Relaxc-Commissioning-Straton

Abstract

Commissioning
Relaxc for Straton-PLC

Full text

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 1 / 8
Commissioning
Relaxc for Straton-PLC
(Copa-Data)
John Masse
Relaxc@appedge.com
Version 3

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 2 / 8
Table des matières
RELAXC ................................................................................................................................................ 3
1 INTRODUCTION ........................................................................................................................... 3
2 WHAT IS IN THIS CHAPTER ..................................................................................................... 3
3 DESCRIPTION ............................................................................................................................... 3
WHY TO USE RELAXC. .................................................................................................................. 3 3.1
FUNCTION DESCRIPTION ............................................................................................................... 3 3.2
EQUATION OF RELAXC ................................................................................................................ 4 3.3
REPRESENTATION IN FBD ............................................................................................................ 4 3.4
PARAMETER DESCRIPTION ........................................................................................................... 5 3.5
RUNTIME ERROR ........................................................................................................................... 6 3.6
SAMPLE TIME TE OR TS ................................................................................................................ 6 3.7
THE BEST CHOICE IS TO SET THE TIME OF THE MAIN TASK EQUAL AT CYCLE=0S. .......................... 6
RELAXC INITIALIZATION.............................................................................................................. 6 3.8
MINIMAL TIME VALUES OF TRE, TV, TG ...................................................................................... 6 3.9
GAIN KS ........................................................................................................................................ 6 3.10
NORMALIZATION OF CONTROLLER RANGE. ............................................................................. 7 3.11
TRACKING MODE TR_S=1 AND PV_SPEED. ............................................................................... 7 3.12
CONSTRAINTS ON URELAXC=[UMAX, UMIN] AND ON THE PROCESS SPEED OR 3.13
ACCELERATION. ..................................................................................................................................... 7
HOW TO TUNE RELAXC............................................................................................................... 7 3.14
4 EXAMPLE OF RELAXC IMPLEMENTATION. ....................................................................... 7

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 3 / 8
RELAXC
1 Introduction
This documentation describes the Relaxc block in Straton -PLC
2 What is in This Chapter
This chapter contains the following Topics
Topics
Description
Relaxc connection
Detailed description
Variables used
3 Description
Why to use Relaxc. 3.1
The Relaxc’ approach is:
• Easy to tune, easy to use without complex calculations or specific tools,
• Robust and efficient,
• Generic for all processes.
• Directly tunable without modelling.
Relaxc allows to control effortless and without overshoot complex processes including
Non minimal phase, small and large pure delay, unstable processes, variable static gain,
strong non-linearities, constraints on U, speed saturations, discontinuities, load disturbances,
etc. While minimizing the operational costs, the energy peaks of the control U ( Urelaxc) at
each Step of (SP: set point) with a more reliable control.
We can use Relaxc where the control is not satisfactory resolved by a PID or other control
laws. It is advantageous to replace for example all the PID by Relaxc. The maintenance and
the predictive maintenance will be easier.
Relaxc stability: Relaxc ensures a good stability by its mathematical nature because it allows
to find the best response in closed loop without overshoot. It is a guarantee of robustness.
Function description 3.2
The function block represents Relaxc Controller.
The function block contains the following operating mode:
• Tracking
• Automatic

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 4 / 8
Operating mode
Tr_S
Tracking
1 ( Urelaxc=U_i)
Automatic:
(Relaxc works)
0
NOTE: This function block performs an internal initialization in the first program cycle after
a warm start or cold start (e.g. application download or power cycle) of the PLC program.
Due to this, you have to make sure that the function block is invoked in the first program
cycle. In case of invoking the function block in a later program cycle, the internal
initialization will not be performed and the output may deliver a wrong value.
WARNING UNEXPECTED OUTPUT BEHAVIOUR
Make sure that the function block is always invoked in the first program cycle.
Equation of Relaxc 3.3
We just recall briefly the algebraic equation of Relaxc:
u(k)=R(u(k-1),tre)+ks*(tg*s*e+e)
• With R the reactivity or Relax function which depends on tre
• e=(yref-Pv) with Yref the reference trajectory that depends on the time
constant tg and Pv (the output of the process).
• Ks the convergence gain on e
• U (the output of Relaxc)
• (s) Laplace variable.
• U(k) is the output of Relaxc (Urelaxc)
Representation in FB 3.4

