14Level 5

Analog level control (introduction to PID)

A proportional valve opens more or less depending on how far the level is from 60 %. It is the P part of a PID, and shows its limitation: the steady-state error.

Open in the simulator

The simulator is designed for computers (screens 1024 px or wider).

Virtual plant

Shown at rest. In the simulator the plant moves according to your program's outputs.

Inputs and outputs

Address	Name	Description
I0.0	CONTROL	Automatic control switch
IW0	LEVEL_TRANSMITTER	Level transmitter: 0–27648 = 0–100 % (plant)
QW0	VALVE	Inlet valve opening: 0–27648 = 0–100 %
MD0	LEVEL	Level in % (REAL)
MD1	ERROR	Setpoint (60 %) minus level
MD2	OPENING	Calculated valve opening in % (REAL)

Program

Ladder diagram (LD)

Rung 1 — Scales the transmitter to level percent.
Rung 2 — Error = setpoint (60 %) − level.
Rung 3 — Proportional action: opening = Kp × error, with Kp = 8.
Rung 4 — Upper limit: at most 100 %.
Rung 5 — Lower limit: at least 0 %.
Rung 6 — With control on, the opening goes to the valve (0–100 % → 0–27648).
Rung 7 — With control off, the valve closes.

Structured text (ST)

(* Analog level control (introduction to PID) — converted from Ladder *)

(* Rung 1: Scales the transmitter to level percent. *)
LEVEL := (TO_REAL(LEVEL_TRANSMITTER) - TO_REAL(0)) * (TO_REAL(100) - TO_REAL(0)) / (TO_REAL(27648) - TO_REAL(0)) + TO_REAL(0);

(* Rung 2: Error = setpoint (60 %) − level. *)
ERROR := 60.0 - LEVEL;

(* Rung 3: Proportional action: opening = Kp × error, with Kp = 8. *)
OPENING := ERROR * 8.0;

(* Rung 4: Upper limit: at most 100 %. *)
IF OPENING > 100.0 THEN OPENING := 100.0; END_IF;

(* Rung 5: Lower limit: at least 0 %. *)
IF OPENING < 0.0 THEN OPENING := 0.0; END_IF;

(* Rung 6: With control on, the opening goes to the valve (0–100 % → 0–27648). *)
IF CONTROL THEN VALVE := (TO_REAL(OPENING) - TO_REAL(0)) * (TO_REAL(27648) - TO_REAL(0)) / (TO_REAL(100) - TO_REAL(0)) + TO_REAL(0); END_IF;

(* Rung 7: With control off, the valve closes. *)
IF NOT CONTROL THEN VALVE := 0; END_IF;

Instruction list (IL)

(* Analog level control (introduction to PID) — converted from Ladder *)

(* Rung 1: Scales the transmitter to level percent. *)
  LD    LEVEL_TRANSMITTER
  TO_REAL
  SUB(  0
    TO_REAL
  )
  MUL(  100
    TO_REAL
    SUB(  0
      TO_REAL
    )
  )
  DIV(  27648
    TO_REAL
    SUB(  0
      TO_REAL
    )
  )
  ADD(  0
    TO_REAL
  )
  ST    LEVEL

(* Rung 2: Error = setpoint (60 %) − level. *)
  LD    60.0
  SUB   LEVEL
  ST    ERROR

(* Rung 3: Proportional action: opening = Kp × error, with Kp = 8. *)
  LD    ERROR
  MUL   8.0
  ST    OPENING

(* Rung 4: Upper limit: at most 100 %. *)
  LD    OPENING
  GT    100.0
  JMPCN SKIP_4
  LD    100.0
  ST    OPENING
SKIP_4:

(* Rung 5: Lower limit: at least 0 %. *)
  LD    OPENING
  LT    0.0
  JMPCN SKIP_5
  LD    0.0
  ST    OPENING
SKIP_5:

(* Rung 6: With control on, the opening goes to the valve (0–100 % → 0–27648). *)
  LD    CONTROL
  JMPCN SKIP_6
  LD    OPENING
  TO_REAL
  SUB(  0
    TO_REAL
  )
  MUL(  27648
    TO_REAL
    SUB(  0
      TO_REAL
    )
  )
  DIV(  100
    TO_REAL
    SUB(  0
      TO_REAL
    )
  )
  ADD(  0
    TO_REAL
  )
  ST    VALVE
SKIP_6:

(* Rung 7: With control off, the valve closes. *)
  LDN   CONTROL
  JMPCN SKIP_7
  LD    0
  ST    VALVE
SKIP_7:

Step by step

1Press ▶ Run (F5) and turn on CONTROL. Rung 1: the level is scaled to percent. Rung 2: ERROR = 60 % − LEVEL.
2Rung 3: the opening is proportional to the error (gain Kp = 8). Rungs 4 and 5: it is limited between 0 and 100 %. Rung 6: it is scaled to the analog output QW0.
3Watch the level: it settles near 55 %, not at 60 %. With proportional-only control some error is needed to keep the valve open: that is the steady-state error. The I (integral) part of a PID exists to remove it.
4Try changing the gain to 20.0: the steady-state error drops, but the valve reacts more strongly. Turn off the consumer in the plant and see how the balance point changes.

Open in the simulator