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# Basic Question about block Diagrams

## Basic Question about block Diagrams

(OP)
Hi there I am new to this forum.

I am doing a project about controlling a thermoelectric module, and for doing so I must reverse the current direction. This is achieved changing the voltage polarity. So the output of the controller (which is percentage) is going to control the voltage level, being:

0% --> -0.68 Volts
100% --> 1.02 volts

I attached a picture where is plotted the line related to %CO (controller ooutput) and voltage.

My concern is about how to apply the Laplace transform to the line itself, because if I consider deviation variables the free component of the line formula will disappear and the Laplace transform will be function only of the slope, which is not correct because doing so will give a error in the actual voltage needed. Other strategy that I could consider is to apply the Laplace Transform diretly to the line ecuation, but again I think is not appropriate because in that case I am not considering deviation variables.

Other strategy could be to use two block diagrams either one for positive values of voltage and the other one for negatives values.

I hope you guys can help me out.

Fabian.

### RE: Basic Question about block Diagrams

I don't understand your math but it should be simple

What is the range of the output module
0 - 100%, 0 - 4096 counts or other
Take th3e output of your calculation and scale it accordingly.

### RE: Basic Question about block Diagrams

(OP)
I forgot to say that all the bloks there, ALL OF THEM are non-linear. Due the range of temperatures used in the application, one can apply linearization to all the bloks. And then create pre-coded blocks in simulink to store those values. So for instance if the input is, let´s say 20°C the algorithm will choose the gain values of the blocks and pick the controller paramaters accordingly.

So what I did (respect to my question upthere) was to apply Laplace Transform directly to the line formula (responsable for converting the controller output to voltage). The problem occurs is when I apply Routh test I can´t find any values of Kc where the system goes unstable. Which is wrong. Something similar happens using the direct substitution method.Here all the gains obtained are negative which is not good due the controller has a reverse action in this application.

What I thought later was that the line formula is just a way to generate a value, so why not generate the value internally using code and use its output as pure gain. That way I could obtain a range of Kc where the system goes unstable. But when the that generated value is negative, then there's no suitable Kc values (all inequalities result in negative ones).

What am I doing wrong here? thanks for replying roydm!

### RE: Basic Question about block Diagrams

I'm sorry, I assume you are doing something purely as a mathematical exercise, my understanding of control theory comes from a practical hands on approach, my math is severely limited.

I assume since you are using non linear temperature/Voltage relationship your transducers are raw thermocouple or thermistor.

For a practical temperature controller transducer response close to the setpoint may not be linear so the gain is reduced to prevent oscillation and Integral (reset) takes care of the rest, I have always used the Siegler and Nichols method.

Good Luck
Roy

### RE: Basic Question about block Diagrams

(OP)
Thanks for you help Roy it was useful!

### RE: Basic Question about block Diagrams

If the system is non-linear you really should use differential equations and Runge-Kutta or a odeint() function in python or Matlab to integrate the system of differential equations.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

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