Field-oriented control for motors

DSCs can shut down PWMs in case of catastrophic faults signaled via digital inputs. European customers can use a DSC-based active powerfactor correction (PFC) to meet that continent’s stringent energy regulations. The only additional component s ne ede d for PFC are an inductor, power switch, and a diode. ADCs on the DSC measure current and voltage from the dc power bus. Based on these inputs, the DSC adjusts the power switch through a PWM module via a PID control loop that keeps power factor close to unity. Without the already present DSC, PFC requires an extra ASIC or many additional components.

How FOC works
FOC of permanent-magnet synchronous motors starts by measuring two of three phase currents, ia and ib. Only two current sensors are needed as third phase current is calculated from ia + ib + ic = 0. The Clarke Transform converts three-phase currents onto a two-axis plot to create variables Iα and Iβ. As viewed from the perspective of the stator, Iα and Iβ are time-varying quadrature-current values.

The two-axis plot is rotated to align with the rotor flux using transformation angle θ. Angle θ is calculated during the last iteration of the control loop. This conversion provides id and iq variables from Iα and Iβ. The Park Transform aligns quadrature currents id and iq with the rotating plot. Both id and iq remain constant during steady-state conditions.

Id, iq and the reference values for each generate error signals. The id reference controls rotormagnetizing flux while the iq reference governs motor torque output. These error signals are fed to proportional-integral (PI) controllers whose outputs are sent to the motor as voltage vectors Vd and Vq.

Vd and Vq are rotated back into the stationary reference frame using the transformation angle to obtain quadrature voltage values, Vα and Vβ. Vα and Vβ are then mathematically transformed back into three phase-voltages Va, Vb, and Vc, which determine the new PWM duty-cycle.

The new coordinate transformation angle is then estimated using Vα, Vβ, Iα, and Iβ as inputs. The new commutation angle guides the FOC algorithm in placing the next voltage vector.

Of course, to determine the required phase voltages it’s necessary to know the current position of the rotor relative to the three phase windings. An encoder or resolver could supply that information, but at added cost and complexity. However, you can estimate the rotor position using motor currents and voltages.

The position estimator starts with a mathematical model to measure motor position indirectly with an observer. Motor position is estimated by assuming the PMSM model is the same as that of a dc motor. The model consists of a series circuit containing the winding resistance, R, winding inductance, L, and the back-EMF, e. Input voltage, v_s, i_s obtained using:

vs = Ris + L	d	is + es
dt

Solving for motor current, i_s, gives:

d	is = -	R	is +	1	(vs - es)
dt	L	L

In both equations, v_s = input voltage and e_s = back-EMF vector.

Current observers indirectly measure back-EMF by ensuring the input to the motor and model are equal. When the motor and its model are fed the same input, the model’s closed-loop controller ensures the estimated value matches the measured value. A sliding-mode controller tracks the input reference and forces the error to zero, correcting the model to make it more accurate.

Depending on the error’s sign, the slide-mode controller applies positive or negative feedback gain, K, to get the estimated current to match measured current. Once estimated and measured currents match, and input voltages are the same for the motor and its model, the motor back-EMF is calculated by solving for e_s. The input currents and voltages then match between the model and actual motor, the model’s correction factor, z, can be filtered to determine the model’s back-EMF.

The FOC algorithm is made up of three operational states: motor stopped; open-loop FOC; and sensorless FOC. When the start button is pressed, the algorithm first enters the initialization state, where variables are set to initial values.

To accurately estimate rotor position, the motor must run at a minimum speed to return a useful back-EMF value. An open-loop start-up procedure helps get the motor up to minimum speed. At motor start-up, sinusoidal voltages from the DSC spin the rotor. Current components for torque (iq) and flux production (id) are manipulated by the FOC based on the model only because there is not enough back-EMF at this point. Current components id and iq are controlled during motor start-up to keep torque constant. The start-up procedure accelerates the rotor by using an internal ramp function to increment angle θ every control cycle until the motor reaches minimum speed.

Once at minimum speed, the speed controller is added to the execution thread and the algorithm switches over to sensorless FOC operation. Here the desired speed is continuously read from an external voltage reference to set motor rpm. Fault inputs, as well as the start/stop button, are monitored continuously. Any fault in the controller stops the motor and returns the algorithm to the “Motor Stopped” state.

Many vendors offer FOC algorithms for free. Usually the source code is downloadable from the Web or comes packaged with a motor-control development board. Graphical-user interfaces in some development software present operation feedback for quick analysis and let engineers quickly change program variables for testing.

Make Contact
Microchip Technology Inc.,
(480) 792-7200, microchip.com