6.8. Appendix 6.1: Control System Input Description

This appendix contains a description of the SAS4A/SASSYS‑1 input block assigned to the control system model.

6.8.1. Input Block Structure

The input block structure is identical to the standard SAS4A/SASSYS‑1 input block structure in all but one respect. A new card format known as a signal card has been introduced. These cards immediately follow the block identifier card and precede the standard data cards. The ordering of the different card types is depicted in the diagram below.

block identifier card
signal card # 1
signal card # 2

.
.
.

signal card # n
end of signal card

data card # 1
data card # 2

.
.
.

data card # m
block delimiter card

6.8.2. Block Identifier Card

Block identifier cards are described in Section 2.8.2. For the control system input block the number is 5 and the block name is INCONT.

6.8.3. Signal Cards

form = "(4I5, 5F10.0)"
read(*,form) ISIG, JTYPE, J1SIG, J2SIG, F1SIG, F2SIG, F3SIG, F4SIG, F5SIG

A signal card is used to define a signal in the user’s control block diagram. There are four signal types: measured, demand, block and control. Each signal must be assigned a unique signal identification number using the ISIG field. The value of ISIG must lie between 1 and 998. The remaining variables that are used to define control system signals are defined in Table 6.8.1.

Table 6.8.1 Signal Card Format

Column	Fortran Symbol	Definition	Variable Type
1	ISIG	Signal number	Integer
6	JTYPE	Signal type	Integer
11	J1SIG	Signal descriptor 1	Integer
16	J2SIG	Signal descriptor 2	Integer
21	F1SIG	Constant 1	Real
31	F2SIG	Constant 2	Real
41	F3SIG	Constant 3	Real
51	F4SIG	Constant 4	Real
61	F5SIG	Constant 5	Real

6.8.3.1. Measured Signal

A measured signal makes available to the block diagram the present value of a referenced SAS4A/SASSYS‑1 variable. The correspondence between the variable that is referenced and the signal card data field values is given in Table 6.8.3. Note that all measured signals have a JTYPE value between -50 and -89.

6.8.3.2. Demand Signal

A demand signal makes available to the block diagram the product of the current value of a time dependent function defined by the user through a demand table and an initial condition value. A demand table is a set of (CTLTAB, CTLTIM) ordered pairs supplied by the user in the format of Table 6.8.4. The code obtains the demand signal value by linearly interpolating among the table entries using the current time. The initial value is obtained as described in Section 6.4. The correspondence between the demand table and the signal card data fields is given in Table 6.8.3. Note that a demand signal has a JTYPE value of -90.

6.8.3.3. Block Signal

A block signal makes available to the block diagram the value at the output of a block. The correspondence between the block characteristics and the signal card data fields is given in Table 6.8.3. Note that all block signals have a JTYPE value between 1 and 23. A measured, demand or block signal can be used as an input to a block by specifying on the block’s signal definition card the signal identification number assigned to the input signal. The signals input to each block type are combined according to the mathematical expressions given in Table 6.8.2.

