Skip to Content

Register Login

Industry Online Support

Technical Forum

Navigation

Numeric Methods to Solve ODEs(Ordinary Differential Equations )

Created by: hdhosseini at: 7/13/2012 9:52 AM (19 Replies)

Rating (18)

Thanks 28

Result pages:: |; 1 | 2; |

20 Entries

Entries per page: 10 | all

7/13/2012 9:52 AM	Rate (8)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	Dear friends , This is an expansion to discussion previously made here: Laplace equations in Step7 Simply this will provide all data and documents required for solving ODEs with SCL.Hopefully, first reading the document may help to refresh the Euler method. Best regards, Hamid Hosseini Attachment ODE.pdf (1670 Downloads)
	Last edited by: hdhosseini at: 6/28/2013 8:09 AM Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 6 thankful Users Lucky123 desmul24 Karls1 Rollex 个月的神 AutoGen_8048316

7/13/2012 10:01 AM	Rate (0)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	1-First Order Differential Equation [code]FUNCTION_BLOCK FB1 //Y 1 //--=------------------------ //F AS + B // Block Parameters VAR_INPUT // Input Parameters F:REAL; A:REAL; B:REAL; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables YNEW:REAL:=0.0; YOLD:REAL:=0.0; K:REAL:=0.0; DELTA:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN YOLD:=0; YNEW:=0; Y:=0; // REST:=0; ELSE DELTA:= (F - (BYOLD))/A; YNEW := YOLD + ( DELTA* T_INTERNAL ); YOLD:=YNEW; Y:=YNEW; END_IF; ; END_FUNCTION_BLOCK[/code] Attachment E1.jpg (1320 Downloads)
	Last edited by: hdhosseini at: 3/5/2013 1:46 PM Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 1 thankful Users KMOU

7/13/2012 10:07 AM	Rate (0)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	2-Casual Differentiator, as a part of PID controller [code]FUNCTION_BLOCK FB2 //Y CS //--=------------------------ //F AS + B VAR_INPUT // Input Parameters F:REAL; A:REAL:=1.0; B:REAL:=1.0; C:REAL:=1.0; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables // FNEW:REAL:=0.0; FOLD:REAL:=0.0; YNEW:REAL:=0.0; YOLD:REAL:=0.0; DELTA:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN YOLD:=0; YNEW:=0; Y:=0; REST:=0; ELSE DELTA:= (((C(F- FOLD))/T_INTERNAL) - (BYOLD))/A; YNEW := YOLD + ( DELTA* T_INTERNAL ); YOLD:=YNEW; FOLD:=F; Y:=YNEW ; END_IF; ; END_FUNCTION_BLOCK[/code] Attachment E2.jpg (1069 Downloads)
	Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 1 thankful Users KMOU

7/13/2012 10:31 AM	Rate (1)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	3- Second order differential equations [code] FUNCTION_BLOCK FB3 //Y 1 //--=------------------------ //F AS^2 + BS +C VAR_INPUT // Input Parameters F:REAL; A:REAL:=1.0; B:REAL:=1.0; C:REAL:=1.0; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables // FNEW:REAL:=0.0; X1:REAL:=0.0; X2:REAL:=0.0; X1OLD:REAL:=0.0; X2OLD:REAL:=0.0; DELTA1:REAL:=0.0; DELTA2:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN X1:=0.0; X2:=0.0; X1OLD:=0.0; X2OLD:=0.0; //REST:=0; Y:=0; ELSE DELTA2 :=(F- (CX1OLD) - (BX2OLD))/A; X2:= X2OLD + (DELTA2 * T_INTERNAL); DELTA1 :=X2; X1 := X1OLD + (DELTA1 * T_INTERNAL); X2OLD:= X2; X1OLD:=X1; Y:=X1; ; END_IF; ; END_FUNCTION_BLOCK [/code] Attachment E3.zip (948 Downloads)
	Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 1 thankful Users KMOU

7/13/2012 1:42 PM	Rate (1)
dchartier Grandmaster Joined: 9/27/2006 Last visit: 12/20/2024 Posts: 12307 Rating: (2695)	Hello Hamid; I must tell you I am very impressed with your implementations of ODEs in a PLC environment. More and more control algorithms being discussed in Control forums require manipulations of ODEs, and it is a great tool you are providing us for furthering our capacity for process control. Congratulations for the work, and thank you for sharing it with us. Many regards, Daniel Chartier P.S. And this gift arrives on Friday the 13th. For us Westerners, it would seem some magic might be involved... D.C,

Suggestion To thank Quote Answer
This contribution was helpful to 2 thankful Users Lucky123 hdhosseini

7/13/2012 9:24 PM	Rate (0)
Marcjan Platinum Member Joined: 4/22/2010 Last visit: 12/13/2024 Posts: 5697 Rating: (715)	Thanks for these impressive calculations Hamid. Stars for you Gives me a chance to pick up the stuff i learned long ago and forgot because all the standard functions build in S7 Good example to learn old things again for me and good for others to learn new things Keep up the good work. regards, Marcjan.
	Problem solved? Please let us know! Please no technical questions by PM, use the forum sections for your questions.
Suggestion To thank Quote Answer
This contribution was helpful to 1 thankful Users hdhosseini

7/14/2012 6:34 PM	Rate (0)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	Hello Daniel and Marcjan, Thank you for your feedbacks.There are some other issues to be shared but there is a small problem .People here are really reluctant to even think a bit of academic issues which are base of all technological functions we are using.All those complexities are hidden from users(programmers) but somehow important to know them. As I traced other experts' posts "those kind of data shared when people ask for them".Hope to have more issues like this especially in "process automation" to challenge our knowledge and learn more. Best regards, Hamid Hosseini
	Last edited by: hdhosseini at: 6/28/2013 8:11 AM Last edited by: hdhosseini at: 8/23/2012 9:40 PM Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 3 thankful Users Lucky123 Marcjan Hunter1331

