Control block diagram's transfer function

[Hackhol]

Homework Statement

I'm designing an open loop 3 way traffic light system. I'm having hard time in deriving the transfer function of the controller or let's I don't even know how to derive it

Relevant Equations

S

The ac signal is converted to DC signal which is connected to a capacitor to filter the DC signal. The filter DC signal is step down for 12volt to 5 volt using a voltage regulator. The regulated DC signal is connected to a crystal oscillator that converts the DC signal to a square wave signal that is connected to the Analog input of the MCU@mega3208p. The MCU the digital output is connected to the LED bulbs .But I don't really even know how to get the

 

[DaveE]

OK, so you have a microprocessor with a power supply and a clock, right? That's every uP ever made, BTW. You have also said you have some LEDs as outputs. What you don't have is any description of the inputs to your system or what that system is supposed to do (something about traffic lights, I guess). Good questions get better answers. Honestly I don't know how to respond... yet. Try again.

 

[Hackhol]

OK, so you have a microprocessor with a power supply and a clock, right? That's every uP ever made, BTW. You have also said you have some LEDs as outputs. What you don't have is any description of the inputs to your system or what that system is supposed to do (something about traffic lights, I guess). Good questions get better answers. Honestly I don't know how to respond... yet. Try again.

Yes. . my main problem is how I will get the equation of the traffic light and the transfer function that will covert the input DC signal to traffic light signal

 

[DaveE]

That "equation" will come from the question asked in your homework assignment. OTOH, if you are free to choose, just set all of the lights to flashing red all of the time.

 

[berkeman]

Yes. . my main problem is how I will get the equation of the traffic light and the transfer function that will covert the input DC signal to traffic light signal

Honestly, this makes no sense. Transfer functions generally refer to Linear Time Invariant systems, and neither the input power supply nor the uP are LTI systems.

For the traffic light control system, you need to draw a State Diagram to implement it. Have you learned about State Diagrams yet in your studies?

And I agree that it would help a lot if you could write out the problem statement/assignment word-for-word. It makes no sense as stated so far. Thanks.

https://cacoo.com/blog/a-simple-guide-to-drawing-your-first-state-diagram-with-examples/

 

[FactChecker]

You are trying to design a "bang-bang" control system, where the light is either on or off, depending on whether certain conditions are exceeded. IMO, a transfer function is not very useful in designing that type of system. It is very non-linear and not even continuous.

 

[Hackhol]

OK, so you have a microprocessor with a power supply and a clock, right? That's every uP ever made, BTW. You have also said you have some LEDs as outputs. What you don't have is any description of the inputs to your system or what that system is supposed to do (something about traffic lights, I guess). Good questions get better answers. Honestly I don't know how to respond... yet. Try again.

Honestly, this makes no sense. Transfer functions generally refer to Linear Time Invariant systems, and neither the input power supply nor the uP are LTI systems.

For the traffic light control system, you need to draw a State Diagram to implement it. Have you learned about State Diagrams yet in your studies?

And I agree that it would help a lot if you could write out the problem statement/assignment word-for-word. It makes no sense as stated so far. Thanks.

View attachment 286883
https://cacoo.com/blog/a-simple-guide-to-drawing-your-first-state-diagram-with-examples/

Thanks I will check it ...but we haven't been about it.
Our assignment was that's we should design a project relating to control system and write the mathematical model of the project. And design the control system where we will derive the transfer function of the entire system. Which will use to draw the bode plot, locus plot, polar plot, well we check for the stability of the system and damping factor and the rest...so I choose traffic light thinking it be easy since it's easy to design physical and my lecture has already agreed...
But currently I'm trying to get something like the internal controller equation explaining how the light bulb of the traffic light is changing

 

[DaveE]

Thanks I will check it ...but we haven't been about it.
Our assignment was that's we should design a project relating to control system and write the mathematical model of the project. And design the control system where we will derive the transfer function of the entire system. Which will use to draw the bode plot, locus plot, polar plot, well we check for the stability of the system and damping factor and the rest...so I choose traffic light thinking it be easy since it's easy to design physical and my lecture has already agreed...
But currently I'm trying to get something like the internal controller equation explaining how the light bulb of the traffic light is changing

Those analysis tools are much more suitable for linear analog systems; i.e. not digital, like lights turning on or off. Analog systems are things like cruise control on your car, where the inputs and outputs are continuous variables that can make small changes. You can have digital controls for analog systems but they will mostly all use several bits to express inputs and outputs as an approximation of continuous variables.

So, I think you probably need to think of a more continuous variable to control. Like the temperature of an oven, the brightness of a lamp, the volume of a radio, the rate of water flowing from a hose, etc.

 

[FactChecker]

Those analysis tools are much more suitable for linear analog systems; i.e. not digital, like lights turning on or off.

A better description of the systems would be "linear continuous" versus "discontinuous, 'bang-bang'" systems. A lot of the analog control systems are now implemented with digital control devices.