Stepper motor driver circuits

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Stepper motor driver circuits

Stepper motor performance is strongly dependent on the driver circuit.

Torque curves may be extended to greater speeds if the stator poles can be reversed more quickly, the limiting factor being the winding inductance.

To overcome the inductance and switch the windings quickly, one must increase the drive voltage.

This leads further to the necessity of limiting the current that these high voltages may otherwise induce.

L/R driver circuits

L/R driver circuits are also referred to as constant voltage drives because a constant positive or negative voltage is applied to each winding to set the step positions.

However, it is winding current, not voltage that applies torque to the stepper motor shaft.

The current I in each winding is related to the applied voltage V by the winding inductance L and the winding resistance R.

The resistance R determines the maximum current according to Ohm's law I=V/R.

The inductance L determines the maximum rate of change of the current in the winding according to the formula for an inductor dI/dt = V/L.

Thus when controlled by an L/R drive, the maximum speed of a stepper motor is limited by its inductance since at some speed, the voltage U will be changing faster than the current I can keep up.

In simple terms the rate of change of current is L / R (e.g. a 10 mH inductance with 2 ohms resistance will take 5 ms to reach approx 2/3 of maximum torque or around 24 ms to reach 99% of max torque).

To obtain high torque at high speeds requires a large drive voltage with a low resistance and low inductance.

With an L/R drive it is possible to control a low voltage resistive motor with a higher voltage drive simply by adding an external resistor in series with each winding.

This will waste power in the resistors, and generate heat. It is therefore considered a low performing option, albeit simple and cheap.

Laplace Transfrom Analysis Example 

Chopper drive circuits

Chopper drive circuits are referred to as constant current drives because they generate a somewhat constant current in each winding rather than applying a constant voltage.

On each new step, a very high voltage is applied to the winding initially.

This causes the current in the winding to rise quickly since dI/dt = V/L where V is very large.

The current in each winding is monitored by the controller, usually by measuring the voltage across a small sense resistor in series with each winding.

When the current exceeds a specified current limit, the voltage is turned off or "chopped", typically using power transistors.

When the winding current drops below the specified limit, the voltage is turned on again.

In this way, the current is held relatively constant for a particular step position.

This requires additional electronics to sense winding currents, and control the switching, but it allows stepper motors to be driven with higher torque at higher speeds than L/R drives.

Integrated electronics for this purpose are widely available.

https://en.wikipedia.org/wiki/Stepper_motor

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RC충전

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RC방전

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라플라스 변환(Laplace transform)은 어떠한 함수 f(t)에서 다른 함수로의 변환으로, 선형 동역학계와 같은 미분 방정식을 풀 때 유용하게 사용된다. 피에르시몽 라플라스의 이름을 따 붙여졌다.

라플라스 변환을 이용하면, 미분 방정식을 계수방정식으로 변환하여, 문제들을 쉽게 해결 할 수 있는 장점이 있다.

https://ko.wikipedia.org/wiki/%EB%9D%BC%ED%94%8C%EB%9D%BC%EC%8A%A4_%EB%B3%80%ED%99%98