Component 130: PID-Controller (with Anti Wind-Up)

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Component 130: PID-Controller (with anti-windup)

Specifications

Line connections
1	Signal in
2	PID out
3	Set Point
4	Control inlet for Kp (as M), TN or Kl (as H) und TV or KD (as P)

General User input values Results Characteristic lines Physics used Display shapes Example

General

The task of this controller is to compensate a control difference (caused e.g. by the transfer behaviour of a transient component) in the case of transient processes. It cannot be applied as a data controller (“iteration controller“) like e.g. Component 12! By means of a correction variable, a chronologically variable actual value is calculated until it has reached the specified set point value. This is a matter of a control algorithm with P-, I and D-fractions and not of calculating a target value by means of a steady-state input variable! This type of controller uses the common differential equation to calculate the transfer function of PID-Controllers:


	Eqn. 1-1

Delivers the output signal y(t) with following parameters:

Kp: Proportional gain factor (P-Controller)
Ki: Integral gain factor (I-Controller)
Kd: Differential gain factor (D-Controller)
e(t): Input signal (Controller difference, Set Point - actual input value)

The integral part of the output signal y(t) can be obtained from the history of the input signals. The integrator is realized via summing the previous input signals e(t).
The differential time steps dt are replaced by the intervals of the sampling time Dt, which are given from the time series dialog in EBSILONprofessional.

Using this kind of discretisation eqn.1-1 changes to the following with regard to time step k:


	Eqn. 1-2

This type of controller requires a specification of the physical quantity to be controlled as well as of the input quantity. Correcting variable has to be one of the base quantities such as mass flow, enthalpy and pressure. Concerning input value derived ones are also possible, e.g. heat flow and temperature. Attention should be paid to set up the right characteristic of the controller:

If both values (corrected one and actual input) show changes in the same direction the characteristic of the controller turns out positive. A typical example for this is controlling the generator performance by the feed water flow. Increasing one means also higher values of the other.
If values react vice versa in opposite directions, the characteristic is negative. For example controlling steam temperature via water injection. The more water is fed to the steam, the less temperatures will be the result. Negative characteristic is realized by negative values of Kp (proportional gain factor). Negative time constants (TN, TV) are not allowed as well as negative gain factors KIA and KD.
Initial values for the quantity to be corrected, e.g. the controller output signal has to be set by means of an internal specification value.

Global Initialization of Transient Components

All transient components that possess the flag FINIT can be commonly controlled via one global flag.

For this, the flag FINIT has been expanded by the position GLOBAL: 0.

If it is set to this value, the control of the transient simulation will be handed over to the global variable “Transient mode“, which can be found under

Extras \Model Options\Simulation\Transient\ Combo Box "Transient mode"

This will then pass on the desired mode (first iteration or following iteration) to the components. This can be controlled from the time series dialog by means of the expression “@calcoptions.sim.transientmode“.

Additional logic line (Pin 4)

For the PID controller, there is an additional logic line (Port 4) that can be switched on optionally. With its help, the controller parameters (Kp, KI, and KD) can be set externally. Here the data are taken over into the model in each iteration step. In connection with this, there is another flag FPARAMIN for selecting the source of the parameters.

Specification value FOUTUS: specification of the outlet signal

Usually, the actual value of the target variable is unknown before the simulation, and it is only determined in the course of the iteration. On the other hand, the outlet signal of the controller (PIN 2) depends on the actual value and on its difference with respect to the reference variable respectively. This may lead to convergence problems. To alleviate this problem, the specification value FOUTUS has been implemented in Component 130.

If FOUTUS = 0, the current value of the outlet signal at PIN 2 will be used in the simulation (as previously).
If FOUTUS = 1, then the value of the outlet signal from the previous time step will be used. This has the advantage that the outlet signal remains constant during the iteration, thus improving the convergence significantly. However, the results are less precise regarding the accuracy in terms of time. The smaller the time step width for the time integration, the smaller the resulting error will become.

The setting FOUTUS = 0 is the default setting. It is recommended to use the setting FOUTUS = 1 only if convergence cannot be achieved by other means.

User input values

FINIT	Flag: Initializing state Like in Parent Profile (Sub profile option only) Expression =0: Global, which is controlled via global variable "Transient mode" under Model Options: "Extras" ->"Model Options" -> "Simulation" -> "Transient" -> Combo Box "Transient mode" (See -> General -> Global Initialization of Transient Components ) =1: First run (TCOUNT set to 0) =2: Continuation run
FTYPE	Switch specification of controller parameters Like in Parent Profile (Sub profile option only) Expression =0: Specification of proportional gain factor and time constants Kp, Tn und Tv =1: Specify gain coefficients KP, KI, KD
FSPIN	Switch source of setpoint/input signal Like in Parent Profile (Sub profile option only) Expression =0: internally given value =1: externally from line 3 =2: input only from line 1 (line 3 and internal set point not taken into account)
FPARAMIN	Source of controller parameters Like in Parent Profile (Sub profile option only) Expression =0: Internally Set =1: Eternally by connection point n
FSPTYPE	Switch for specification of the type of controller parameters Like in Parent Profile (Sub profile option only) Expression =1: Pressure =2: Temperature =3: Enthalpy =4: Mass flow =5: Power, Enthalpy flow
FPIDOUT	Switch for type of control variable Like in Parent Profile (Sub profile option only) Expression =1: Pressure =3: Enthalpy =4: Mass flow
SETPOINT	Internal set point dependent on FSPSOURCE
KP	Proportional gain factor <0: Negative characteristic of controller >0: Positive characteristic of controller
KI	Integral gain factor, dependent on FTYPE, not active in case of FTYPE = 0
KD	Differential gain factor, dependent on FTYPE, not active in case of FTYPE = 0
TN	Reset time, dependent on FTYPE, not active in case of FTYPE = 1
TV	Rate time, dependent on FTYPE, not active in case of FTYPE = 1
YINI	Initial Value for output signal
FPIDMODE	Switch for controller algorithm Like in Parent Profile (Sub profile option only) Expression =1: Difference equation =2: Position algorithm
FINTEGRAL	Switch method of integration Like in Parent Profile (Sub profile option only) Expression =1: Backward integration =2: Forward integration =3: Trapezoidal integration
FYLIMIT	Switch for controller limiting Like in Parent Profile (Sub profile option only) Expression =0: no limitation =1: Saturation feedback =2: Stop integrator =3: Limitation of integrator
YMIN	Minimal value of output signal
YMAX	Maximal value of output signal
TPRE	Index of previous time step (if set to 0, all buffers are going to be initialized)
TIMEINT	Total integration time
FOUTUS	Corrected value usage (see under "General") Like in Parent Profile (Sub profile option only) Expression =0: From current time step ( highest accuracy) =1: From previous time step ( highest convergence rate)
CLAG	indicated value for integrator clamping (no input), active for FYLIMIT =3. If indicated value (CFLAG)= 1, then it indicates, that Clamping was active in the last time step.

