CTMS: Simulink Modeling Tutorial
Simulink Modeling Tutorial
Train system
Free body diagram and Newton's law
Model Construction
Running the Model
Obtaining MATLAB Model
In Simulink, it is very straightforward to represent a physical system or a model. In general, a
dynamic system can be constructed from just basic physical laws. We will demonstrate
through an example.
Train system
In this example, we will consider a toy train consisting of an engine and a car. Assuming that
the train only travels in one direction, we want to apply control to the train so that it has a
smooth start-up and stop, along with a constant-speed ride.
The mass of the engine and the car will be represented by M1 and M2, respectively. The two
are held together by a spring, which has the stiffness coefficient of k. F represents the force
applied by the engine, and the Greek letter, mu (which will also be represented by the letter u),
represents the coefficient of rolling friction.
Free body diagram and Newton's law
The system can be represented by following Free Body Diagrams.
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CTMS: Simulink Modeling Tutorial
From Newton's law, you know that the sum of forces acting on a mass equals the mass times
its acceleration. In this case, the forces acting on M1 are the spring, the friction and the force
applied by the engine. The forces acting on M2 are the spring and the friction. In the vertical
direction, the gravitational force is canceled by the normal force applied by the ground, so that
there will be no acceleration in the vertical direction. We will begin to construct the model
simply from the expressions:
Sum(forces_on_M1)=M1*x1''
Sum(forces_on_M1)=M1*x1''
Constructing The Model
This set of system equations can now be represented graphically, without further manipulation.
First, we will construct two copies (one for each mass) of the expressions sum_F=Ma or
a=1/M*sum_F. Open a new model window, and drag two
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