Switch frequency issues

[ElectroxX]

I'm trying to decide the switch frequency on a DC motor on a small robot.

The switch frequency should be higher than 1kHz as the robots speed regulator with a cascaded average current regulator is designed to work at a sampling rate of 1 kHz and therefore at least one whole PWM period should be averaged between each iteration.

The upper limit seems trickier. I thought that having a switching period a lot shorter than the motors L/R time constant would drive the current low, as the motor wouldn't get the time to build up a significant current.

However after playing around a little bit with paper and pen and the laplace transform with initial values I understand that there will be some sort of accumulation of current between each switch period.

Before spending too much time perhaps walking in the wrong direction, I ask if there is some simple analytical expression that can be used to calculate the average motor current related to L/R, the switch frequency and the duty cycle or do I need to simulate/try out this?

Tips about publications regarding this is appreciated.

 

[chuckey]

If the robot already has a speed regulator, then this is the way to control its speed. What do you hope to achieve by feeding the controller with PWM? In general most, non low-inertia motors have sufficient mechanical inertia with their added L/R time constant that they will appear to run properly at any PWM frequency over a few hundred hertz. The switching frequency once over the lower limit, can be anything,limited only by the switching losses and radiation problems. The motor speed is governed by the mark/space ratio of the PWM not its frequency.
Frank

 

[ElectroxX]

I want the current regulator cascaded with the speed controller. This is a common way to improve DC motor speed controller performance, as it helps removing disturbances in the fast electric circuit before it these affect the slower speed control loop. Also it's a linearisation of the very non linear PWM-actuator and will make the speed controller behave more equally regardless of what power source is used.

More on cascade control:
https://blog.opticontrols.com/archives/105

Anyhow, back to the switch frequency issue