Representing Control Systems in Block Diagrams: Tips and Techniques

[ineedmunchies]

Ok, so I have an assignment I need help with. Hopefully some of you here will be able to help me with it.

The Question is shown in the attatched files question2a + question2a2.

I think what I need to do first is represent the system in a block diagram. I have included a rough one of what I think it will be. Where it says Ki0i it should infact say $$K_{1}$$$$\theta_{o}$$. I couldn't figure out how to do subscript in paint.

I don't know whether I should then try and simplify this as much as possible, or whether I should try and split it into sections.
One section to represent the second order terms, one section to represent the first order terms and one section to represent the output angle.

Any help or discussion about this would be greatly appreciated. Thank you.

 

[zyh]

This is a so complex problems on modern control theroy, sorry I can only give your some advice. This is a very typical model to represant the X'=AX+BU Y=CX+D term, did you have some books like "Modern control systems", I think it will help you very much, Also,
I have found a very good website for you,it's here:http://www.engin.umich.edu/group/ctm/examples/motor2/motor.html

 

[momentum_waves]

Ogata has some good texts in this area.

 

[ineedmunchies]

Ah, yes I do have "modern control systems". I've been reading through that trying to work out what's relevant to the question. Thank you for the website, it looks quite useful. I'll try doing some more work on the question later today and see how I get on.

Also who or what is Ogata?

Thank you.

 

[TheAnalogKid83]

what are the rectangles with the arrows running into the centers of them? I've never seen this in a control block diagram.

You need to enter in the transfer functions for those blocks. Use the equations given to find the transfer functions. The Inertia block is 1/Js in laplace domain, so it will be an integration, which will result in a velocity. Remember d(theta) is your velocity.

You start with a voltage, this goes through your motor, who's inductance and resistance will convert your voltage into a current. You multiply this current by your Kt value, which converts it into a torque. This torque value passes through the mechanical transfer function, which includes the inertia (friction + inertia, where inertia is represented in laplace domain just like the inductance of the motor is). This changes the torque into a velocity. this velocity is fed in through your Kv constant (I think its Km in your equations), which is your Back EMF. This is represented by that inner loop of the given block diagram. I notice the arrow is bidirectional, and this is incorrect. It only feeds out from the mechanical part through the Kt constant and back into the summer symbol; one direction. The gearbox is like a transformer, it steps up or down your velocity. You should have a velocity as your output, not a position. I question figure 2, it doesn't seem correct. It shows you are getting a voltage as your output, and how is this even possible? Where is the conversion from the output of the motor to voltage? You have the output node of voltage also being fed back into the controller as a position. This does not make sense, you need to pass it through a conversion block. The real output is velocity, and this should be passed through a 1/S block to feedback the position, and that isn't even present.

Anyway, once you have the transfer functions in place, you can convert them back to differential equations. Use the control loop equations to convert your feedback block into a transfer function.

This is just what I see, don't take it for 100% fact. Its my opinion that figure 2 is inaccurate.

 

[TheAnalogKid83]

what are the rectangles with the arrows running into the centers of them? I've never seen this in a control block diagram.

You need to enter in the transfer functions for those blocks. Use the equations given to find the transfer functions. The Inertia block is 1/Js in laplace domain, so it will be an integration, which will result in a velocity. Remember d(theta) is your velocity.

You start with a voltage, this goes through your motor, who's inductance and resistance will convert your voltage into a current. You multiply this current by your Kt value, which converts it into a torque. This torque value passes through the mechanical transfer function, which includes the inertia (friction + inertia, where inertia is represented in laplace domain just like the inductance of the motor is). This changes the torque into a velocity. this velocity is fed in through your Kv constant (I think its Km in your equations), which is your Back EMF. This is represented by that inner loop of the given block diagram. I notice the arrow is bidirectional, and this is incorrect. It only feeds out from the mechanical part through the Kt constant and back into the summer symbol; one direction. The gearbox is like a transformer, it steps up or down your velocity. You should have a velocity as your output, not a position. I question figure 2, it doesn't seem correct. It shows you are getting a voltage as your output, and how is this even possible? Where is the conversion from the output of the motor to voltage? You have the output node of voltage also being fed back into the controller as a position. This does not make sense, you need to pass it through a conversion block. The real output is velocity, and this should be passed through a 1/S block to feedback the position, and that isn't even present.

