Variable Translational Spring and Variable Translational Damper.
The spring constant is varied during the simulation using open loop control and the damping coefficient adjusts to ensure critical damping is achieved. Closed loop control can be added to simulate an adaptive suspension system.
Shock absorber :
A shock absorber or damper is a mechanical or hydraulic device designed to absorb and damp shock impulses. It does this by converting the kinetic energy of the shock into another form of energy which is then dissipated. Most shock absorbers are a form of dashpot.
Non-linear spring :
A nonlinear spring has a nonlinear relationship between force and displacement. A graph showing force vs. displacement for a nonlinear spring will be more complicated than a straight line, with a changing slope.
Variable spring :
Variable Spring Supports. Variables use coiled springs to support a load and allow movement. The resistance of the coil to a load changes during compression, which is why these devices are called “variables”.
Sprung weight transfer :
Sprung weight transfer is teh weight transfered by only weight of the veichel resting on the spring and not the total weight of the veichel.The forces upon the springs are reacted by the tyres, and that contributes to lateral load transfer. Because of this interaction with the springs, this component is also referred as the elastic weight transfer of component When cornering, the sprung mass of the car will roll by an amount , the roll angle.
Unsprung weight transfer :
Unspring weight transfer is the weight of the veichel components that are not supported by the spring.
In a ground vehicle with a suspension, the unsprung mass (or the unsprung weight) is the mass of the suspension, wheels or tracks (as applicable), and other components directly connected to them, rather than supported by the suspension (the mass of the body and other components supported by the suspension is the sprung mass.
Osillating velocity :
Explanation:
sine wave with amplitude of .1 , frequency 3 and pulse from pulse generator with amplitude 1 and time period of 120 sec is sent to the product operator , then the product of all the sine and pulse generator is sent to the sum operator where they ar all added and sent to goto where the value is stored. The signal is converted into physical quantity by using simulink-PS convertor . Finally a scope operator is connected to get the ouptput in graph form.vel is used to connect the subsystem to the main simulink model.
Graph output from scope :
Observation :
The study has helped us in understanding different types of shock absorbers with respect to velocity, damper ,unsprung mass , sprung mass, tire stiffness,censor sprung mass, shock absorber and spring variations . Taking all the factors in to account we come to the conclusion that a linear shock absorber is the best one for damping the variation when veichel runs on rugged surface.
The above image is the noise to input signal ratio for the three suspension system