Electronic – Why use PI controller for speed, instead of full PID

controlpid controller

I am building a two-wheels self-balancing robot and using PID controller to control its speed. The measured value is the encoder signals from the Hall sensors on the back of the DC geared motors. But in my notes, it mentions only to use PI controller, meaning that the Derivative term is set to zero. But i can't understand why? Isn't it better to use a full PID controller to achieve the best results?

I researched online and the best explanation i could find is that for a PI controller which controls the speed, there is a need for faster response so the Derivative term can be omitted. But i am not convinced of this explanation… Maybe someone can offer a better and more complete explanation?

Also, for the angle balancing part, why is the PD controller preferred instead of PI controller and why not use full PID?

Best Answer

You do already have a D-term when control velocity. It is the differentiation of the position, so no need to do double differentiation - not stable.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

EDIT:

User DKNguyen has probably found a good reason why PI instead of PID is used: Let' take for exapmle a real servo driver having 62.5us sampling time for current controller, 125us for speed controller and 1ms for position controller. Now, the most straightforward to tune is the current controller. You can compute the Kp, Ti directly from motor resistance and inductance.

The velocity parameters are more tricky, the load and its inertia comes to play here. The algorithm for an integrator can suffer from precision while doing computation. Tiny increments could not be summed in a floating point number. But the real pain is to make a differentiation. In a book it was mentioned that sampling time has to be somewhere from 1/5 to 1/20 of dominant system time for PID controller to work as expected. Thus, high sample rate could spoil the PID, which in servo drive has a fixed sampling time.

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Self Balancing Robot using Computer Vision

I have worked with self balancing robots in my bachelor and master thesis. Ad hoc I see these problems, that will very likely get in your way.

Self balancing robots are instable by definition. You have to collect data from your sensors (the camera) fast enough, to react to changes in the attitude of the robot. So the question is: can you process the information from the camera fast enough to stabilize the system (dead-time)?
Gyros will give you the angular acceleration along the axis. But with your camera you have something that correspond to the angle. To clarify this, you can not get the angular velocity or even angular acceleration with just one picture. You have to do some processing based on multiple pictures. That means you need more time => greater dead-time. Also this processing will probably introduce noise, which will complicate the controller design.

Electronic – arduino – Motor speed control using arduino and quadrature encoders

It looks to me that your control loop is essentially:

if speed is too slow:
    increase PWM duty cycle one unit
if speed is too fast:
    descreate PWM duty cycle one unit

As you have observed, this doesn't work so well. Your control loop cyclically overshoots the target speed.

The canonical solution to this sort of problem is a PID controller. The concept is essentially the same, measure a thing and compare it to a target to calculate an error. Then adjust something (in your case, PWM duty cycle) based on the error.

However, a PID controller has three error terms:

P: the current error
I: the integral of the error
D: the derivative of the error

For each of these terms, the controller has programmed some gain. It then multiplies each term by the respective gain to calculate how much the control input (PWM duty cycle) should be changed. Properly tuned, this allows you to get a feedback loop that at first ramps up the duty cycle, then as your vehicle approaches the target speed, backs off smoothly so you get a minimum of overshoot.

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Self Balancing Robot using Computer Vision

Electronic – arduino – Motor speed control using arduino and quadrature encoders

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