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Km/(s*L+R) is part of the motor equation. It's the electrical part of the motor. The 'L' is the inductance of the armature, and the 'R' is the resistance of the winding of the armature.
Km is the motor constant which acts as a voltage vs speed constant so the higher the Km the faster the speed for a given voltage. The resistance R is the resistance of the armature, so that partly determines the current into the motor with a given armature voltage.
This is the transfer function for that part of the motor, and it written in the frequency domain so in the time domain with a step input this would be:
Km/R*(1-e^(-t*R/L))
which is just an exponentially increasing value with form 1-e^(-at), so it shoots up quickly but as time goes by it starts to level off and then settles at some fixed value, just like a capacitor charging through a resistor powered by a source voltage.
1/(s*J+f) is the part of the motor and load that has inertia and friction. The output of this block is the speed of the motor.
Kb is the "back emf" constant of the motor, which acts to reduce the available drive voltage as the speed increases.
When we purchase a motor, we have most control over Km. Sometimes we can get the system response we want by compensating a system just by selecting a motor with the right Km.
Let me ask you this:
In the past have you worked with equations like:
Vout/Vin=1/(s+a)
I've included a quick diagram of a system we can look at. The sensor for this system would be two LDR's wired in series and two LEDs, with a positive reference voltage to the top LDR and a negative reference voltage to the bottom LDR so that when the car goes off the line one LDR increases in resistance and the other LDR decreases in resistance and that provides us with an error signal for the feedback.
For this discussion i'll use:
w for motor speed
O for shaft angle
Od for disturbance torque
OT for result angle
and the following values:
Km=10
L=0.1
R=0.1
J=2
f=10
Steering and Sensor=2/(s+2)
C=controller
I really think you should work on the motor speed controller first and see how that works because that's a very good example of how to get a controller working, and it's simpler math too. Once you do that you can then easily move on to other systems that are more complex like a line following robot.
I want to know more about stability zone for z transform also as there is unit circle like that .......
we have used S for continuous time and freq. doman, Z is used in discrete solution please tell me about Z transform stability in unit circle.
In the time domain the order of a system is the number of derivatives required to describe the system. For one differential equation the order is 1, for two it is second order, etc.
In the frequency domain the order is the highest power of s required to describe the system. So an equation with highest power s^3 represents a third order system.
The type number specifies the number of integrations. For one integration it's a Type 1, for two integrations, it's a Type 2, etc., and for no integrations it is Type 0.
What kind of book do you have to study with? It sounds like your jumping around quite a bit so i wonder how much you are getting out of this.
z transforms are a little different but basically you look at the roots and see that they are all within a circle with radius 1. With the s plane we look at left and right half planes.
So in the s plane we look at left and right planes, and in the z plane we look at inside and outside of the unit circle.
In the time domain the order of a system is the number of derivatives required to describe the system. For one differential equation the order is 1, for two it is second order, etc.
In the frequency domain the order is the highest power of s required to describe the system. So an equation with highest power s^3 represents a third order system.
The type number specifies the number of integrations. For one integration it's a Type 1, for two integrations, it's a Type 2, etc., and for no integrations it is Type 0.
But what the need to diff. or integrate the system twice or thrice??
for eg: which system 1st and 2nd if we see them how to know without coming to these equation.
The signal flow graph gives you a good idea what is going on in the system by outlining each main part and showing the connection scheme.
It's like a schematic for signal flows.
Mason's is a formula that can be used to reduce the flow graph to a single forward gain.
You're other question is related to this...
By making a signal flow graph you can see how many integrations you have.
You dont always have a choice how many integrations there are, but sometimes if you add one you get zero steady state error.
If you've never done a signal flow graph i suggest you try it next. It's not hard to do.
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