Simulink representation model.

Now let’s construct our model of angular sensor with the help of simulink.

In the base of our scheme we will put 2 integrators that are connected in series. With getting from outside the initial data. On the input on 1^st integrator we will put the angular acceleration. As the initial data we will use initial angular velocity φ ’(0) as output we will obtain current value of φ ’(τ).Then we will make the function S(τ, φ, φ ’) as subsystem.

This subsystem you can see below:

Fig.13. Subsystem S(τ, φ, φ ’)

Using the obtained subsystem we are able to connect two processes φ (τ) and φ ’(τ) with the corresponded inputs of subsystem. Also we must prepare the signal sin(φ) and connect the scheme of integration. For screening of results we will use XY Plot for phase representation of pendulum and Scope for motion pattern.

The general system will be:

Fig.14. General model of sensor

Now we are able run the model. So, as we use XY Graph and Scope we may observe following pictures of pendulum motion.

Fig.15. XY graph of pendulum vibration

Fig.16. The scope of the model

Conclusion:

We were correspond essence of mathematical pendulum. Design and calculate mathematical model of pendulum angle sensor and shown it with the help of MatLAB software. As visual representation we were use Simulink construction workspace. As the result we were obtain the operational model of the pendulum angular sensor and may change any data of this model corresponding to studying objectives.