Table 6.8.2 Summary of Mathematical Block Signals

JTYPE	Block	Mathematical Form	Representation	Type
1	Summer	\(y = g(g_{1}u_{1} + g_{2}u_{2})\)		function
2	Multiplier	\(y = gu_{1}u_{2}\)		function
3	Divider	\(y = g\frac{u_{1}}{u_{2}}\)		function
4	Differential	\(y = g\frac{d}{dt}u\)		function
5	Integrator	\(y = y_{0} + g \int_{0}^{t}{u\,dt}\)		dynamic
6	Lag Compensator (See also Variable Lag Compensator)	\(y + \tau\frac{d}{dt}y = g\,u(t)\) \(y\left( 0 \right) = y_{0}\)		dynamic
7	Lead-Lag Compensator	\(y + \tau_{1}\frac{dy}{dt} = g\left(u + \tau_{2}\frac{du}{dt}\right)\) \(y(0) = y_{0}\)		dynamic
8	Function Generator	\(y = g\,f(u)\)		table
9	Maximum Value	\(y = \max\left( u_{1},u_{2} \right)\)		function
10	Minimum Value	\(y = \min\left( u_{1},u_{2} \right)\)		function
11	Time Delay	\(y = u(0); 0 \leq t \leq T\) \(y = u(t - \tau); t > T\)		function
12	Natural Logarithm	\(y = \ln u\)		function
13	Exponentiation	\(y = u_{1}^{u_{2}}\)		function
14	Velocity limiter	\(y = y_{\text{down}}; gu < y_{\text{down}}\) \(y = y_{\text{up}}; gu > y_{\text{up}}\) \(y = gu; \text{otherwise}\) \(y_{\text{down}} = y\left( t - h \right) - h\ v_{\text{down}}\) \(y_{\text{up}} = y\left( t - h \right) + h\ v_{\text{up}}\)		function
15	AND	\(y = 1; u_{1} > 0, u_{2} > 0\) \(y = 0; \text{otherwise}\)		logic
16	OR	\(y = 0; u_{1} \leq 0, u_{2} \leq 0\) \(y = 1; \text{otherwise}\)		logic
17	NOT	\(y = 1 \ \ u \leq 0\) \(y = 0 \ \ u > 0\)		logic
18	Comparator	\(y = 0\) if \(u_{1} < u_{2}\) \(y = 1\) if \(u_{1} \geq u_{2}\)		logic
19	Sample and Hold	\(y(t) = u_{2}(t)\) when \(u_{1}(t) \leq 0\) \(y(t) = u_{2}(t_{s})\) when \(u_{1}(t) \geq 0; t_{s} < t\) where \(u_{1}(t') \leq 0; t_{-} \leq t' < t_{s}\)		function
20	J-K Flip-Flop	\(y^{n + 1} = Q^{n}; u_{1} \leq 0, u_{2} \leq 0\) \(y^{n + 1} = 0; u_{1} > 0, u_{2} \leq 0\) \(y^{n + 1} = 1; u_{1} \leq 0, u_{2} > 0\) \(y^{n + 1} = {\overline{Q}}^{n}; u_{1} > 0, u_{2} > 0\)		logic
21	Constant	\(y = g\)		function
22	Sine	\(y = g_{1} \sin\left( g_{2}u(t) + g_{3} \right)\)		function
23	Variable Lag Compensator	\(y + \tau(t)\frac{d}{dt}y = g\,u(t)\) \(y\left( 0 \right) = y_{0}\)		dynamic

6.8.3.4. Control Signals

A control signal is used to set the value of a SAS4A/SASSYS‑1 variable equal to the value of a block signal. The correspondence between the block signal and the SAS4A/SASSYS‑1 variable and the signal card data fields is given in Table 6.8.3. Note that all control signals have a JTYPE value between -1 and -8.

6.8.3.5. End of Signals

A sequence of signal definition cards is delimited by a signal card with the ISIG field entry equal to ‘999’.

This card also contains flags for the binary output file print interval and control of the stead state solution finder. First, the absolute value of the JTYPE field for the 999 card is sets the print interval for control system results output to the binary output file CONTROL.dat. Second, the J1SIG field is used to determine whether the steady state solution finder is to be used. An entry of ‘1’ indicates that the steady state solution finder is to be used, while any other entry in this field causes the solution finder to be bypassed. (A discussion of the initial condition option is given in Section 6.4). Finally, the J2SIG field allows the user to control the amount of steady state output generated. An entry of ‘1’ produces an extended output for trouble shooting purposes, while any other entry produces a standard output.

The JTYPE field is also used to generate an extended printout during the transient for debug purposes. The debug is generated by setting the JTYPE field of the 999 card to a negative value. The printout begins at the time specified on the F1SIG field.

