1. Session 6 - Sensor Modelling
MIO400S
Mechatronic Design and Simulation
 (Mathematical Modelling)
Session 6 - Sensor Modelling

2. What is a Sensor?
It is a device that receives and responds to a signal or stimulus.
Examples
Position sensor
Temperature sensor
Speed sensor
Voltmeter
Microphone

3. Sensor Components A sensor usually consists of The Sensor
The conditioning circuit
Both need to be modelled
Inaccuracies need to be modelled
Random errors
Systematic errors (bias)
Dynamic response

4. Sensors Contd Other characteristics of Sensors may need to be modelled
Input Range
Sensitivity
Linearity
Hysterisis
Sample rate
Slew rate
Noise

5. Sensors Contd Dynamic response
Response to a changing signal is different to that of a steady state input
The response “lags” - this is due to energy storing components in the sensor.
Examples
Intertia
Capacitance
Inductance

6. Sensors Contd Types of Dynamic behavior of sensors
Web resource
1. Zero order – responds instantaneously
2. First order – Example a Voltage sensor with an RC circuit as a filter
How do we models this – we will use the RC circuit example
The differential equation for this is
DV/dT = (1/RC)[Vin - Vc]

7. Sensors Contd This equation is modelled in Xcos/Simulink as follows
Step Input V
Integrator
Gain 1/RC
dV/dt V
Feedback
If this is plotted we see the RC curve

8. Sensors Contd 3. Second order – Example a mass spring damper
How do we models this
The differential equation for this is
Where Xddot is the acceleration A of mass m
And Xdot is the Velocity V of the mass
And x is the displacement

9. Sensors Contd This is modelled in the following way
Produces a plot as follows

10. DC Motor Simulation Example
The parameters of a measured DC motor as [resented in
And
were
Where
Input V = Source voltage
Output I = current
w = angular velocity
Parameters
R = Resistance (1 Ohm)
L = Inductance (0.1H)
J = Inertia (0.01kg*m2/s2)
K = Ke = Kt = EMF Force constant (0.05Nm/Amp)
b = damping ratio (or viscous friction)0.1Nms

11. DC Motor Contd 1
The motor torque, T, is related to the armature current, i, by a constant factor Kt. The back emf, e, is related to the rotational velocity by the following equations:
T = Ki
Back emf e = K w
Therefore
J dw/dt + b w = Ki
L di/dt + Ri = V - Kw

12. DC Motor Contd 2

13. DC Motor Contd 3