Consider the simplest case, a body is acted on only by the force that you control. You want to reach certain speed; how should you control the force. If we elect to use the proportion gain control, i.e. the force is proportion to the difference between the desired speed and the current speed. We would have an exponential speed profile, that approaches the desired speed asymptotically with a time constant of m/K, which m is the mass and K is the proportional constant.
If there is a constant force also acting on the body, such as the gravity, and we apply the proportional control, the speed profile is again an exponential with the same time constant. But now our final asymptotic speed is not the desired speed, but offseted by mg/K. So the proportional control results in a steady state error.
The common cure is to add another force that is proportional to the accumulated or integrated velocity error. Now we have a second order system. If the integrated gain is sufficiently high, we would have an oscillatory response.
Sunday, July 14, 2013
Motor winding current and supply current
When the motor drive operates in the torque mode, a constant torque implies a constant current in the motor winding. But we see the supply current varies as the motor speed changes. The supply current is at the lowest when the motor stalls and the highest when the motor moves the fastest. The total energy provided by a constant voltage source is consumed by the winding resistive loss and the work done by the motor. When the armature current is constant, the resistive loss is constant. The work done by the motor is the torque multiplied by the motor speed.
How does the motor drive keep the winding current constant when the supply varies? When the load is greater than the motor torque, the motor slows down and stalls. If the drive keeps the same PWM on period, the current would increase; so the PWM duty cycle is reduced to keep the current constant by the current loop. The PWM duty cycle is proportional to the motor speed (assume the winding resistance is small). The drive circuit draws current from the supply during the on period of the PWM cycle. The peak current is same if the constant winding current is maintained. So the average supply current is smaller when the motor speed is reduced.
Therefore to infer winding current from the supply current, the PWM duty cycle has to be known.
How does the motor drive keep the winding current constant when the supply varies? When the load is greater than the motor torque, the motor slows down and stalls. If the drive keeps the same PWM on period, the current would increase; so the PWM duty cycle is reduced to keep the current constant by the current loop. The PWM duty cycle is proportional to the motor speed (assume the winding resistance is small). The drive circuit draws current from the supply during the on period of the PWM cycle. The peak current is same if the constant winding current is maintained. So the average supply current is smaller when the motor speed is reduced.
Therefore to infer winding current from the supply current, the PWM duty cycle has to be known.
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