Table 6.8.3 Signal Cards

Signal	Card
Type	Variable	JTYPE	J1SIG	J2SIG	F1SIG	F2SIG	F3SIG	F4SIG	F5SIG
Measured	Compressible volume pressure, PRESL3	-50	Volume number, ICV
Measured	Liquid segment flowrate; FLOSL3	-51	Liquid segment number, ISGL
Measured	Liquid cover gas interface elevation, ZINTR3	-52	Volume number, ICV
Measured	Liquid mass, XLQMS3	-53	Volume number, ICV
Measured	Cover gas volume, VOLGC3	-54	Volume number, ICV
Measured	Time	-55
Measured	Pump head, HEADP3	-56	Pump number, IPMP
Measured	Liquid temperature, TLQCV3	-57	Volume number, ICV
Measured	Liquid density, DNSCV3	-58	Volume number, ICV
Measured	Wall temperature, TWLCV3	-59	Volume number, ICV
Measured	Cover gas pressure, PRESG3	-60	Volume number, ICV
Measured	Cover gas mass, GASMS3	-61	Volume number, ICV
Measured	Cover gas temperature, TGASC3	-62	Volume number, ICV
Measured	Not used	-63
Measured	Liquid segment temperature, TSLIN3	-64	Segment number, ISGL	Inlet=1 Outlet=2
Measured	Pump speed, PSPED3	-65	Pump number, IPMP
Measured	Core channel coolant flowrate, CHFL03	-66	Channel number, ICH	Inlet=1 Outlet=2
Measured	Liquid node temperature, TLNOD3	-67	Node number, INOD
Measured	Wall node temperature, TWNOD3	-68	Node number, INOD
Measured	Liquid element temperature, TELEM	-69	Element number, IEL	Inlet=1 Outlet=2
Measured	Not used	-70
Measured	Core channel outlet temperature, CHFCOF	-71	Channel number, ICH	Inlet=1 Oulet=2
Measured	Normalized reactor power, DEXP (POWVA (3,1))	-72
Measured	Normalized fission power, POWFSO * AMPO	-73
Measured	Normalized decay heat \(\sum_{i = 1}^{\text{POWDK}}{\text{POWWT}\left( i \right) \times \text{POWDKH}(i)}\)	-74
Measured	Equivalent Circuit EM Pump Voltage	-75	Pump number, IPMP
Measured	Equivalent Circuit EM Pump Frequency	-76	Pump number, IPMP
Measured	Equivalent Circuit EM Pump Current	-77	Pump number, IPMP
Measured	Equivalent Circuit EM Pump Phase Angle	-78	Pump number, IPMP
Measured	Not used	-79,… -82
Measured	Steam generator, feed-water mass flowrate in	-83		SG number
Measured	Steam generator, feed-water enthalphy in	-84		SG number
Measured	Steam generator, steam mass flowrate	-85		SG number
Measured	Steam generator, steam temperature out	-86		SG number
Measured	Steam generator, steam pressure	-87		SG number
Measured	Steam generator, water level	-88		SG number
Measured	Steam generator, steam enthalpy out	-89		SG number			Initial condition flag	yo
Demand	Demand Table	-90	Demand table number	Number of entries in table				yo
Measured	Fuel Centerline Temperature	-101	Channel number	MZ mesh number	Scaling factor	Offsetc
Measured	Fuel Average Temperature	-102	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Fuel Surface Temperature	-103	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Clad Inner Wall Temperature	-104	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Clad Mid Wall Temperature	-105	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Clad Outer Wall Temperature	-106	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Coolant Temperature	-107	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Coolant Pressure	-108	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Coolant Saturation Temperature	-109	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Coolant Boiling Margin	-110	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Coolant Average Temperature	-111	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Structure Inner Temperature	-112	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Structure Outer Temperature	-113	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Reflector Inner Temperature	-114	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Reflector Outer Temperature	-115	Channel number	MZC mesh number	Scaling factor	Offset
Measured	Peak Fuel Temperature	-116	Channel number	(Optional) If non-zero, peak fuel temperature is provided over all channels in the range J1SIG ≤ ICH ≤ J2SIG	Scaling factor	Offset
