Fractional-order proportional-resonant controller
A closed-loop system may include a plant (an elctric machine requiring control) and a fractional-order proportional-resonant controller. The fractional-order proportional-resonant controller may have an order greater than zero and less than or equal to one. The order for the fractional-order proportional-resonant controller may be selected to yield a target amplitude and target slope for frequency response. The frequency response may be such that a steady-state error associated with a speed of the electric machine is inversely proportional to the target amplitude and less than a predetermined threshold. The order of the controller may be 0.9.
1. A vehicle comprising:
an electric machine; and
a fractional-order proportional-resonant controller programmed
with an order greater than zero and less than or equal to one and
to generate, responsive to a signal indicative of a speed of the electric machine, a target amplitude and target slope for frequency response such that a steady-state error associated with the speed is inversely proportional to the target amplitude and less than a predetermined threshold.
2. The vehicle of claim 1 , wherein a gain of the controller is 22 dB greater than a proportional-resonant controller having same coefficients.
3. The vehicle of claim 2 , wherein the order is 0.9.
4. The vehicle of claim 3 , wherein a natural frequency of the controller is 120π Hz.
5. The vehicle of claim 4 , wherein a proportional gain is four.
6. The vehicle of claim 5 , wherein an integral gain is 300.
7. The vehicle of claim 1 , wherein the controller has a gain of at least 50 dB at 60 Hz.
8. A vehicle comprising:
an inverter for an electric machine; and
a fractional-order proportional-resonant controller programmed
with at least three degrees of freedom and an order greater than zero and less than or equal to one and
to generate, responsive to a signal indicative of a speed of the electric machine, a target amplitude and target slope for frequency response such that a steady-state error associated with the speed of is inversely proportional to the target amplitude and less than a predetermined threshold.
9. The vehicle of claim 8 , wherein a gain of the controller is 22 dB greater than a proportional-resonant controller having same coefficients.
10. The vehicle of claim 9 , wherein the order is 0.9.
11. The vehicle of claim 10 , wherein a natural frequency of the controller is 120π Hz.
12. The vehicle of claim 11 , wherein a proportional gain is four.
13. The vehicle of claim 12 , wherein an integral gain is 300.
14. The vehicle of claim 8 , wherein the controller has a gain of at least 50 dB at 60 Hz.
15. The vehicle of claim 14 , wherein a natural frequency of the controller is adjusted to coincide with a frequency demand.
16. A control system comprising:
an inverter connected to a power grid; and
a fractional-order controller having an order greater than zero and less than or equal to one, inputs having a stationary reference frame, and controller constants selected to yield a target amplitude and target slope for frequency response such that a steady-state error associated with a frequency of the power grid is inversely proportional to the target amplitude and less than a predetermined threshold, wherein a gain of the controller is 22 dB greater than a proportional-resonant controller having same coefficients.
17. The control system of claim 16 , wherein a natural frequency of the controller is 120π Hz.