Difference between revisions of "Motor Control"
Etrain Troy (talk | contribs) (Wrote some stuff about current regulation) |
Etrain Troy (talk | contribs) (Added more sections to FOC) |
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=Six-Step Control= | =Six-Step Control= | ||
=Field Oriented Control for Synchronous Machines= | =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 | ||
==Transformations== | ==Transformations== | ||
===Clarke Transform=== | ===Clarke Transform=== | ||
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==Current Regulation== | ==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). | 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). | ||
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<math> | <math> | ||
I_{dq} = \frac{V_{dq} - V_{emf}}{R_s + sL_{dq}} | I_{dq} = \frac{V_{dq} - V_{emf}}{R_s + sL_{dq}} | ||
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| − | V_{dq} = (I_{dq,requested} - I_{dq,measured}) | + | V_{dq} = (I_{dq,requested} - I_{dq,measured}) \frac{1}{s}(k_i + sk_p)) + V_{EMF,dq} |
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</math> | </math> | ||
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| + | ==Torque Regulation== | ||
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==Surface Mount Permanent Magnet Machines== | ==Surface Mount Permanent Magnet Machines== | ||
==Interior Permanent Magnet Machines== | ==Interior Permanent Magnet Machines== | ||
| + | ==Position Feedback<br />== | ||
| + | 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. | ||
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| + | ===Resolvers & Encoders=== | ||
| + | ==Space Vector PWM== | ||
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=Field Oriented Control for Asynchronous Machines= | =Field Oriented Control for Asynchronous Machines= | ||
Revision as of 21:24, 2 June 2020
Contents
DC Brushed Motor Control
Six-Step 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
Transformations
Clarke Transform
Park Transform
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). 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 I_{dq} = \frac{V_{dq} - V_{emf}}{R_s + sL_{dq}} }
We can then write the equation for the system 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(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}} }
Torque Regulation
Surface Mount Permanent Magnet Machines
Interior Permanent Magnet Machines
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.