Anyway, once you have the transfer functions in place, you can convert them back to differential equations. Use the control loop equations to convert your feedback block into a transfer function.

This is just what I see, don't take it for 100% fact. Its my opinion that figure 2 is inaccurate.

The error of making many of those arrows bidirectional in the control block figure really leads me to believe the person who made it doesn't know what they're doing. There is no reason to do that, and its unconventional at best, and probably just wrong. It leads me to believe the other things i question about this diagram to be incorrect as well.

 

[TheAnalogKid83]

I put together a block diagram of what really is happening I think. This is accurate and I attached it to this post.

Also, questions I have when looking at figure 2 you provided:
-How does the tachometer determine velocity by measuring current (it has current going into some motor symbol and then into the tach, and tachs don't use current or voltage to measure velocity)
- Where is the back emf feedback shown (motor voltage)? This is negative feedback inherent to the motor.
-Where is K2 shown in the block diagram?

there's a few more, but this diagram has me lost and I have doubts it is correct, and if it is correct, it has been made much more complex than it needs to be.

 

[ineedmunchies]

I don't know what the rectangular symbols with the arrows are meant to represent in figure 2 either. I do not think it is meant to be a block diagram, but rather a basic diagram of the apparatus used in an experiment (which i am currently trying to obtain the report for).

I would of assumed that there would need to be a velocity output as well.

If the diagram given by the analogkid is correct, how would I go about giving the formula relating the input position and output velocity?

Would I be right in assuming that:

T = $$T_{m}$$ - $$T_{L}$$

L and R are the armature inductance and resistance respectively.

V_emf is the feedback voltage (is this what is given as motor voltage, $$v_{m}$$ , in the question?)

$$\frac{K_{1}}{s}$$ is the position feedback?

$$K_{amp}$$ I am unsure of, is this $$K_{g}$$ $$K_{}$$ and $$K_{t}$$ simplified into one term??

Thank you for your help.

 

[ineedmunchies]

If it helps there is a second part to the question which is included in an attatchment.

 

[zyh]

I put together a block diagram of what really is happening I think. This is accurate and I attached it to this post.

Also, questions I have when looking at figure 2 you provided:
-How does the tachometer determine velocity by measuring current (it has current going into some motor symbol and then into the tach, and tachs don't use current or voltage to measure velocity)
- Where is the back emf feedback shown (motor voltage)? This is negative feedback inherent to the motor.
-Where is K2 shown in the block diagram?

there's a few more, but this diagram has me lost and I have doubts it is correct, and if it is correct, it has been made much more complex than it needs to be.

the attatched pdf seems very beautiful.
TheAnalogKid83, can I ask a queation, which tools did you use to draw these charts?
thanks

 

[ineedmunchies]

If anyones interested I've got the solution to this and I can post it if you like.

Thanks for the help

 

[TheAnalogKid83]

the attatched pdf seems very beautiful.
TheAnalogKid83, can I ask a queation, which tools did you use to draw these charts?
thanks

I drew it in MS Visio while at work, and just printed it off into a PDF with PrimoPDF. The block diagram is from when I did my senior project which was a nonlinear model and software/hardware design of a DC motor-clutch-generator control system. The diagram is of course the simplified linear version, and just the motor, I excluded the clutch and generator. I'm sure you can find this block diagram in similar versions in just about any controls systems textbook.

 

[zyh]

Thanks kid83.
now I'm using Dia。。。It's like "visio" but It's open source and free...