Motor Control

Field Oriented Control for Synchronous Machines

Most high performance motor controllers use field oriented control. This is due to the improved efficiency and dynamic performance of the controller

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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{dq} = (I_{dq,requested} - I_{dq,measured}) \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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G_{open loop}(s) = G(s)G_c(s) = \frac{1}{s}\frac{k_p}{L_{dq}} }

Position Feedback

Field oriented control relies on having the magnetic angle of the motor for the park transform. This can either be directly measured through an encoder or resolver (sensored control), or estimated/calculated from either the back EMF or motor impedance (sensorless control). One of the main limitations of sensorless control is that the angle is only easily estimated at either high or low speeds (depending on the method). A sensor ensures reliable angle feedback across the operating range.