UAP0025 - USC Application

This application contains a standard PID algorithm that can be used to control any number of devices. The USC can be programmed to accept an input signal, condition it, compare it to a set point signal and produce a corrective output signal.

Steps To Implement PID Control Using a USC701

Import UAP and Setting Inputs For PID

The Ziegler Nichols Tuning Method

The Standard Program Details

USC PID Program List

Determine Equation Update Time

USC PID Application Program

Steps To Implement PID Control Using a USC701

1. Follow the application section to set up UAP0025 for use with your input devices.
2. To change the sampling rate read the section about the Equation Update Time.
3. The standard program details and program listing are explained so that you may modify it to suit your application. To change to reverse acting operation reverse the inputs or reverse the order of Read Ch1, Read Ch2 commands in the program list.
4. The AM702-02 in trim mode can be used to adjust the PID operation using the Ziegler Nichols tuning method.

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Import UAP and Setting Inputs For PID

This application procedure will apply each step to a specific control example.

EXAMPLE A PID controller will control the temperature of a vessel to a set point stored within the USC where; Measurement input CH1 = Thermocouple type J (Input range used will be 200 to 900°C) Set point (equation constant e) = 600°C Output to controller = 4-20mA

1. Import UAP0025x.USC module definition file into the USC Config PC software.
2. The measurement input must now be configured to match the input or sensor type.
3. 1. Click on CH1 and press configure.
   2. The example uses type J thermocouple measurement input.
   3. Click the small r button to open the change range wizard and select Type = temperature, Range = thermocouple and press next.
   4. In the channel 1 list select T/C Type J, click on Scale C and fill in Eng. Units as 0 to 1000.
   5. It may be necessary to click in the Scale list to copy the required scale over into the engineering units column.
   6. Set to 40ms on fast rate.
   7. Press next until the "evaluate equation outputs" screen appears.
4. Enter the initial PID control parameters;
   1. PB(%) = 50
   2. I time S = 9999
   3. D time S = 0.
   4. Input span is 200 to 900
5. Enter the integral reset value
   
   
6. Enter the set point in constant e = 600.
7. Enter the engineering range for memories 6, 7, 8 and 9 as the measurement range.
   1. M6 200-900I
   2. M7 200-900PiD
   3. M8 200-900 delta
   4. M9 200-900 olddelta.
   Press Ok to continue.
8. The output type and range must be configured to match the required control output type and engineering range.
1. The example has 4 to 20mA control output.
2. Ensure that the control output is connected to the PID output M7.
3. Enter the engineering range of the measurement input Cal Min = 200, Cal Max = 900. Failure to follow this step will cause incorrect PID factors.
9. Press finish to close the wizard, connect and program the USC701. The PID control must now be tuned.

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The Ziegler Nichols Tuning Method

10. Use the AM702-02 in trim mode to adjust constants I set and D set to minimum values.
11. Reduce constant PB in small steps until the process just begins to cycle continuously
    
    and determine the cycle period Pu
12. Calculate final settings:
    

Example Tuning and Caculation

1. I set an example system up with;
   • PBcycle = 6
   • I = 999
   • D = 0
2. I then started a circular reading log of 40 points and recorded the results shown. The white vertical lines on the graph represent a 10-second period.
3. Reading from the graph PBcycle is about 1.5 cycles for 10 seconds or 6.66 seconds for 1 cycle.
4. I then calculated PB = 9.6, I = 0.3 and D = 0.833.
5. I updated the USC program and ran the test again.
6. As the process was still unstable I then reduced the PB until stable operation was achieved at PB(%)= 11.
7. Finally the integral reset value (PB% of input range) should be recalculated.
   As PB(%) is now = 11 and the input range is 200 to 900.
   