7/11/2013 10:15 PM	Rate (1)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	Hello friends, Recently I received an improvement report for this algorithm to avoid inadvertent division by zero .As discussed, the algorithm is vulnerable with explicit division by "A" parameter that can be selected freely.Modified version is being shared, providing an extra error bit and disabling "ENO" in case of error.I checked the performance of each block and it remains unchanged. REVISED:(1-First Order Differential Equation) [code]FUNCTION_BLOCK FB1 TITLE = 'ODE_EULER' //Y 1 //--=------------------------ //F AS + B VERSION: '2.0' AUTHOR: HD NAME: first FAMILY: FORUM_E // Block Parameters VAR_INPUT // Input Parameters F:REAL; A:REAL; B:REAL; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; error:BOOL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables YNEW:REAL:=0.0; YOLD:REAL:=0.0; K:REAL:=0.0; DELTA:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN YOLD:=0; YNEW:=0; Y:=0; OK:=false; error:=1; // REST:=0; ELSE IF A= 0 THEN ; OK:=false; error:=1; YOLD:=0; YNEW:=0; Y:=0; ELSE DELTA:= (F - (BYOLD))/A; YNEW := YOLD + ( DELTA* T_INTERNAL ); YOLD:=YNEW; Y:=YNEW; OK:=true; error:=0; END_IF; END_IF; ; END_FUNCTION_BLOCK[/code] Best regards Hamid Hosseini Attachment NEU_ODE.jpg (1049 Downloads)
	Last edited by: hdhosseini at: 06.11.2013 08:00 // REVISE Last edited by: hdhosseini at: 7/13/2013 2:21 PM Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 3 thankful Users Lucky123 metwally mustafa Hunter1331

7/13/2013 2:27 PM	Rate (3)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	REVISED:(2-Casual Differentiator, as a part of PID controller) [code]FUNCTION_BLOCK FB2 TITLE = 'ODE_EULER' //Y CS //--=------------------------ //F AS + B VERSION: '2.0' AUTHOR: HD NAME:DIFF FAMILY: FORUM_E VAR_INPUT // Input Parameters F:REAL; A:REAL:=1.0; B:REAL:=1.0; C:REAL:=1.0; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; error:BOOL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables // FNEW:REAL:=0.0; FOLD:REAL:=0.0; YNEW:REAL:=0.0; YOLD:REAL:=0.0; DELTA:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN YOLD:=0; YNEW:=0; Y:=0; // REST:=0; OK:=false; error:=1; ELSE IF A= 0 THEN ; YOLD:=0; YNEW:=0; Y:=0; OK:=false; error:=1; ELSE DELTA:= (((C(F- FOLD))/T_INTERNAL) - (BYOLD))/A; YNEW := YOLD + ( DELTA* T_INTERNAL ); YOLD:=YNEW; FOLD:=F; Y:=YNEW; OK:=TRUE; error:=0; ; END_IF; END_IF; ; END_FUNCTION_BLOCK[/code]
	Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 4 thankful Users UMENCHO Lucky123 metwally mustafa Ahmad Magdy

7/15/2013 10:39 PM	Rate (2)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 12/12/2024 Posts: 6858 Rating: (1365)	REVISED:(3- Second order differential equations) [code]FUNCTION_BLOCK FB3 TITLE = 'ODE_EULER' //Y 1 //--=------------------------ //F AS^2 + BS +C VERSION: '2.0' AUTHOR: HD NAME:SECOND FAMILY: FORUM_E VAR_INPUT // Input Parameters F:REAL; A:REAL:=1.0; B:REAL:=1.0; C:REAL:=1.0; INTERVAL:TIME:=T#1S; END_VAR VAR_IN_OUT REST:BOOL:=FALSE; END_VAR VAR_OUTPUT // Output Parameters Y:REAL; error:BOOL; END_VAR VAR_TEMP // Temporary Variables END_VAR VAR // Static Variables // FNEW:REAL:=0.0; X1:REAL:=0.0; X2:REAL:=0.0; X1OLD:REAL:=0.0; X2OLD:REAL:=0.0; DELTA1:REAL:=0.0; DELTA2:REAL:=0.0; T_INTERNAL:REAL:=1.0; END_VAR // Instruction Section T_INTERNAL := (DINT_TO_REAL(TIME_TO_DINT (INTERVAL)))/1000.0; IF REST=1 THEN X1:=0.0; X2:=0.0; X1OLD:=0.0; X2OLD:=0.0; //REST:=0; Y:=0; OK:=false; error:=1; ELSE IF A=0 THEN ; X1:=0.0; X2:=0.0; X1OLD:=0.0; X2OLD:=0.0; Y:=0; OK:=false; error:=1; ELSE DELTA2 :=(F- (CX1OLD) - (BX2OLD))/A; X2:= X2OLD + (DELTA2 * T_INTERNAL); DELTA1 :=X2; X1 := X1OLD + (DELTA1 * T_INTERNAL); X2OLD:= X2; X1OLD:=X1; Y:=X1; OK:=TRUE; error:=0; END_IF; ; END_IF; ; END_FUNCTION_BLOCK[/code] Attachment NEU_ODE.jpg (1054 Downloads)
	Last edited by: hdhosseini at: 7/15/2013 10:46 PM Demo Channel on Youtube
Suggestion To thank Quote Answer
This contribution was helpful to 5 thankful Users dchartier Lucky123 metwally mustafa forsage FouadM

|

Share this page:

Share this page on...

Follow us on