Measured	Peak Clad Temperature	-117	Channel number	(Optional) If non-zero, peak cladding temperature is provided over all channels in the range J1SIG ≤ ICH ≤ J2SIG	Scaling factor	Offset
Measured	Peak Coolant Temperature	-118	Channel number	(Optional) If non-zero, peak coolant temperature is provided over all channels in the range J1SIG ≤ ICH ≤ J2SIG	Scaling factor	Offset
Measured	Minimum Boiling Margin	-119	Channel number	(Optional) If non-zero, minimum boiling margin temperature is provided over all channels in the range J1SIG ≤ ICH ≤ J2SIG	Scaling factor	Offset
Measured	Coolant Inlet Temperature	-120	Channel number		Scaling factor	Offset
Measured	Coolant Inlet Pressure	-121	Channel number		Scaling factor	Offset
Measured	Coolant Inlet Flowrate	-122	Channel number		Scaling factor	Offset
Measured	Coolant Outlet Temperature	-123	Channel number		Scaling factor	Offset
Measured	Coolant Outlet Pressure	-124	Channel number		Scaling factor	Offset
Measured	Coolant Outlet Flowrate	-125	Channel number		Scaling factor	Offset
Measured	Maximum Coolant Outlet Temperature	-126			Scaling factor	Offset
Measured	Minimum Coolant Outlet Temperature	-127			Scaling factor	Offset
Measured	Pin Bundle ΔT	-128	Channel number		Scaling factor	Offset
Measured	Pin Bundle ΔP	-129	Channel number		Scaling factor	Offset
Measured	Assembly Bundle ΔT	-130	Channel number		Scaling factor	Offset
Measured	Assembly Bundle ΔP	-131	Channel number		Scaling factor	Offset
Measured	Assembly Power	-132	Channel number		Scaling factor	Offset
Measured	Pin Linear Power	-133	Channel number	MZ mesh number	Scaling factor	Offset
Measured	Peak Pin Linear Power	-134	Channel number		Scaling factor	Offset
Measured	Fission Gas Plenum Temperature	-135	Channel number		Scaling factor	Offset
Measured	Fission Gas Plenum Pressure	-136	Channel number		Scaling factor	Offset
Block	Summer	1	Input signal 1, ISIG	Input signal 2, ISIG	g1	g2	g
Block	Multiplier	2	Input signal 1, ISIG	Input signal 2, ISIG	g
Block	Divider	3	Input signal 1, ISIG	Input signal 2, ISIG.	g
Block	Differentiator	4	Input signal 1, ISIG		g
Block	Integrator	5	Input signal 1, ISIG		g		Initial condition flag	yo	ezb
Block	Lag compensator	6	Input signal 1, ISIG		g	τ		yoa	ezb
Block	Lead-lag compensator	7	Input signal 1, ISIG		g	τ1	τ2	yoa	ezb
Block	Function generator	8	Input signal 1, ISIG	Function generator table number	g
Block	Maximum	9	Input signal 1, ISIG	Input signal 2, ISIG
Block	Minimum	10	Input signal 1, ISIG	Input signal 2, ISIG
Block	Time delay	11	Input signal 1, ISIG		τ			yoa
Block	Natural logarithm	12	Input signal 1, ISIG		g
Block	Exponentiation	13	Input signal 1, ISIG	Input signal 2, ISIG	g
Block	Velocity limiter	14	Input signal 1, ISIG		Vdown	Vup	g
Block	AND	15	Input signal 1, ISIG	Input signal 2, ISIG
Block	OR	16	Input signal 1, ISIG	Input signal 2, ISIG
Block	NOT	17	Input signal 1, ISIG
Block	Comparator	18	Input signal 1, ISIG	Input signal 2, ISIG
Block	Sample and hold	19	Input signal 1, ISIG	Input signal 2, ISIG
Block	JK flip-flop	20	Input signal 1, ISIG	Input signal 2, ISIG				Qo
Block	Constant	21			g
Block	Sine	22	Input signal 1, ISIG		g1	g2	g3
Block	Variable Lag Compensator	23	Input signal 1, ISIG	Input signal 2, ISIG	g			y0 (opt)	ezb
Control	Reactivity, $	-1	Signal number used						ezb
Control	Pump motor torque, normalized	-2	Signal number used	Pump number					ezb
Control	Steam generator, feedwater mass flowrate	-3	Signal number used	Steam generator number					ezb
Control	Steam generator, feedwater enthalpy	-4	Signal number used	Steam generator number					ezb
Control	Steam generator, steam mass flowrate	-5	Signal number used	Steam generator number					ezb
Control	Sodium valve loss coefficient	-6	Signal number used	Valve number					ezb
Control	Steam generator, steam pressure	-7	Signal number used	Steam generator number					ezb
Control	Air dump heat exchanger, air mass flowrate	-8	Signal number used	Air dump heat exchanger number					ezb

