Cascading PID DC Motor Position & Velocity Controllers

Question

I'm trying to build a robot with a differential drive powered by two DC Motors. First I implemented a PID Controller to control the velocity of each motor independently. Estimated the TF using the MATLAB's System Identification Toolbox, of the open loop system by the acquiring the velocity of each wheels encoder in function of the PWM signal applied by an Arduino microcontroller. All went well and i successfully dimensioned the PID gains for this controller.

What I'm trying to accomplish now is to control the exact (angular) position of the DC Motor. I thought in cascading a PID controller in the input of the other already implemented. So this way, I can give a position to the first controller, which will be capable of generate an output reference to the second (velocity) controller so it generates the appropriate PWM value signal to drive the DC Motor accordingly.

Will it work? Is that a good approach? Or should I try to implement a different controller which outputs the PWM signal in response to a position reference signal?

Many thanks for your attention and I hope somebody can help me with these doubts.

Answer 1

I have done this myself, controlling the exact position of a brushless DC motor as its velocity ramps up and down. And I did it using a position controller only. Sounds obvious, but it worked extremely well.

The integral term of the controller is key to this. Since you want the position error to be as close to zero as possible the whole time, but you need a large output from the controller to drive the motor, most of this comes from the I term.

The other thing you need to add is a feed forward term, which feeds some of the demanded acceleration to the output. This will give the controller the extra power it needs to track rapid velocity changes. We could call this an FPID controller.

Answer 2

I'm a little confused, are you trying to control each wheel's exact position or the overall position of the robot. For the former, a cascaded structure makes sense where the robot position control loop defines desired velocities for each motor.

For the latter (which sounds a little strange to me), you should just be able to treat the velocity as the 'D' part of your position controller, and not do a separate velocity controller.

$$ \begin{align} u = - k_p (p - p^d) - k_d (v - v^d) - k_i \int_0^t (p(t) - p^d(t)) dt \end{align} $$ where $p$ and $v$ are the measure position and velocity respectively, and $\cdot^d$ indicates the desired value.