Motor Control

Field Oriented Control for Synchronous Machines

Current Regulation

A PI controller is commonly used to regulate the phase currents. This is explained by starting with a simple motor model in the DQ-frame (the motor is represented by a voltage source, resistance, and inductance).

$I_{dq}={\frac {V_{dq}-V_{emf}}{R_{s}+sL_{dq}}}$

We can then write the equation for the system as follows:
$G(s)={\frac {I_{dq}(s)}{V_{dq}(s)-V_{EMF,dq}}}={\frac {1}{R_{s}+sL_{dq}}}={\frac {\frac {1}{L_{dq}}}{(s+{\frac {R_{s}}{L_{dq}}})}}$

The pole of the system can be cancelled out by a an appropriately tuned PI controller. The equation for the entire current controller can then be written as follows: $G_{c}(s)={\frac {V_{dq}-V_{EMF,dq}}{I_{e,dq}(s)}}=k_{p}+{\frac {k_{i}}{s}}={\frac {1}{s}}(k_{i}+sk_{p})$

More explicitly, the desired output voltage at any given point in time can be written as:
$V_{dq}=(I_{dq,requested}-I_{dq,measured})(k_{p}+{\frac {k_{i}}{s}}={\frac {1}{s}}(k_{i}+sk_{p}))+V_{EMF,dq}$

The back EMF is estimated using motor parameters and rotational speed. Also note that the entire system simplifies as follows:
$G_{openloop}(s)=G(s)G_{c}(s)={\frac {1}{s}}{\frac {k_{p}}{L_{dq}}}$