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K
LAB
= K
LAB
Report By: Erick Rodriguez-Seda
Lab Partner: Aaron Becker
Lab TA: Dan Block
Section: Thursday at 10:00am
Part I. Effects of Saturation Block in Simulations: ___/
Discuss the effect of the saturation block in the simulations (if any). Overlay plot for the saturated and the
non-saturated cases.
Part II. Motor DC Gain: ___/
Compute the transfer function of the system from the data obtained from the DSA. Then, compute the DC
gain (K) of the motor (Show how you solved for K). Compare the computed value with the value obtained
in Lab 4 or PreLab 5a.
Note: First, you need to rewrite the transfer function from the DSA in radians. Then, remember that
the DC gain K obtained from the DSA includes the gains of the tachometer, amplifier and compensator.
That means you need to solve for K.
K
DSA
= z
[Hz]
= p
1[Hz]
= p
2[Hz]
1 2
s s
s
p
s
p
s
z
s
K
V s
V s
Hz Hz
DSA Hz
in
tach
Part III. Real and Simulated Response of the Low and High DC
Gain Compensator: ___/
Table of M
p
, t
r
, t
s
and e
ss
___/
Table 1. Real and simulated response for low and high DC gain compensators
Low DC Gain Lead Compensator High DC Gain Lead Compensator
M
p (%) t r (ms) t s (ms) e ss
(V) M
p (%) t r (ms) t s (ms) e ss
(V)
Actual
Simulated
Lab 4
**
Simulated
Lab 6
*Values from Sections II and III of Lab 6.
**Data from simulating the closed loop system with both lead controllers and parameters found in Lab 4.
***Data from simulating the closed loop system with both lead controllers and parameters found in Lab 6 from DSA.
Discuss results in Table 1. ___/
Total: /
From Fit in DSA:
c
= PM =
o
From data in fresp.m:
c
= PM =
o
Specifications:
c
= PM =
o
Part IV. Meeting the Specifications: ___/
Did you meet the specification (Mp ≤ 15%, tr ≤ 20ms)? Discuss.
Table 2. Overshoot and Rise time for Lead Compensators and PD controller
Experimental Values M p (%) t r (ms)
Low DC Gain Lead Compensator
High DC Gain Lead Compensator
PD Controller
†
†
Use PD controller from lab 5 with gains designed in Prelab 5(c)
Part V. Bode Plots of transfer function
V s
V s
in
tach
: ___/
Plot the Bode plots (Magnitude and Phase) in dB and Degrees for the empirical data saved in fresp.m and
using the transfer function estimated by the DSA (part II of this report). Overlay both plots. Use
“semilogx” to scale the x-axis (frequency). Comment on the similarities or differences! They should match
well.
Part VI. Bode Plots of transfer function
V s
V s
in
: ___/
Use the relation between equations (6.2) and (6.3) of Lab Manual to graph the Bode plots for the transfer
function V θ / V in (in dB and degrees) using the parameters given by DSA. Use “bode” command in Matlab.
Overlay both plots. Follow hints in Lab Manual and overlay the bode plot with the data in fresp.m (after
computing V θ / V in ). They should match well.
Find the crossover frequency and phase margin. Do they meet the design specifications from PreLab 6 part
(d)? Discuss.
Part VII. Bode Plots, Closed-loop transfer function
V s
V s
in
___/
Use the transfer function from the fit (parameters obtained with DSA) and compute the closed-loop
transfer function (unity feedback). Make a Bode plot with MATLAB. Overlay both plots. They should
match well. Compute the samples of the closed-loop response of V θ / V in and overlay both plots. What is
the closed-loop bandwidth? Is it reasonable? Explain.
Attachments (8)
Plots from saturated and non-saturated responses for V in = 0.5, 5, and 50 volts (2)