Results

RKP	Calculated proportional gain factor
RKI	Calculated integral gain factor
RKD	Calculated differential gain factor
RTN	Calculated reset time
RTV	Calculated rate time
RPROP	Actual proportional part of the controller output signal
RINT	Actual integral part of the controller output signal
RDIFF	Actual differential part of the controller output signal
RTCURR	Index of actual time step
RTIMETOT	Total time at end of calculation
RCFLAG	Status of integrator clamping

Characteristic curves

These "characteristic" curves don´t give any specifications or correlations to characterize the component. They are necessary to just as memory for the signals.
Normally, there´s no need to set any values or give specifications, because the are transferred automatically by the time series calculations.

CCONTROLIN - History of input signal at line 1

This line stores the course of the input signal at line 1.

x-axis: Time steps, accumulated in seconds starting at Dt from first step.

y-axis: Values of input signals.

COUTPUT - History of output signal at line 2

This line stores the course of the output signal at line 2.

x-axis: Time steps, accumulated in seconds starting at Dt from first step.

y-axis: Values of output signals.

CINTEGRATOR - History of integral part of the output signal

This line stores the course of the integrator values representing the I-Part of the output signal at line 2.

x-axis: Time steps, accumulated in seconds starting at Dt from first step.

y-axis: Values of output signals.

CSETPOINT - History of set points (line 3 or internal)

This line stores the course of the set points.

x-axis: Time steps, accumulated in seconds starting at Dt from first step.

y-axis: Values of set points

Result curves

RACONTROLIN - History of input signals at line 1

RAOUTPUT - History of output signals at line 2

RAINTEGRATOR - History of integral part of the output signal at line 2

RASETPOINT - History of set points (line 3 or internal)

The output curves are correlated to the correspondent characteristic lines, all of them show the values at the end of the time step.
For calculation of the following time step the values of the result curves are copied to the characteristic lines, what forms a kind of circular buffer.

Physics used

Equations

With respect to users needs there are two algorithms to determine the numerical treatment of the controller equation eqn. 1-2.:

PID difference equation
Position algorithm

Difference equation

Position algorithm

y(k) = y(k-1) + b0*e(k)+b1*e(k-1)+b2*e(k-2)

with b0 = KP + KI*DT+KD/DT

b1 = -KP-2KD/DT

b2 = KD/DT

Relationship of input parameters (based on the model of ideal PID-Controller)

KI = KP/TN, and TN = KP/KI

KD = KP*TV, and. TV=KD/KP

Possibilities to control the output signal (Anti Windup)

All real controllers reach an almost physically determined limit of the quantity to be controlled. Either a lower or an upper limit will cut the range of possible output values governing the controlled system. For example at given conditions the output of a water tap can only vary between zero and max flow.

Hence, if there´s a remaining control deviation the integrator part can cause problems without being controlled (wind-up effects). In fact that means the integrator can end up with values, which take a long time to be balanced again.

To control the output signal, especially the integrators part of the signal various methods can be applied:

Saturation Feedback (FYLIMIT = 1)

y(k) <= ymax && y(k) >= ymin

y(k) = ymax, resp. ymin

y(k-1) = (ylim - KP*e(k) - KD/DT*(e(k) -e(k-1)))/KI*DT

This method compares the output signal to a given limiting value. While under- or overflow, the limit value will be set to the controller output and the integral part is fixed using feed back of a differential value, which simulates a zero input to the integrator. In this way the stored values remain active, but won´t cause any crossings of the thresholds.

Stop Integration (FYLIMIT = 2)

y(k) <= ymax && y(k) >= ymin

y(k) = ymax, resp. ymin

y(k-1) = const. (y(k-2))

This method stops the integration by setting it to a constant value, e.g. the value of the previous time step.

Clamp Integration (FYLIMIT = 3)

y(k) <= ymax && y(k) >= ymin

Se(i) = ymax, resp. ymin

This method clamps the integration to the given limits.

Integration methods

For the calculation of the summations in the controller equation three methods can be chosen:

Forward
	Se(i) = e(k)

Backward
	Se(i) = e(k-1)

Trapoidal
	Se(i) = 1/2*(e(k)+e(k-1))

Displays

Form 1

Example

Click here >> Component 130 Demo << to load an example.