Mixing
Custom Simulink Discrete-time integrator block for Bogacki Shampine
I am trying to create my own discrete time integrator in Simulink Using the Bogacki Shampine rule. The general formula for the rule (when it is only a function of time) is:
y(n+1) = y(n) + (t/9)*(2*s1+3*s2+4s3)
where:
s1 = x(n)
s2 = x(n+h/2)
s3 = x(n+3h/4)
which is also equal to :
y(n) = y(n-1) + (t/9)*(2*s1+3*s2+4s3) ;
where:
s1 = x(n-1)
s2 = x(n-h/2)
s3 = x(n-h/4)
Then I compared the results with the simple integrator block that uses ode3 (Bogacki Shampine). Results were close to each other but not too much.
Also I am not sure that I create this integrator in a correct way. Since Bogacki Shampine is 3rd order. I thought I should have used 3 unit delay, but 2 was enough for me.
How can I improve this or create another one to get more accurate results?
integration simulink integrator
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
add a comment |
I am trying to create my own discrete time integrator in Simulink Using the Bogacki Shampine rule. The general formula for the rule (when it is only a function of time) is:
y(n+1) = y(n) + (t/9)*(2*s1+3*s2+4s3)
where:
s1 = x(n)
s2 = x(n+h/2)
s3 = x(n+3h/4)
which is also equal to :
y(n) = y(n-1) + (t/9)*(2*s1+3*s2+4s3) ;
where:
s1 = x(n-1)
s2 = x(n-h/2)
s3 = x(n-h/4)
Then I compared the results with the simple integrator block that uses ode3 (Bogacki Shampine). Results were close to each other but not too much.
Also I am not sure that I create this integrator in a correct way. Since Bogacki Shampine is 3rd order. I thought I should have used 3 unit delay, but 2 was enough for me.
How can I improve this or create another one to get more accurate results?
integration simulink integrator
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05
add a comment |
I am trying to create my own discrete time integrator in Simulink Using the Bogacki Shampine rule. The general formula for the rule (when it is only a function of time) is:
y(n+1) = y(n) + (t/9)*(2*s1+3*s2+4s3)
where:
s1 = x(n)
s2 = x(n+h/2)
s3 = x(n+3h/4)
which is also equal to :
y(n) = y(n-1) + (t/9)*(2*s1+3*s2+4s3) ;
where:
s1 = x(n-1)
s2 = x(n-h/2)
s3 = x(n-h/4)
Then I compared the results with the simple integrator block that uses ode3 (Bogacki Shampine). Results were close to each other but not too much.
Also I am not sure that I create this integrator in a correct way. Since Bogacki Shampine is 3rd order. I thought I should have used 3 unit delay, but 2 was enough for me.
How can I improve this or create another one to get more accurate results?
integration simulink integrator
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
I am trying to create my own discrete time integrator in Simulink Using the Bogacki Shampine rule. The general formula for the rule (when it is only a function of time) is:
y(n+1) = y(n) + (t/9)*(2*s1+3*s2+4s3)
where:
s1 = x(n)
s2 = x(n+h/2)
s3 = x(n+3h/4)
which is also equal to :
y(n) = y(n-1) + (t/9)*(2*s1+3*s2+4s3) ;
where:
s1 = x(n-1)
s2 = x(n-h/2)
s3 = x(n-h/4)
Then I compared the results with the simple integrator block that uses ode3 (Bogacki Shampine). Results were close to each other but not too much.
Also I am not sure that I create this integrator in a correct way. Since Bogacki Shampine is 3rd order. I thought I should have used 3 unit delay, but 2 was enough for me.
How can I improve this or create another one to get more accurate results?
integration simulink integrator
integration simulink integrator
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
edited Jan 3 at 10:43
Sardar Usama
15.6k82649
15.6k82649
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
asked Jan 2 at 17:16
Mr.SamuelMr.Samuel
32
32
Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05
add a comment |
Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05
Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05
add a comment |
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Your implementation seems dubious. For instance, you are assuming that x(n-1/2) = (x(n)+x(n-1))/2, which is almost certainly not the case. It would mean that the mid-point is just an average of the end points, which would be the same as the Trapizoidal Rule.
– Phil Goddard
Jan 3 at 3:39
Yes sir you are right. But i did it the way you said since matlab does not allow me to put different sampling times in one model. Do you have any suggestions to deal with this problem? Thank you for your answer!
– Mr.Samuel
Jan 3 at 4:49
In Simulink each block can have a sample time independent of the overall model sample time. At a minimum you need to have 2 additional states, one of them with a rate to give you x(n-1/2) and one to give you x(n-1/4). You would then combine those with you states giving x(n-1) and y(k-1) to get the result.
– Phil Goddard
Jan 4 at 4:05