I want to make a matlab (simulink) control model for the system in the image below.
The original pdf is only accessible if logged in Carleton's Learning Management System.
How do I get the dynamics of the system with given details in the image?
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the Simulink diagram is straightforward. It is a matter of connecting blocks. For the differential equations provided in your post, the simulink is
For $u_1$ and $u_2$, I've chosen the unit step. You can change that of course. For $L$, I've set it to 0.5 since you didn't provide the actual value. The result of the position of the vehicle is shown below:
A very broad but a valid question. Simulink and the Simscape Addon are used both as a physical simulation toolkit and as an environment for controller development. On the concept drawing in the OP a marsrover is seen which probably should move around and make some tricks. The first thing is to create a simulation. Thats like a computergame where Simulink works as a physics engine. One step further is to develop a controller on top of the simulation. In most cases this is done with a Domain Specific Language. An example for the "Differential Drive implementation" is given on A Domain Specific Language for Modeling Differential Constraints of Mobile Robots, page 4 That paper is not Simulink specific but gives a more general idea.