Lab 01: Servo Modeling | Anuranan Bharadwaj

Lab Overview

Course: AE 443 – Experimental Dynamics and Control Laboratory (Bernardo Restrepo / Jared Getz) | February 13, 2026
Objective: Identify a first-order transfer function for the Quanser SRV02 servo-motor gear system by applying a square-wave step input, extracting the steady-state gain (K) and time constant (τ) from the load shaft speed response, then validating and tuning the model against measured hardware data.
Hardware: Quanser SRV02 rotary servo-motor, Q2-USB DAQ board, VoltPAQ amplifier
Software: MATLAB/Simulink 2020, QUARC real-time control toolbox
Transfer function model: Ω(s)/V_m(s) = K / (τs + 1)

SRV02 servo-motor hardware

Simulink signal generator configuration

Bump test method diagram

Procedure & Methodology

Bump Test: A square-wave voltage (amplitude 1.5 V, offset 2.0 V, frequency 0.4 Hz) was applied to the SRV02 using the Simulink model. The load shaft speed ω_l (rad/s) and motor input voltage V_m (V) were recorded over 5 seconds. The steady-state gain was computed as K_e,b = (y_ss − y_0) / (u_max − u_min), where y_ss is the steady-state speed and y_0 is the initial speed. The time constant was identified as the time for the response to reach 63.2% of the steady-state change from the step onset.

Model Validation: The Simulink model was re-run with four sets of (K, τ) values — nominal theoretical, bump-test, and two manual iterations — to overlay simulated responses against the measured speed trace. The pair producing the closest visual match was selected as the validated model.

Voltage & speed vs time — bump test (Fig. 1)

Best-fit validation K=1.68, τ=0.044 (Fig. 7)

Comparison K=0.8, τ=0.06 (Fig. 3)

Results & Analysis

Source	K (rad/s/V)	τ (s)
Nominal (theoretical)	1.53	0.0253
Bump test (experimental)	1.7866	0.048
Model validation (best fit)	1.68	0.044

K_e,b was calculated as (6.051 − 0.6912) / (3.5 − 0.5) = 1.7866 rad/s/V.
τ_e,b was found at t_63% = 1.298 s relative to step onset at 1.25 s: τ = 0.048 s.
The nominal model (K = 1.53, τ = 0.0253) under-predicted the steady-state speed and over-predicted the response speed due to parameter uncertainty and unmodeled friction.
The bump-test model improved accuracy; further manual iteration yielded the best-fit (K = 1.68, τ = 0.044), with simulated and measured responses nearly indistinguishable.
The time constant governs how quickly the motor reaches steady-state; the gain determines the magnitude of the speed output per unit voltage input.

Nominal model overlay (Fig. 5)

Validation K=1.25, τ=0.2 (Fig. 4)

Parameter summary table (Table 1)

MATLAB Code

Data was saved from the Simulink workspace and plotted with subplots showing motor voltage and load shaft speed. The bump test gain and time constant were read from cursor coordinates on the MATLAB figure. Full script: Lab 1 Appendix B.

% Plot voltage and rotational speed vs time
figure();
subplot(2,1,1)
plot(Vm(:,1), Vm(:,2), 'r', 'LineWidth', 1.5);
grid on;
xlabel('Time (s)');  ylabel('Voltage (V)');

subplot(2,1,2)
plot(wl(:,1), wl(:,2), 'LineWidth', 1.5);   % measured
hold on
plot(wl(:,1), wl(:,3), 'LineWidth', 1.5);   % simulated
grid on;
xlabel('Time (s)');  ylabel('Rotational Speed (rad/s)');

% Bump test gain calculation
K_eb = (y_ss - y_0) / (u_max - u_min);       % = 1.7866 (rad/s)/V

% Time constant: locate t at 63.2% of steady-state change
y_63 = 0.632 * y_ss;                          % ≈ 3.824 rad/s
% From cursor: t1 = 1.298 s, t0 = 1.25 s
tau_eb = t1 - t0;                             % = 0.048 s

Full MATLAB script — Lab 1 Appendix B

Simulink model: q_srv02_mdl

Workspace .mat data files