Linear, Nonlinear and Model Predictive Control

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CFC – PID-ControllerExample of use PID-Controller CTRL_PID (PLS Siemens PCS 7):

(Source: https://pcs.khe.siemens.com/index.asp?Nr=5844 - PCS 7 Library V6.0)

Functionality: continuous PID-Controller (default control-ciruit)• Fixed comand control• Cascade controle (single-/multiple cascade) • Ratio control

More possibilities of processing: • Switching between control mode: hand drive, automatic or tracking• Limit value monitoring of the variable, error signal and generating of messages• Disturbance variable compensation• Setpoint tracing• Valuation adjustment of setpoint and actual value (physical standardization) • Valuation adjustment of setpoint (physical De-standardization) • deadband (reaction point) in the sector of the actuating variable • Individual detachable and shiftable P-, I- and D-Part • P- and D-Part could be place in the refeed• Adjustment of the working point (P- rather PD-control operation)

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Step response• ER – error signal• LMN – gate of

control point• LMN_HLM – Limit

of the controlpoint

• LMN_LLM –Lower limit of thecontrol point

• GAIN –proprotionalcoefficient

• TN – reset time• TV – derivate time• TM_LAG – time

lag D-Part• SAMPLE_T –

aperture time

Step response:

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Setpoint creation –Structure

Setpoint creation:

• SP – active Setpoint• SP_EXT – external setpoint• SP_OP – control access for the

setpoint• PV_IN – actual value

• SP_TRK_ON – setpoint SP_OP tracking

• SPBUMPON – latitude impact for thesetpoint Sollwert

• SPxRLM – maximal draft setpoint

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Setpoint creationSetpoint creation:• Internal Setpoint

– Handling and limitation of the internal setpoint SP_OP is foundedabout OP_A_LIM rather OP_A_RJC.

• External Setpoint– The external setpoint SP_EXT can be connected and is limited in the

range of (SPEXTLLM,SPEXTHLM).• Updated Setpoint

– If SP_TRK_ON=1 then PV_IN is used as setpoint value. Thetracking of the setpoint to the actual value is only active during thehand drive (with internal setpoint and if SPBUMPON = 1), and ist primary conduced for the switching between hand drive to automaticto find the right setpoint.

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Regler – PID-Kernel – StructureSystem deviationand PID-Kernel:

• ER – system deviation• PVx_ALM – actual value: alarm limit• PVx_WRN – actual value: warning limit• QPVxx_xxx – alarm/warning limit

• NM_PVxR – standardization of themeasurement range

• INT_Hxxx – freezing I-Part • LMN_INT – internal control point• LMN_OFF – Working point

SPLMN_INT

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Regler – System deviationSystem deviaton - Creation:• The system deviation ER is build with the active setpoint SP and the actual

value PV_IN and is available on the exit ER after the dead zone DEADB_W.

• System deviation - Control– The system deviation ER is controlled with an collective hysteresis

(ER_HYS) on the arlarm limits(ERL_ALM, ERH_ALM). • Actual value - Control

– The actual value PV_IN is controlled with an collective hysteresis (HYS) on the warning and alarm limits Alarmgrenzen (PVL_ALM, PVL_WRN, PVH_WRN, PVH_ALM). The inducation is shown of the outputs(QPVL_ALM, QPVL_WRN, QPVH_WRN, QPVH_ALM).

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – PID-KernelAlgorithm PID-Kernel :• Controller working with standardized Variables(-100 % - 100 %).• P-Part could be activated and deacitvated by P_SEL.• With PFDB_SEL and DFDB_SEL it‘s possible to add P- und D-Part to the

refeeding independent of each other.– Pro: P- rather D-Part is not affected by the leaps of the setpoint, this means

the control point does not change by leaps on leaps of the setpoint.• With TN = 0 (I-Anteil ist ausgeschaltet) the working point is given explicit by

LMN_OFF.• With INT_HPOS = 1 and INT_HNEG = 1 you can freeze the P-Part

– Pro: You can avoid that the Integrator integrates to endless high values, ifthe deviation is constant.

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller –PD-Part in reduction

PID Drift-SP ER LM PV

I

Drift

-SP

LM PVPD-SP0=0

++

PID-Controller in a standart structure:

PID-Controller with a PD-Part in reduction:

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Controller algorithm

Implementation of the Controller algorithm during „normal mode“:

( )1)ER(kER(k)SAMPLE_T/2TM_LAG

TVGAINER(k)TN

SAMPLE_TGAIN1)kLMN_INT_I(ER(k)GAINLMN_INT(k) −−+

+⎟⎠⎞

⎜⎝⎛ +−+=

Controller algorithm during „normal mode“:

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – StandardizationPhysical standardization• The actuating variable(ER) is standardized (in percent) by the physical

measurement range of the actual value (NM_PVHR, NM_PVLR).

• Atfer the PID-Algorithm the actuacting variable is … (denormiert)… from percentto the physical measurement range of the control point(NM_LMNHR, NM_LMNLR).

• Internal rather external Setpoint, actual value such as associated parameterhave to be entered in the physical measurement range of the actual value.

• Manual value, time of setpoint tracing of the actuating variable, circuit-entering of the disturbance variable such as associasted parameter have to be entered in the physical measurement range of the contol point.

• The amplification of thecontroller GAIN is shown in standardized form(withoutdimension).

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Actuating variable –Structure

LMN_INT

Actuating variable-creation:

• LMN – actuating variable (a.v.)• DISV – circuit-entering of the disturbance

variable• NM_LMNxR – standardization of the

actuating variable

• LMN_xLM – Limits of the actuating variable• MAN_OP – ext. a.v. (Input Operator)• LMN_TRK – external actuating variable• QMAN_AUT – Output Manual/Automatic

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Actuating variable –Choice

Choice of the actuating variable:

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – circuit-entering of the disturbance variable

circuit-entering of the disturbance variable :During the automatic mode the circuit-entering of the disturbance variable DISV is added on the output and after that the result is limited in therange from LMN_LLM to LMN_HLM.

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – ParameterThe Parameter of the Controller GAIN, TN(TI), TV(TD) and TM_LAG are

usually not combinable. • In case they have to be connected , for example „Gain-Scheduling“,the

attribute of the system s7_link has to be changed.• Changeover of the Parameter during the running automatic mode may

lead to leaps of the actuating variable.

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Setpoint tracingmode

Setpoint tracing mode:• In this situation (LMN_SEL=1) the acuating variable is taken by the

comined setpoint tracing value LMN_TRK and put on the output. • The Outputs QLMN_HLM and QLMN_LLM are set on FALSE. • The mode „tracking" has priority against all other modes, so that via this

input a security shutdown of the machine can be projected.

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Plugs (I)

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Plugs (II)

Linear, Nonlinear and Model Predictive Control

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CFC – PID-Controller – Plugs (III)