Obtain the mathematical model of the position control system of the figure. Get the block diagram and the ansfer function between the angle of the load and the reference angle θc(s)/θc(s).
1. System dynamic
2. Laplace Transform
3. Block Diagram
Simplifying conveniently to obtain a model whose transfer function is known:
4. Transfer function of each block of the previous diagram.
We obtain the following:Then, using:
and substituting, we obtain:
Substituting the value of the data in the previous equation, we obtain:
On the other hand, the gain of the amplifier is obtained using:
Finally, the gear constant is given by the data and is n = 1/10. We then obtain a block diagram with the following transfer functions:
5. System Transfer function.
The open-loop transfer function Ga(s) of the system shown in the previous diagram is:
From where we can easily obtain the closed-loop transfer function Gc (s), which is what the statement asked, using the unit feedback:
NEXT: Example 2 – Electromechanical system transfer function (English)
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