Separately Excited DC Motor Cascade Speed Control ATM Milano

Tram "Carelli 1928"
Simulation Results

Simulink simulation results for the cascade PI speed controller of the ATM Carelli 1928 tramway. Three control loops — excitation current, armature current, angular speed — validated across the full 10 km urban route with slope disturbances and field-weakening region.

0%
Overshoot
≈ 0
Steady-state error
156 A
Max Ia (clamped)
≈2.6 A
Ie min (FW region)
90°
Phase margin
10 km
Track simulated

01 Simulation Overview

Simulink model implements three-loop cascade controller for separately excited DC motor driving Carelli 1928 tramway. Control hierarchy — outermost to innermost: angular speed PI → armature current PI → excitation current PI. Each loop tuned via pole-zero cancellation → 90° phase margin.

Additional features: back-EMF feedforward decoupling (cancels coupling between electrical/mechanical dynamics), anti-windup back-calculation (prevents integrator windup during saturation), rate limiter on speed reference (limits acceleration to 0.545 m/s² for passenger comfort, αmax ≈ 9.13 rad/s² at motor shaft), dynamic field-weakening above base speed (Ie,ref = En / (Ks·ω)).
Speed loop BW
2 rad/s
Armature BW
20 rad/s
Excitation BW
40 rad/s
ωbase → ωmax
101.6 → 195.3 r/s
Slope Tdist (5%)
743 Nm · 89.8%
Back-EMF at vmax
538.8 V < 600

02 Vehicle Speed — v(t)

✓ No overshoot Field weakening km 4–6
Speed profile v(t) showing vehicle speed tracking the kinematic reference across the 10 km route
// Figure 7 — Speed profile v(t) · Simulink · Carelli 1928 · PoliMi 2026

Speed profile confirms correct tracking of kinematic reference across all seven route segments. Rate limiter on ωref produces smooth linear ramps at each acceleration/deceleration phase, limiting acceleration to amax = 0.545 m/s² (passenger-comfort threshold, αmax ≈ 9.13 rad/s² at motor shaft).

Zero overshoot

PI speed loop, tuned with pole-zero cancellation, PM = 90° → reaches each reference step without overshoot. Validates bandwidth separation strategy (ωm = 2 rad/s).

Zero steady-state error

Integral action of PI eliminates steady-state tracking error at constant speed, including in presence of slope disturbances (±5% at km 3–4 and 8–9).

Field-weakening region (km 4–6)

At vmax ≈ 11.67 m/s motor operates above base speed. Speed tracking remains accurate despite excitation current dynamically reduced below nominal.

Slope disturbance rejection

At km 3 (uphill +5%) Tdist = 743 Nm — 89.8 % of Tn. PI integral action drives the steady-state error back to zero; the transient speed dip lasts τs = 1/ωm ≈ 2 s. On downhill (km 8) the armature current reverses for regenerative braking.

03 Armature Current — ia(t)

Clamped at 156 A Anti-windup ✓
Armature current ia(t) showing saturation at 156A during acceleration phases and low steady-state values at constant speed
// Figure 8 — Armature current i_a(t) · Simulink · Carelli 1928 · PoliMi 2026

Armature current confirms inner PI loop correctly limits Ia to rated value 156 A during all acceleration phases. Back-calculation anti-windup (Kb,a = 100) prevents current spikes at transitions from saturation to unsaturated operation.

Saturation at rated current

During acceleration ramps speed PI demands max torque. Saturation block clamps Ia at +156 A — max traction while protecting motor windings from thermal overload.

Anti-windup effectiveness

Back-calculation (Kb,a = 100) prevents integrator windup. Transitions saturated → unsaturated: smooth — no current spikes that would trip electrical protection.

Low steady-state current

At constant speed on flat track Ia only overcomes viscous friction (β = 0.81 Nms) → low steady-state value, efficient operation. On the 5 % uphill the gravity component alone draws ≈ 140 A; with friction included the total approaches the saturation limit of 156 A.

Regenerative braking

During deceleration km 9–10 armature current reverses → regenerative braking. Negative Ia confirms motor acts as generator, feeding energy back to DC line.

04 Excitation Current — ie(t)

Field weakening active Ie,min ≈ 2.6 A ✓
Excitation current ie(t) showing constant value at 5A in base-speed region and field-weakening reduction to ~2.6A at max speed
// Figure 9 — Excitation current i_e(t) · Simulink · Carelli 1928 · PoliMi 2026

Excitation current plot validates field-weakening strategy. Current holds at nominal 5 A until base speed reached. Beyond this point controller dynamically reduces excitation via 1/ω law — keeps back-EMF below 600 V DC supply.

Constant excitation (km 0–3, 6–10)

In base-speed region Ie held at nominal 5 A. Excitation PI (ωe = 40 rad/s, PM = 90°) tracks constant reference without error.

Field-weakening activation

As ω exceeds ωbase = 101.6 rad/s: Ie,ref = En/(Ks·ω). At ωmax = 195.3 rad/s (vmax = 42 km/h) the reference drops to ≈ 2.60 A; the resulting back-EMF e = Ks·Ie·ω = 538.8 V stays 0.05 % below En, strictly under the 600 V line voltage. Constant-power region spans a factor 1.92 in speed.

Smooth transitions

Transitions into/out of field-weakening region smooth — no underdamped oscillations. Validates 90° phase margin design for excitation loop.

Restoration to nominal

When speed ref drops below ωbase at km 6, FW block restores Ie,ref = 5 A. Excitation PI tracks step without overshoot.

05 Key Control Diagrams

Simulink diagrams illustrate main control subsystems. Cascade architecture decouples three loops via bandwidth separation (factor ≥ 10× between adjacent loops).

// Speed control scheme — overall cascade architecture
Speed control scheme of the DC machine showing the cascade PI architecture
// Excitation current loop — field weakening logic
Simulink diagram of excitation current control with field-weakening
// Armature current loop — back-EMF decoupling
Simulink diagram of armature current control with back-EMF feedforward
// Mechanical control — kinematic profile & rate limiter (amax = 0.545 m/s², αmax ≈ 9.13 rad/s²)
Simulink mechanical control subsystem with kinematic profile and rate limiter

06 Conclusions

Cascade PI architecture proves capable of controlling Carelli 1928 tram drive across full operating envelope — rated-speed traction, above-rated field-weakening, slope disturbances — while respecting every electrical and mechanical constraint.

Three design decisions proved essential: interpreting Kt as total machine constant Ks (verified by dual KVL/power-balance check), strict bandwidth separation (40/20/2 rad/s) for independent loop stability, back-calculation anti-windup to prevent integrator saturation during frequent current-limiting events typical of urban traction cycles.

Project submitted for course Dynamics of Electrical Machines and Drives (10 CFU) — MSc Automation and Control Engineering, Politecnico di Milano, under supervision of Prof. Francesco Castelli Dezza.

Full Report GitHub Repository