System Architecture Overview

A complete FOC simulation in Simulink comprises several key subsystems:

• Motor model: Mathematical representation of a Permanent Magnet Synchronous Motor (PMSM)
• Inverter stage: Three-phase bridge inverter with PWM generation
• Coordinate trensformation blocks: Clarke and Park transforms (forward and inverse)
• Cascaded control loops: Inner current loop and outer speed loop, both using PI regulators
• Position feedback: Emulated encoder or Hall-effect sensor
• Mechanical load: Time-varying torque profile to mimic real-world conditions

Step-by-Step Modeling (PMSM Focus)

1. Define motor parameters

% Base electrical and mechanical properties
n_p = 4;           % Number of pole pairs
Rs = 0.5;          % Stator resistance (Ω)
Ld = 0.01;         % d-axis inductance (H)
Lq = 0.01;         % q-axis inductance (H)
J_rotor = 0.001;   % Rotor inertia (kg·m²)
B_visc = 1e-4;     % Viscous damping coefficient

2. Inverter implementation

Use the built-in Three-Phase Inverter block from Simscape Electrical. Set switching frequency to 10 kHz and optionally integrate a dead-time compensation unit to mitigate non-ideal switching effects.

3. Coordinate transformations

% Add Clarke transform block
add_block('simscapeelectrical/Measurements/Clarke', 'foc_model/Clarke');

% Add Park transform block
add_block('simscapeelectrical/Control/Field-Oriented Control/Park Transform', ...
          'foc_model/Park');

4. Dual-loop controller design

% Current controller gains
Kp_iq = 5.0;
Ki_iq = 0.5;

% Speed controller gains
Kp_spd = 10.0;
Ki_spd = 1.0;

% Space Vector PWM generator
add_block('simscapeelectrical/Power Electronics/SVPWM Generator', ...
          'foc_model/SVPWM');

5. Position sensor emulation

% Quadrature encoder model with 2048 pulses per revolution
add_block('simscapeelectrical/Sensors/Quadrature Encoder', 'foc_model/Encoder');
set_param('foc_model/Encoder', 'PulsesPerRevolution', '2048');

Critical Simulation Configuraton

1. Solver settings

set_param('foc_model', 'StopTime', '0.5');
set_param('foc_model', 'Solver', 'ode23tb');
set_param('foc_model', 'FixedStep', '1e-6');

2. Initial motor state

init_state.elec_angle = 0;    % Rotor electrical position (rad)
init_state.mech_speed = 0;    % Mechanical speed (rad/s)
init_state.id = 0;            % d-axis current (A)
init_state.iq = 0;            % q-axis current (A)

3. Load torque profile

% Time-dependent load: sinusoidal disturbance
loadTorque = @(t) 50 * sin(2*pi*5*t);  % 5 Hz oscillation, 50 N·m amplitude

Performance Evaluation

Key metrics to analyze include:

• Speed tracking accuracy: Rise time, overshoot, and steady-state error
• Current quality: THD computed via FFT of phase currents
• Torque ripple: Peak-to-peak variation under steady-state operation

Common tuning issues:

• Oscillatory currents often stem from misalignment between rotor angle and Park transform reference frame
• Excessive torque ripple may require retuning of current loop bandwidth
• Speed overshoot can be mitigated with feedforward decoupling or anti-windup strategies

Advanced Enhancements

Flux-weakening operation

% Limit d-axis current to enable high-speed operation
if id_cmd < -id_max
    iq_cmd = min(iq_cmd, sqrt(i_max^2 - id_cmd^2));
    flux_weakening_active = true;
end

Thermal-aware resistance compensation

% Adjust stator resistance based on estimated temperature
R_corrected = Rs * (1 + 0.0039*(temp_est - 25));

Multi-motor synchronization

% Phase-locked loop for master-slave coordination
phase_error = theta_master - theta_slave;
sync_correction = Kp_sync * phase_error;

Code Generation and Deployment

To deploy on embedded targets like TI C2000:

% Configure for C code generation
set_param('foc_model', 'SystemTargetFile', 'ert.tlc');
set_param('foc_model', 'HardwareBoard', 'TI Delfino F28379D');

% Enable ADC offset calibration
set_param('foc_model', 'ADCOffsetCalibration', 'on');

Real-time debugging can be achieved by streaming variables over SCI or capturing signals via external mode scopes.