How can I combine two transfer function?

The control system diagram as follows;

I derived the transfer functions seperately for the two loops where one loop has angles as inputs and other one has a voltage input. But in order to check the stability of the system through simulink, I need to find the transfer function of the overall system. Could anyone can help me with solving this?

Answer 1

[William Rose]

@Raveesha Bandara,

The diagram indicates that the upper loop (or loops*) affects the lower loop, but the opposite is not true. Therefore the stability of the upper loop (or loops) is unaffected by activity in the lower loop. Since the lower loop does not affect the upper loop, the input from the upper loop to the lower loop can be regarded as a disturbance input to the lower loop, and analyzed accordingly.

It seems a bit odd to me that the angle tracking loops produce a "reference voltage", and the input to the lower loop is "Solar panel voltage". I would expect the solar panel voltage to be an output from the panel tracking. But it's not my field.

*The upper part of your diagram has two inputs (angles) and two outputs (angles), so it looks like there are two transfer functions, not one, related to the upper part of the diagram. The output angles are inputs to the "Position Irradiance Temperature" block, the output from which is an input to the lower loop.

[Sam Chak]

Hi William,

Your observations are correct. The upper part of the block diagram is a dual axis solar tracking system that controls the orientation of the solar panel, so that the sunlight can hit the surface of the panel perpendicularly. This maximizes the power generation, in theory.

On the lower part is the Maximum Power Power Tracker for maximizing the energy extraction as the conditions from the battery or utility grid vary. But these conditions are not explicitly shown in the diagram, but simply labelled the Reference MPPT Voltage. By the way, the Solar Panel Voltage and Reference MPPT Voltage should swap places.

[William Rose]

@Sam Chak, thank you. I suspected that Solar Panel Volatge and Reference MPPT were reversed, and that is why I made the comment "It seems a bit odd... but it's not my field."

[Raveesha Bandara]

Thank William and Sam

[Sam Chak]

@Raveesha Bandara, If you find the explanation helpful, please consider clicking 'Accept' ✔ on William's answer and voting 👍 for it.