Lab 3 - Aero Kit Rotor Speed Control

Scripts

Code snippet for calculating gains according to requirements

% Proportional gain (V.s/rad)

kp = (2*zeta*wn*tau-1)/(K)

% Integral gain (V/rad)

ki = wn^2*tau/K

Models

Variant Subsystem Block

Subsystems

Results

Given Parameters

K = 19.0; % dc gain
tau = 0.165; % time constant
tp = 0.3; % peak time (s)
PO = 5; % percent overshoot (%)

Calculated Parameters

zeta = 0.7613 % damping ratio
wn = 32.3023 % natural frequency
kp = 0.3745 % proportional gain
ki = 9.0615 % integral gain

Overview

Using $k_p$ and $1.5k_i$

tp = 0.1; % peak time (s)
PO = 8.3; % % percent overshoot (%)

Using $1.5k_p$ and $k_i$

System is not underdamped

Using $k_p$ and $k_i$

tp = 0.15; % peak time (s)
PO = 2.5; % percent overshoot (%)

Conclusion

• Requirements satisfied
• Best peak time comes from using $1.5k_i$, but overshoot becomes significantly worse
• System did not become underdamped when using $1.5k_p$

Assets