Lab 03: SRV02 Position Control | Anuranan Bharadwaj

Lab Overview

Course: AE 443 – Experimental Dynamics and Control Laboratory (Bernardo Restrepo / Jared Getz) | March 13, 2026
Objective: Design PV (proportional-velocity) and PIV controllers for the SRV02 load shaft position, validate transient performance against second-order specifications (t_p = 0.20 s, PO = 5%), and demonstrate elimination of ramp tracking steady-state error by adding an integral term.
Plant parameters: K = 1.53 rad/s/V, τ = 0.0254 s
Control structure: PV = proportional + velocity feedback; PIV adds integral action to reduce e_ss under ramp input
Design specs: Desired ζ = 0.69, ω_n = 21.7 rad/s (from t_p = 0.20 s, PO = 5%)

Simulated step response — PV (Fig. 1)

Filtered PV step response (Fig. 2)

Implemented PV step response (Fig. 3)

Controller Design

The desired transient response (t_p = 0.20 s, PO = 5%) was converted to second-order system parameters: ζ = 0.69 and ω_n = 21.7 rad/s. The PV controller gains were then derived from the closed-loop pole placement equations:

k_p = τω_n² / K = 7.82 V/rad k_v = (2ζω_nτ − 1) / K = −0.157 V·s/rad

Maximum allowable k_p was bounded by the amplifier limit V_max = 10 V: k_p,max = 28.7 V/rad for a 20° step, 12.7 V/rad for 45°. The ramp steady-state error under PV control (Type-1 system) was predicted as e_ss = R(1 + Kk_v) / (Kk_p) = 0.214 rad. To eliminate this, an integral gain k_i was designed: k_i = (V_max − k_p·e_ss) / (e_ss·t) = 38.9 V/(rad·s) for t = 1 s.

Ramp response — PV simulation (Fig. 4)

Ramp response — PV hardware (Fig. 5)

PIV ramp — near-zero e_ss (Fig. 7)

Results & Analysis

Test	t_p (s)	PO (%)	e_ss (rad)
Step sim (PV)	0.194	5.0	0
Step sim (filtered PV)	0.204	5.7	0.002
Step impl (PV)	0.170	7.86	0.004
Ramp sim (PV)	—	—	0.213
Ramp impl (PV)	—	—	0.186
Ramp sim (PIV)	—	—	0.005
Ramp impl (PIV)	—	—	0.007

PV step response met the 5% overshoot and 0.20 s peak time design specs in simulation; hardware showed marginally higher overshoot (7.86%) due to friction and noise.
Adding the low-pass filter slightly increased peak time but smoothed the response — e_ss remained negligible at 0.002 rad.
Adding the integral term (PIV) reduced ramp e_ss from ~0.19 rad to ~0.007 rad, confirming the Type-2 behavior introduced by the integrator.

Controller gains and design calculations

PV vs PIV ramp error comparison

Full summary table (Table 1)

MATLAB Code

The plotting script overlaid the setpoint and measured/simulated position responses. Full script: Lab 3 Appendix A.

% Plot setpoint vs measured position
figure()
plot(data_pos(:,1), data_pos(:,2))   % setpoint
hold on
plot(data_pos(:,1), data_pos(:,3))   % measured/simulated
xlabel('Time (s)')
ylabel('Load Shaft Position (rad)')
title('Measured SRV02 PV ramp response')
legend('Setpoint Position', 'Simulated Position')

% Steady-state error calculation
index = (time >= 4.9) & (time <= 9.9);
r_ss  = mean(data_pos(index, 2));
y_ss  = mean(data_pos(index, 3));
e_ss  = r_ss - y_ss;    % ≈ 0.186 rad (PV ramp), 0.007 rad (PIV ramp)

Full MATLAB script — Lab 3 Appendix A

Simulink PV controller block diagram

PIV controller with integral block