^a Not required if steady state solution finder is used, J1SIG(999)=1.

^b Zero crossing parameter.

^c Measured channel signal result is Scaling Factor \(\times\) Raw Value + Offset.

6.8.4. Data Cards

form = "(2I6,5F12.0)"
read(*,form) LOC, N, VAR1, VAR2, VAR3, VAR4, VAR5

A data card appearing in the control system block has a format identical to the standard SAS4A/SASSYS‑1 data card used in floating-point input blocks and is processed in the same way. This means that free-formatted input may be used as an alternative to the fixed format shown above.

Data cards are used to construct demand tables, function generator tables and to supply solution convergence parameters. These quantities and their storage locations are defined in Table 6.8.4.

Table 6.8.4 Table Card Data

Location	Fortran Symbol	Definition/Comments
1	CTLTAB (J,J1SIG)	Table of normalized demand values. A table is defined when at least two entries are provided. Index J1SIG designates the table number and J is the entry number in the table. Dimension (20,100).
2001	CTLTIM (J,J1SIG)	Times for CTLTAB table. Values must be in ascending order. Dimension (20,100).
4001	CTLFNC (J,J1SIG)	Table of function generator dependent variables. A table is defined when at least two entries are provided. Index J1SIG designates the table number and J is the entry number in the table. Dimension (20,100).
6001	CTLSIG (J,J1SIG)	Table of independent variables for CTLFNC table. Values must be in ascending order. Dimension (20,100).
8001	EPSCS	Convergence parameter for dynamic blocks over a subinterval. Must be greater than zero.
8002	EPSCPL	Maximum relative change in a control signal over a subinterval. Must be greater than zero.

6.8.5. Sample Input

Listing 6.8.1 and Listing 6.8.2 show examples of input for the control system. The first listing utilizes a weighted average of the liquid temperature in four compressible volumes to control a valve and additional reactivity. (Note that 0.0245+0.7026+0.2435+0.0294 = 1.) The second listing shows how to access core channel state variables and apply scale and offset parameters. It also demonstrates the calculation of a simple average.

Listing 6.8.1 Using the Control System to Control Flow through a Valve

INCONT     5
!
! Use the Control System to control overflow through Valve 1
!
!        JTYPE: Signal Type
!        |    J1SIG
!ISIG    |    |    J2SIG
!   |    |    |    |         F1SIG     F2SIG     F3SIG     F4SIG     F5SIG
!   |    |    |    |         |         |         |         |         |
    1  -57    1    0                                             100.0    ! TL(CV1)
    2  -57    2    0                                             100.0    ! TL(CV2)
    3  -57    3    0                                             100.0    ! TL(CV3)
    4  -57    4    0                                             100.0    ! TL(CV4)
    5    1    1    2    0.0245    0.7026       1.0               100.0    ! 0.0245*TL(CV1)+0.7026*TL(CV2)
    6    1    3    4    0.2435    0.0294       1.0               100.0    ! 0.2435*TL(CV3)+0.0294*TL(CV4)
    7    1    5    6       1.0       1.0       1.0               100.0    ! TLBAR
    8    8    7    1       1.0                                  1.0E06    ! Table of K_orf
    9   -6    8    1                                            1.0E07    ! K_orf for Valve 1
   10    8    7    2       1.0                                    0.01    ! Table of Reactivity
   11   -1   10    0                                              0.01    ! Control Reactivity

  999 ! End of signal definitions

!                      Function Generator 1: Dependent Value (orifice)
!                      |           |           |           |           |
  4001     5      1.0E10      1.0E10      1.0E09      1.0E06      1.0E03
  4006     2         0.0         0.0

!                      Function Generator 1: Independent Value (TLBAR)
!                      |           |           |           |           |
  6001     5         0.0       738.5       739.0       739.5       740.0
  6006     2       740.5     10000.0

!                      Function Generator 2: Dependent Value (reactivity)
!                      |           |           |           |           |
  4021     5         0.0         0.0        0.01        0.05        0.10
  4026     2      0.1954      0.1954

!                      Function Generator 2: Independent Value (TLBAR)
!                      |           |           |           |           |
  6021     5         0.0       738.5       739.0       739.5       740.0
  6026     2       740.5     10000.0

!                      EPSCS: Convergence parameter for dynamic blocks
!                      |           EPSCPL: Maximum relative change in a control
!                      |           |       signal over a subinterval
  8001     2         0.1         0.5

END

Listing 6.8.2 Average of Inlet and Outlet Temperature for Channel 1, in Degrees Fahrenheit.

INCONT     5
!
!        JTYPE: Signal Type
!        |    J1SIG
!ISIG    |    |    J2SIG
!   |    |    |    |         F1SIG     F2SIG     F3SIG
!   |    |    |    |         |         |         |
    1 -120    1    0       1.8   -459.67             ! Coolant Inlet Temperature, °F
    2 -123    1    0       1.8   -459.67             ! Coolant Outlet Temperature, °F

!   |    |    |    |         |         |         |
    3    1    1    2       1.0       1.0       0.5   ! Summer/Average, °F

  999
!                      EPSCS: Convergence parameter for dynamic blocks
!                      |           EPSCPL: Maximum relative change in a control
!                      |           |       signal over a subinterval
  8001     2         0.1         0.1
END