# Modelling the speed control of a mobile robotic system

I am attempting to model a robot and develop a PID based off of the paper at the bottom of this post before developing a physical model. However, the research paper appears to give parameters for wheel radius, a geared motor inertia and a tachometer constant but these are not included in the overall transfer function stated in the paper - unless these would be factored in by the parameters for equivalent damping / inertia?

Were I to include these parameters so to achieve a more realistic model how would that be done? The transfer function relates the speed of the robot to the voltage applied across the DC motor - so I presume this multiplied by the wheel radius can give the velocity of the wheels.

Edit: Section of paper below

• Do you think, that we all have a subscription to IEEE? – Marko Buršič Feb 26 at 18:08
• This question is likely to be answered with opinions rather than facts and citations. It should be updated so it will lead to fact-based answers. – Andy aka Feb 26 at 18:32
• Please quote relevant section(s) of the linked paper for users who don't have access to it. – Null Feb 26 at 19:04
• Edited so to include a drive link of the paper vs. IEEE link - thank you – Brandon Kellett Feb 26 at 19:26
• Um, are you now publishing a copyright IEEE paper? – Transistor Feb 26 at 19:36

This is the block diagram of DC motor, similar you should have in your article:

And this is the transfer function of it:

$$\dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_\Phi}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_\Phi^2}}$$

Replacing the upper $$\k_{\Phi}\$$ in the diagram with $$\k_T\$$ and the lower one with $$\k_v\$$ we get almost the same transfer function as your blurry one, except B=F, :

$$\dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_T}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_v\cdot k_T}}$$

You have to place the inertia and friction parameter in the feedforward path of your position controller $$\T=J \alpha + F \Omega\$$. The approx. amount of torque is known "a priori" with these two parameters known.

Where to place Radius-R(not resistance)? $$\l=\Theta R\$$; $$\\Theta =\dfrac{\Omega}{s}\$$