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 5 / 8
Parameter description 3.5
Description of input parameters:
Parameter
Data type
Description
EN
Bool
Enable Input : Relaxc is processed if EN=1 (Edge Rising). Because Relaxc
does not use an internal function time
Sp
real
Set point
Pv
real
Measure of the process value
Rparam
Rparam
(structure)
Tuning parameters of Relaxc
Tr_s
bool
Initialization Command ( 0 => Relaxc works, 1=> Urelaxc =U_i)
U_i
real
Initialization of the output U of Relaxc (Urelaxc) on a edge rising of Tr_S
or Tr_S=1
Te
time
Sample time with respect to EN
Description of output parameters:
Parameter
Data type
Description
ENO
Bool
Enable output
UR
real
Output of Relaxc ( Urelaxc)
PV_SPEED
real
Display the the speed of the process output (PV).
Rinfo
real
Version of Relaxc.
Description of the internal parameters: Param
Parameter
Data type
Description
tg
real
Time constant of the reference trajectory in seconds
tre
real
Relaxc time or reactivity time (delay+lag) in seconds
Ks
real
Speed convergence gain or throttle between the reference trajectory and PV
Umax, Umin
Real
Upper limit and lower limit on the Relaxc output: (Urelaxc). For example
[100 to -100]
tv
real
Time filter of smoothing in second on the derivative ( speed) of PV

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 6 / 8
Runtime error 3.6
For a list of all block error codes and values :- None.
Sample time Te or Ts 3.7
The user controls the sample time of Relaxc with Te (Time format example t#10ms). The
sample time of Relaxc can be different from the Mast sample time because it is controlled by
a Blink block. (See Figure 1 Relaxc in tracking mode with a PID).
The Sample time (Te) has to be the same for the block Blink and Relaxc. The output Q
of Blink has to be connected to the input EN of Relaxc.
The best choice is to set the Time of the main task equal at cycle=0s.
In all the case Te= #txxx+ TM with xxx the value of the sample time.
To see the real sample time used by relaxc set appedge=2 and see the output info.
Relaxc Initialization 3.8
During the cold or warm start, Relaxc initializes the data such as Urelaxc=U_i .
Minimal time values of tre, tv, tg 3.9
These times use a real format. For example to set tre at 100ms we write tre=0.1. For 10
seconds, tre=10.0. It is possible to set tre and tv at zero or under the value of the sample time.
For example tre=Te/10.0. We recommend the minimal value tg=8.0*Te or more for Shannon
and numerical integration rules.
Gain ks 3.10
Note that the gain ks gives the initial value of Urelaxc. Urelax(t=0 seconde)=ks*SP.
With ks=0, Relaxc does nothing. Urelaxc=0. The value of ks controls the response time or
the overshoot in closed loop with respect to tg and tre.

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 7 / 8
Normalization of controller range. 3.11
The best and the more practicable way to control a process is to normalize the input (PV)
between [0,100] or [-100,100] and to do the same thing on Urelaxc and the set point (SP).
This facilitates process understanding, process maintenance and the commissioning. This step
is necessary if we want to know the process normalized speed (v) to compute the parameter
ks.
Tracking mode TR_S=1 and Pv_speed. 3.12
When the mode TR_S=1, thus Relax does not work and Urelaxc=U_I. It is a useful mode
when we perform a normalized step of the process independently of SP. It allows measuring
the speed (v) of the process. This value is necessary to compute ks.
The value of v is the maximal normalized speed of the process v=measured/U_I
And  =
(
)
Remark: When TR_S=0(Relaxc works). The Pv_speed is also computed during the
control and the speed must be at least close to the measured speed. This rule allows to
reach a safe and optimal control without overshoot.
Constraints on Urelaxc=[Umax, Umin] and on the process speed 3.13 or acceleration.
Relaxc take into account naturally all these constraints without using complex anti windup
scheme or complex saturation tuning. There is nothing to do. Just let Relaxc to work.
How to tune Relaxc 3.14
See the documentation about tuning.
4 Example of Relaxc implementation.
This example shows how to plug Relaxc and Rcalibration which allows to compute tre,tg and
ks. The example controls y=exp(-tds)+disturbance.

Relaxc
10/2020
Relaxc is controller software or block function under ‘EULA’ license. It is a copyrighted work of APPEDGE 8 / 8