2. Brief snapshot of solution
» Understand system functionality and get available technical details
» Define reference system for measurement of linear and rotational displacements in inertial frame
of reference
» At any instant‘t’, define the state of system and draw free body diagram of its individual systems.
» By applying Newton’s laws for translation and rotational motion, write force and torque balance
equations.
» Reassemble these force and torque balance equations for calculation of desired variables of
interest.
» Model these equations in Matlab-simulink (most preferable) or Easy5 or Amesim environment
for different systems and sub-systems.
» Model linear actuator system using available transfer function b/w voltage as input and actuation
Force as output. Integrate different subsystems and system to form plant model for complete
system. Provide Linear actuator Voltage as input to plant model and Primary and secondary
displacement as plant model’s Output with ‘C1’ & ‘C2’wheeldisplacement.
» Model system in simulink to calculate error between a desired primary displacement and plant
model’s calculated primary displacement. Model PI controller and connect it across plant model
with primary displacement as model output and regulated voltage as Input to plant model.
» Check secondary output of model whether it is in range or out of bounds. Below are different
options to minimize secondary displacements :
Open loop system: Carry out sensitivity analysis by varying design variables & Inputs to
the system within their tolerance band by creating different sets using crystal ball. After
carrying out this analysis, it will be clear which variables are positively or negatively
impacting the secondary displacement and how much system is sensitive by their impact.
Thereafter a sensible decision can be taken with available geometrical, practical and cost
constraints to minimize the secondary displacement.
Closed Loop system: Tune controller gains to minimize secondary displacement in
closed loop system.
3. Dimensioning
Where,
KCi,X : Transverse Spring constant in X-Direction for Ci (i=1,2) Spring
KCi,Z : Longitudinal Spring constant in Z-Direction for Ci (i=1,2) Spring
li : Distance between specified section
h : Height of Accuracy point from horizontal axis passing through CG
Define Reference ‘X’ & ‘Z’ axis
4. Assumptions
Wheels are assumed as rigid and are sliding on surface
Transfer function b/w input voltage and force output is known for linear actuator
All other dimensions and material properties are provided for calculation of mass , Centre of
gravity etc.
Springs are considered linear.
Software’s to be used
Plant modeling & Controls (Any of below soft ware’s)
Matlab-simulink
Amesim
Easy5
Miscellaneous
Crystal Ball for data set generation
Ms excel for steady state calculations
Ms power point for report generation
System dynamics state at instant‘t’
5. Note: All the displacements shown above are measured from initial position. For example: XC1 & XC2
is the relative displacement of wheels measured wrt the initial position of the wheel. For
simplification it is shown in above figure from reference axis
System 1: Free body diagram
System 1: Force and Moment Equations
7. System 3: Linear actuator
Suppose transferfunctionforlinearactuatorisknownbetweenvoltage andforce itappliestogiven
mechatronicssystem
Build plant model for subsystems
)(
)(
)(
sV
sF
sG
Voltage
Actuator
8. Integrate sub-systems to form plant model
of mechatronics system
Sensitivity analysis
Use crystal ball to generate set of inputs by using upper and lower tolerance band of design
variables and Input sets with specified distribution
Record the Models output (Secondary Displacement at accuracy Point) for complete set of
inputs and design variables.
Examine which few critical factors (Inputs and design variables) in your analysis cause the
predominance of variation in the response variable of interest ( Secondary Displacement at
accuracy Point )
Tune your design variables sensibly by analyzing below curves
