# Mathematical modelling of system dynamic on matlab

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?

• Are you looking for the actual differential equations of the system or the Simulink diagram? The actual equations already given in the page you've posted! – CroCo Mar 8 '17 at 13:06
• I am looking for simulink model of the system, which I believe should be derived from given equation . I just dont know how to begin. It can either be in laplace transformation or state-space model. – user137000 Mar 8 '17 at 13:32
• What are your inputs (i.e. $u_1, u_2$)? – CroCo Mar 8 '17 at 13:49
• the values are not given, they are variable. u1 is the forward velocity of rear wheel and u2 is the angular velocity of front wheel. the speed range of the rover in the range of 0.01-0.5km/h . – user137000 Mar 8 '17 at 17:51
• Welcome to Robotics user137000. On stack exchange, it is better to edit your question to add information requested in comments, rather than adding more comments. Comments are for helping to improve questions and answers, and are distracting, so we try to keep them to a minimum. If all of the information needed to answer the question is contained within it, the comments can be tidied up (deleted). – Mark Booth Mar 9 '17 at 10:07

## 2 Answers

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: • thank you for the help .I will try doing for the F(x,y,t)=sin(t) and check for the solution – user137000 Mar 9 '17 at 17:27

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.