Lab 05: Speed Control | Anuranan Bharadwaj

Lab Overview

Course: AE 443 – Experimental Dynamics and Control Laboratory (Bernardo Restrepo / Jared Getz) | April 17, 2026
Objective: Design PI and lead compensators for SRV02 motor speed regulation, evaluate their performance in simulation and hardware, and compare them using frequency-domain stability metrics (Bode plot, gain margin, phase margin).
Plant with integrator: P_i(s) = K / [s(τs + 1)] = 1.53 / [s(0.0254s + 1)]
Stability margins: Gain Margin = ∞, Phase Margin = 87.8° at ω = 1.53 rad/s
Reference signal: Square wave alternating between 2.5 and 7.5 rad/s (step magnitude = 5 rad/s)

Bode diagram — gain and phase margins (Fig. 6)

PI step response — simulation (Fig. 1)

PI step response — hardware (Fig. 2)

Frequency-Domain Analysis & Controller Design

The plant transfer function P_i(s) = K / [s(τs+1)] was evaluated in frequency domain. The magnitude is |P_i(jω)| = K / [ω√(1 + (τω)²)]. The Bode plot shows a pole at the origin (−20 dB/decade slope) and a second pole at ω = 1/τ = 39.4 rad/s. Phase starts at −90° and approaches −180° asymptotically, never crossing −180° → Gain Margin = ∞. Phase Margin = 87.8° at the gain crossover of 1.53 rad/s. Since one pole is at s = 0, P_i(s) is marginally stable.

The PI controller adds an integrator to eliminate steady-state error for step references and uses the proportional gain for transient shaping. The lead compensator adds phase lead to improve transient response while maintaining stability margins. Both were tuned in Simulink and then deployed to the SRV02 hardware via the QUARC interface.

Lead step response — simulation (Fig. 4)

Lead step response — hardware (Fig. 5)

PI ripple — signal noise analysis (Fig. 3)

Results & Analysis

Controller / Test	t_p (s)	PO (%)	e_ss (rad/s)
PI — simulation	0.04	4.4	0
PI — hardware	0.034	23.8	−3.17×10⁻⁵
Lead — simulation	0.04	2.0	0
Lead — hardware	0.03	44.4	−0.0012

Both controllers met simulation specs; lead showed lower overshoot (2% vs 4.4%) in simulation.
On hardware, both had significantly higher overshoot than simulation due to friction, encoder quantization noise, and unmodeled dynamics.
PI hardware overshoot (23.8%) was much more moderate than lead (44.4%), making PI the preferred controller for this physical system.
Measured peak-to-peak ripple for PI: 1.16 rad/s vs. theoretical estimate of 0.525 rad/s — real encoder noise exceeded the theoretical bound.
The lead compensator is more sensitive to physical non-idealities because its derivative-like action amplifies high-frequency noise in the velocity signal.

PI vs Lead overshoot comparison

Ripple analysis — measured vs theoretical

Full summary table (Table 1)

MATLAB Code

The Bode plot was generated using MATLAB's margin() function on the P_i(s) transfer function. Response plots overlaid setpoint and measured speed. Full script: Lab 5 Appendix A.

% Plant with integrator: Pi(s) = K / [s(tau*s + 1)]
K   = 1.53;
tau = 0.0254;
s   = tf('s');
PI  = K / (s * (tau*s + 1));
margin(PI)    % Gm = Inf, Pm = 87.8 deg at 1.53 rad/s

% Speed response plot
figure()
plot(data_spd(:,1), data_spd(:,2))   % setpoint
hold on
plot(data_spd(:,1), data_spd(:,3))   % measured
xlabel('Time (s)');  ylabel('Speed (rad/s)')
title('Step response implementation with Lead Control')
legend('Setpoint', 'Measured', Location='northwest')

% Steady-state error over settling window
index = (time >= 4.9) & (time <= 9.9);
e_ss  = mean(r(index)) - mean(y(index));   % ≈ -3.17e-5 rad/s (PI)

Full MATLAB script — Lab 5 Appendix A

PI controller Simulink speed loop

Lead compensator Simulink block