# DC motor and encoder for pendulum with low static friction

I would like to build a pendulum from scratch and model/control via Matlab. I don't know what DC motor should I use that has low friction (low static friction), so the pendulum can rotate by its self. Moreover, I would like to have an encode with "good" precision, less then 1^o. I want to control the position of the pendulum by using the motor to put energy in the system. It will be a closed loop control and the controlled variable is the voltage drop on the motor. How to check in a technical specification if the motor has low static friction?

Eg. the technical specification for a motor include:

Values at nominal voltage: Nominal voltage; No load speed; No load current; Nominal speed; Nominal torque (max. continuous torque); Nominal current (max. continuous current); Stall torque; Starting current; Max. efficiency; Terminal resistance; Terminal inductance; Torque constant; Speed constant; Speed / torque gradient; Mechanical time constant; Rotor inertia.

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– pipe
Commented Jul 28, 2016 at 11:14
• You are right, I reformulate my question.
– Elod
Commented Jul 28, 2016 at 11:22
• Do you mean inverted pendulum?
– Chu
Commented Jul 28, 2016 at 11:52
• No, just a simple pendulum, I added an image to be more specific.
– Elod
Commented Jul 28, 2016 at 12:14
• Typically this kind of thing isn't done with an ordinary motor at all, but just with an electromagnet that can influence the pendulum during part of its swing. Though if you want a "hold it at one extreme and let go" type starting mode, then yes you would need something more like an ordinary motor. Commented Sep 26, 2016 at 16:55

The problem with motors is that while static friction and dynamic friction can be addressed by selecting the right bearings, many motors have other undesiderable characteristics:

• Brush friction is present in all brushed motors.

• Torque ripple affects all electric motors to some degree, with the exception of the impractical homopolar motor. The reluctance of the magnetic circuit changes as the rotor and stator poles step in and out of alignment while the rotor turns. This causes a torque which tries to align the rotor at certain specific angles.

• Cogging torque is a specific case of torque ripple which occurs in all slotted permanent magnet motors and persists even when the motor is at rest and unpowered. Affected motors include permanent magnet brushed DC motors, brushless DC motors and stepper motors. Coreless DC motors, induction motors, reluctance motors and electrically excited (field winding) DC motors are immune.

Torque ripple can be alleviated by increasing the motor pole count or adding a transmission between the motor and pendulum, but this will obviously cause additional friction and add inertia to the system.

Given the fairly specific requirements, it might make more sense to use a voice coil rotary actuator (like what is found in hard disk drives) rather than a motor.

Not only does such an actuator have zero torque ripple, but there is no physical contact and the moving part can be made very lightweight to reduce its impact on the system. The variations in torque in response to position can be fairly linear as well, and are easily compensated out:

The downside is a reduced range of motion.

Actually, you need to rethink your controller. As stated, forcing the motor voltage to zero will cause the motor to provide a large damping force to the pendulum. The reason is that any motion of the motor shaft will cause the motor to act as a generator. Keeping the motor voltage at zero is effectively the same as providing an extremely small resistance across the motor (E = iR, after all), and this will resist any motor motion. So simply controlling the motor voltage will not allow the pendulum to swing freely, regardless of friction.

You could start by looking at brushless motors. Try looking for motors that are described as "high quality" or "precision." There are motors sold for laboratory or prototype building that are described in more detail by the sellers than motors sold for hobby or toy use. The same is true for encoders.

WhatRoughBeast has a good point. The controlled variable needs to be pendulum position as determined using the encoder. The circuit that energizes the motor will need to "open circuit" the motor at the end of the pulse. I think it will need to provide a trapezoidal shaped pulse.

Upon further consideration:

I was thinking a trapezoidal pulse would minimize the back emf generated when the pulse is shut off. Upon further consideration, I think that it is going to be more difficult to prevent any permanent-magnet motor from producing some braking torque when it is not energized. You can shut it off without providing a path for generated current, but there will still be some reluctance torque. An induction motor might be better, but you would need an inverter to energize it.

• Can you elaborate on why the signal should be trapezoidal?
– Elod
Commented Jul 28, 2016 at 12:51