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The Standard Program Details

Declarations

Variable	Label	Description	Value
CH1	Measure	Measurement input	0 to 100%
Con_a	PB(%)	Proportional band setting	(25)
Con_b	I time S	Integration setting	(1)
Con_c	D set	Differential setting	(0)
Con_e	SetPoint	Controller set point	(60)
Con_f	IntReset	Used to limit the integral value when outside proportional band and when control is not possible	(25)
Mem6	i	Integral error signal
Mem7	PiD	Controller output error signal
Mem8	delta	Difference between set point and process feedback (error)
Mem9	old delta	value of delta in previous sample.
Timer enable:			Y
Timer sec:			0.1
Update on input:			N

Variable		Label	Description	Value
Issue c	Issue d
Con_d	Var04	EquTime	Set to same value as the equation evaluation timer.	(0.1)
Con_i	Var01	Val 2	equation constant	2
Con_j	Var03	Val 100	equation constant	100

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USC PID Program List (for issue c)

Program List	Comment
Con_e	Read set point (measurement if reverse)
Read Ch1	Read measurement (set point if reverse)
Subtract	Determine difference
Save Mem8	Save delta
Con_j	Start PREPOSITIONAL. Read 100 into stack
Multiply	Multiply delta by 100
Con_a	Read PB% setting
Divide	Determine proportional error for this reading Proportional correction signal is left on stack
Goto INTERGRL
Exit
Lab: DIFERENT	Start DIFFERENTIAL
Read Mem9	Read delta this reading
Read Mem8	Read delta last reading
Subtract	Get change in value
Con_c	Read differential setting
Multiply	Calculate differential value
Con_d	Read sample time
Divide	Convert differential value to time domain
Add	Add integral error
Add	Add proportional error
Save Mem7	Save PID output
Send M7
Read Mem8	Read new delta
Save Mem9	Update old delta
Exit	The program will always finish here.
LAB: INTERGRL	Determine if the integration calculation should be skipped
Read MEM8
ABS
Con_f
Subtract
If > Goto Skip Int
Del S	Start INTEGRATION calculation
Read Mem8	Read delta this reading
Read Mem9	Read delta last reading
Add	Add old and new delta
Con_d	Read equation update time
Multiply	Convert delta into time domain
Con_I	Read the value 2
Divide	Get average
Con_b	Get integration setting
Divide	Calculate integration correction for this reading
Read Mem6	Read previous integration value
Add
Save Mem6	Save new accumulated integration value
Send M6
Goto DIFERENT	Go to differential calculation
Exit
LAB: Skip Int
Del S
Read Mem6	Read last integral value onto stack
Goto DIFERENT

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Determine Equation Update Time

When designing a PID controller the rate that the measurements are available for use in the equation is very important.

1. The equation update time MUST NOT be faster than the measurements are available from the analogue to digital converter.
2. The equation update time should be about ten times faster than the cycle period or the oscillation frequency that occurs when the PB% is too low (gain too high).
3. The PID algorithm takes 60ms to execute therefor the fastest possible equation update time is 70ms with any input configuration.
4. The equation update time can run at the same time as the update for one channel.
5. Also the equation update time must be extended by 20ms per linearisation table (add 20ms per RTD input, 40ms per thermocouple input.

In general it is better to run the system at the maximum possible rate for best PID control however better noise immunity is achieved at the slow sample rate.

Analogue to Digital Converter Measurement Rates

For one channel of measurement, there is an overhead of one cycle of the sample rate after each sample time. For a 50Hz system, slow overhead is 20msec, fast overhead is approximately 1msec.

Sample Time Setting	Slow Rate Slow 50Hz Update Time	Fast Sample Rate 900Hz Update Time
20ms	40	21
40ms	60	41
100ms	120	101
200ms	220	201
500ms	520	501

For two channels of measurement, there is an overhead of ten cycles of the sample rate after each sample time. If we consider two channels at the same sample times and rates, then the number of samples (per channel) and update time (2 channels of overhead) is:

Sample Time Setting	Slow Rate Slow 50Hz Update Time	Fast Sample Rate 900Hz Update Time
20ms	440	60
40ms	480	100
100ms	600	220
200ms	800	420
500ms	1400	1020

USC PID Application Program

File	Comment
Help	If unexpected results occur when loading the .usc file press back and click on help for instructions.
UAP0025c.usc	This program is designed for use with UscConfig 105 or higher. Add integral reset function.
UAP0025d.usc	This program is designed for use with UscConfig 106 or higher. Add power on branch and replaced the use of three constants to make then available for use on the AM702 trim menu if required. Con_d has been replaced by Var04 Con_i has been replaced by Var01 Con_j has been replaced by Var03.