Electrical and Computer Engineering Homework Solutions
Problem
#15527

Develop a state space model for a mass m on a smooth horizontal surface

Develop a state space model for a mass m on a smooth horizontal surface. Assume that the friction force acting on the mass is Bv Newtons, where v is the horizontal velocity of the mass. Your model should output (i) the horizontal displacement to the right of an arbitrary reference point on the horizontal surface x, (ii) the velocity of the mass relative to the reference point v, (iii) the acceleration of the mass relative to the reference point, (iv) the momentum of the mass, and (v) the kinetic energy of the mass.Use this model to investigate and understand the dynamic behaviour and response of this system to a horizontal disturbing force F via simulations in Simulink.Modify your model in part 1 above to determine the effect of dynamically tilting the horizontal surface by an input angle a(t) relative to the positive x-axis.

Attached file(s):
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BLOCK.doc  View File
simulink.zip  View File

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BLOCK.doc


REFER TO THE SCHEMATIC ABOVE WHICH SHOWS THE FORCES ACTING ON THE BLOCK
OF MASS m . THE FORCE Bv IS THE FRICTIONAL FORCE . WE NEGLECT SURFACE
FRICTION IN THIS CASE .WE CONSIDER ONLY AIR FRICTION. X IS THE
DISPLACEMENT FROM THE LIGHT BLUE LINE . THE REFERENCE POINT OF THE
BLOCKIS ON THE LIGHT PURPLE LINE. HERE IS THE EQUATION OF FORCES WHICH
I GOT,

. – eqn1

SO BEFORE DOING THE ACTUAL MODEL OF THE SYSTEM , DO THE FFG . STEPS :

STEP1 --- For part 1 GET eqn1 INTO ITS STATE VARIABLE REPRESENTATION.

STEP2 --- IDENTIFY THE STATE VARIABLE AND DETERMINE ANY RELATIONSHIP
BETWEEN THEM

STEP3 --- IDENTIFY THE INPUTS AS WELL AS THE OUTPUTS YOU ARE INTERESTED
IN .

STEP4 --- SIMULATE THE DYNAMIC BEHAVIOUR OF THE STATE SPACE MODEL USING
SIMULINK – DEVELOP THE MODEL FILE

STEP 5 --- SHOW AS WELL AS PROVIDE written STEPS AS HOW I CAN SIMULATE
THE BEHAVIOUR AND COMMENT ON THE ENERGY TRANSFORMATIONS WITHIN THE
SYSTEM .

STEP 6 --- Modify your model in part 1 above to determine the effect of
dynamically tilting the horizontal surface by an input angle a(t)
relative to the positive x-axis. Note that when this happens the block
will now start to slide down. There the displacement now will be in the
negative direction . We are creating a kind of see-saw effect . So we
have to develop another state –space model for this situation where
the block is on an incline and at an angle a(t) just like in step 1 , 2
and 3 .

Step 7 --- SIMULATE THE DYNAMIC BEHAVIOUR OF THE STATE SPACE MODEL USING
SIMULINK – DEVELOP THE MODEL FILE

Step 8 --- SHOW AS WELL AS PROVIDE written STEPS AS HOW I CAN SIMULATE
THE BEHAVIOUR AND COMMENT ON THE ENERGY TRANSFORMATIONS WITHIN THE
SYSTEM – most importantly ;determine the effect of dynamically tilting
the horizontal surface by an input angle a(t) relative to the positive
x-axis.

STEP9 --- E-MAIL THE SIMULINK FILEs TO MY E-MAIL ADDRESS BELOW :
HYPERLINK "mailto:mwanwarl@mweb.co.za" mwanwarl@mweb.co.za AND SUBMIT
THE REST OF THE SOLNS TO THE WEBSITE

x

mm





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