Download - Lab 8. Speed Control of a D.C. motor
![Page 1: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/1.jpg)
Lab 11. Speed Control of a D.C. motor
Motor Characterization
![Page 2: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/2.jpg)
Motor Speed Control Project
1. Generate PWM waveform2. Amplify the waveform to drive the motor3. Measure motor speed4. Estimate motor parameters from measured data5. Regulate speed with a controller
ComputerSystem
12v DCMotor Tachometer
SpeedMeasurementAmplifier
9vPowerSupply Labs 11/12
![Page 3: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/3.jpg)
Goals of this lab
Experimentally determine the control system model of the motor/hardware setup Measure response to a step input
(determine time constant, gain, etc.)
This model will be used in the design of a speed controller
![Page 4: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/4.jpg)
Motor control system modeled as a feedback system
PWM signal
Tachometer + comparator/counter (period)or envelope detector (amplitude)
Software
Userentry
(systeminput)
(Frequency domain model)
![Page 5: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/5.jpg)
Simplified system modelDuty cycle of PWM signal
periodor amplitude
Switchsetting
Determineexperimentally
The PlantG(S)
ControllerC(S)
+_
Measured SignalY(S)
SetpointR(s)
ErrorE(S)
Computer Software
Motor andElectronicsControl
ActionX(S)
![Page 6: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/6.jpg)
What goes into the plant G(s)?
Amplifier dynamics Electrical dynamics (motor winding has
inductance and resistance) Mechanical dynamics (motor rotor has inertia
and experiences friction) Sensor dynamics (filter has capacitance and
resistance)
OVERALL: A 3rd order model (or higher)
![Page 7: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/7.jpg)
An Empirical Modeling Approach
Experimentally determine “plant” model, G(s)1. Apply a “step input” to the Plant
step change in the duty cycle of the PWM signal driving the motor
2. Measure the motor system “response” to this step input
measure speed change over time
3. Derive parameters of G(s) from the measured response
![Page 8: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/8.jpg)
Response y(t) of a 1st-order system to a step input x(t)
)(ty
t
Motor speed(ADC
reading)
Plant input = change in PWM duty cycle(at t = 0)
)(tx
![Page 9: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/9.jpg)
First-order system model
x(t) = system inputy(t) = system outputK = gainτ = time constant
Solution if step input applied at t=0 (step response):
System equation:
∆x = input changeat time t=0
Laplace transform (plant transfer function):
)()( tydtdytKx += τ
))(()( /τtetxKty −−∆=∆ 1
1+==
sK
sXsYsG
τ)()()(
![Page 10: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/10.jpg)
Experimentally determining G(s) for the first-order system After the transient period (t large), study output y:
At t=τ, step response is:
xyK
xKy
∆∆
=
∆=∆ Experimentally measurechange in y (after large t)to compute gain, K.
)632.0()()1()( /
xKyexKy
∆=−∆= −
ττ ττ Experimentally measure
time at which y(t) = 63.2% of final value to determinetime constant, τ.
![Page 11: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/11.jpg)
Finding gain K
t
y∆
x∆ xyK
∆∆
=
large t
![Page 12: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/12.jpg)
Finding time constant τ
τ t
y∆
t = 0
y∆6320.
x∆
ττ 5 or 4 time settling ≈
![Page 13: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/13.jpg)
Verify model in MATLAB/Simulink
(Controller to be added to this to compute the controller parameters.)
![Page 14: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/14.jpg)
Later: Design a controller in Matlab/Simulink
Select P-I-D constants to produce the desired response.•Start with P value to improve response time•Use I term to eliminate steady-state error•Use D term to further improve response
One method: Proportional-Integral-Derivative (PID) controller
dttdeKdtteKteKta D
t
IP)()()()(
0
++= ∫
Plant
![Page 15: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/15.jpg)
First-order response with delay
)(ty )( tty ∆−
tt∆
x∆
![Page 16: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/16.jpg)
First-order system with delay
tsesKsG ∆−
+=
1τ)(
represents time delay ∆ttse ∆−
![Page 17: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/17.jpg)
Second-order step response
overdamped(real, unequal poles)
underdamped
critically damped
![Page 18: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/18.jpg)
Underdamped 2nd-order model
( )( ) 22
2
2 nn
n
ssK
sXsYsG
ωζωω
++==)(
dampingfactor undamped natural
frequency
gain
![Page 19: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/19.jpg)
2nd-order model character (a) Underdamped ( 0 < ζ < 1 ) model has
complex conjugate poles:
Time constant: inverse of the |Re| part
ImRe
,2
21 1 ζωζω −±−= nn js
τ =1
ζωn
![Page 20: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/20.jpg)
Underdamped step response
t
y∆
x∆xyK
∆∆
=
overshootperiod
frequency
noscillatio dampedπω 2
=d
τ4 time settling ≈
![Page 21: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/21.jpg)
2nd-order model character (b) oscillation frequency (rad/s): Im part
overshoot (% of final value)
a function only of damping factor
ωd = ωn 1−ζ 2
% overshoot = e−
ReIm
π
×100
![Page 22: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/22.jpg)
Other 2nd-order forms Critically damped model has 2 equal poles
Overdamped model has unequal poles
( )( )21+
=s
KsGτ
( ) ( )( )11 21 ++=
ssKsG
ττ
![Page 23: Lab 8. Speed Control of a D.C. motor](https://reader030.vdocument.in/reader030/viewer/2022012019/61687cfbd394e9041f6fe56a/html5/thumbnails/23.jpg)
Lab Procedure Re-verify hardware/software from previous labs Modify software to measure the period (or voltage) of
the tachometer signal following a step input “Step input” = change in selected speed Save values in an array that can be transferred to the host
PC after the motor is stopped Plot measured speed vs. time Choose a model (1st-order? 2nd-order?) Determine model parameters and write the transfer
function G(s) Compare step response of G(s) to the experimental
response (suggested tool: MATLAB/Simulink)