Lab 2 Report:
Modeling of Electromechanical Systems
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jh=1.070000000000000e-06;
jm=4.000000000000000e-06;
md=0.054;
rd=0.0248;
jd=0.5*md*rd.^(2);
km=0.036;
kt=0.036;
rm=6.3;
jeq=jm+jh+jd
A=(-km*kt)/(rm*jeq);
B=kt/(rm*jeq);
C=1;
D=0;
sys = ss(A,B,C,D);
figure
step(sys)
stepinfo(sys)
figure
plot(y6(:,1),y6(:,2))
figure
plot(y7(:,1),y7(:,2))
figure
plot(y8(:,1),y8(:,2))
figure
plot(y4(:,1),y4(:,2))
figure
plot(y4(:,1),y4(:,2))
hold
step(sys)
jeq =
2.1676e-05
ans =
RiseTime: 0.2315
SettlingTime: 0.4122
SettlingMin: 25.1250
SettlingMax: 27.7770
Overshoot: 0
Undershoot: 0
Peak: 27.7770
PeakTime: 1.1112
Current plot held
State-Space Model Step Response
Question 1: The rise time and settling time can be found from the step info in the code above and are
.2315 seconds and .412 seconds.
Qube-Servo Response Gain of 1
Qube-Servo Angular Displacement Output
Question 2
When the gain block was updated to account for angular displacement in degrees, we saw this
correspond to out output on the motor. Rotating the motor 360 degrees resulted in a full cycle.
Qube-Servo Constant Source
Question 3:
The response of the motor to a constant input resulted in a straight linear increase in our scopes
output. I would estimate that the scopes angular velocity would be proportional to the constant
value being fed into the motor of .4. In part a the DC gain was equal to 27, however the velocity
in this question would result in a linear velocity to reach that value.
Question 4:
The signal generator creates the signal input. The scope measures the output signal. The gain
blocks amplify our signal and the HIL write and HIL read blocks connect the model to the
physical motor. The inverse modulus block computes the accumulated output for a wrapped
signal. The addition of poles tot eh system, in our case 2200, pull the root locus of the signal to
the right, making it more unstable. The poles affect the transient response of the system. A
“zero” in our case inversely affects the signal, pulling the root locus to the left and making our
signal more stable. Zeros also affect the rise time and speed of the response.
Mathematical model vs Actual Qube-Servo Response
Mathematical model vs Actual Qube-Servo Step Response
Published with MATLAB® R2015b
Question 5
After comparing the step responses of the mathematical model vs the actual Qube-Servo, it is
clear that there is a strong correlation between the two. However, some of the amplitde is lost on
the physcial sense, likely do to lost energy and heat.
Question 6
In this lab we correctly determined the transfer function and state-space from a set of physcial
values that were given to us. Next we correctly modeled the state-space function in Matlab’s
simulink with an input signal and a scope. To physcially connect this model to our Qube motor
the QUARK software was used and a USB cable to connect the motor to our work station and
thie simulink model. Running our simulated model alongisde with the measured model of the
motor in use, proved that the model thar we calculated was accurate. This lab helped us find a
real life usage of control systems and allowed us to utilize what we learned in class within the
lab. The next step in the control system process is to build upon what we have doen so far and
find ways to control the motor for a specified speed and purpose.
TA Checks