Analog, PID and Drive Control with a PLC: 4–20 mA Scaling, the PID Block, a Constant-Pressure Pump and Modbus RTU

The real world is not just 0 and 1: pressure, level, temperature and motor speed are continuous quantities. This page goes from the raw number in an analog module to a pressure-control loop that commands a drive — the most common job in buildings and factories.

By Ajarn ModUpdated 14 Oct 2026

In 30 seconds

Scaling: $y = y_{min} + (x - x_{min})(y_{max} - y_{min})/(x_{max} - x_{min})$ , computed in REAL
Below 3.6 mA or above 21 mA is a fault, not a measurement
PID: $u = K_p\left(e + \frac{1}{T_i}\int e\,dt + T_d\frac{de}{dt}\right)$ · start tuning with PI
Commanding a VFD: DI + AI is simplest · Modbus returns data (current, faults) over a single pair

From raw counts to engineering units Basic

Figure 1 · A 0–10 bar, 4–20 mA pressure transmitter into an analog module that returns raw counts of 0–27648

P1 Linear scaling

y = y_{min} + (x - x_{min})\,\frac{y_{max} - y_{min}}{x_{max} - x_{min}}

P2 Resolution per raw count

\Delta y = \frac{y_{max} - y_{min}}{x_{max} - x_{min}} \qquad \text{e.g. } \frac{10\ \text{bar}}{27648} = 0.36\ \text{mbar}

P3 Signal validity (NAMUR NE 43)

3.8 \le I \le 20.5\ \text{mA: valid measurement} \qquad I \le 3.6 \text{ or } I \ge 21\ \text{mA → fault}

Example P-1

Scaling a raw value of 13824 with INT gives zero

Wrong: Bar := Raw / 27648 * 10; in INT → 13824/27648 = 0 (truncated) → 0 bar
Also wrong: Raw * 10 / 27648 in INT → 27648 × 10 = 276480 overflows INT
Right: Bar := INT_TO_REAL(Raw) * 10.0 / 27648.0; → 5.0 bar
Check P3: Siemens modules return negative raw values when the current is below 4 mA (down to −4864 ≈ 1.185 mA), and with wire-break diagnostics enabled they report a special value (32767) — check both the raw range per P3 and the module's status bits.

The PID block in a PLC Intermediate

Figure 2 · Constant-pressure loop: SP − PV = e → PID → frequency → VFD → pump → pressure → transmitter

P4 PID (standard form)

u(t) = K_p\left(e + \frac{1}{T_i}\int_0^t e\,d\tau + T_d\,\frac{de}{dt}\right) \qquad e = SP - PV

P5 Discrete PID (sample time $T_s$ )

u_k = K_p\left(e_k + \frac{T_s}{T_i}\sum_{j=0}^{k} e_j - \frac{T_d}{T_s}(PV_k - PV_{k-1})\right)

The derivative term uses PV instead of e (derivative on measurement) so the output does not kick when SP changes, and anti-windup is needed: when the output hits its limit (e.g. 50 Hz), stop accumulating the integral. Most pump and fan loops use PI only (Td = 0) because pressure signals are noisy.

Initial tuning for a constant-pressure pump

Start with a small Kp (e.g. 0.5 of full scale), a long Ti (e.g. 5 s) and Td = 0
Increase Kp until it starts to oscillate, then halve it
Reduce Ti gradually until the value returns to setpoint quickly enough without oscillating (typically 1–5 s for water pressure)
Test by actually opening and closing taps, watching both the dip and the overshoot

Try the effect of Kp, Ti and Td in the PID lab (Thai), and a pressure loop with a VFD pump in the virtual instrumentation lab (Thai).

Commanding a drive from the PLC Intermediate

Method	Wiring	Advantages	Limitations
Digital + preset speeds	Several DO → DI wires	Simple, noise-immune	Only a few speeds
Digital + analog	DO → RUN · AO → AI (4–20 mA)	Continuous adjustment, easy to understand	Feedback limited to what is wired (AO, relays)
Modbus RTU (RS-485)	One twisted pair, several drives	Read current, frequency and faults; set parameters	Communication settings needed; slower response with many stations
Industrial Ethernet	PROFINET, EtherNet/IP, Modbus TCP, EtherCAT	Fast, lots of data, full diagnostics	Needs a module and network configuration

P6 Frequency setpoint over Modbus

\text{Reg} = \frac{f}{0.01\ \text{Hz}} \quad (35.5\ \text{Hz} \to 3550) \qquad \text{or} \quad \text{Reg} = \frac{f}{f_{max}}\times \text{Scale}_{100\%}

Example register map (hypothetical, for learning — every brand differs; use the real manual)
Register	Name	Read/write	Value
40001	Control word	W	Bit 0 = RUN · bit 1 = REV · bit 2 = RESET
40002	Frequency reference	W	0.01 Hz
40011	Status word	R	Bit 0 = Ready · bit 1 = Running · bit 3 = Fault
40012	Output frequency	R	0.01 Hz
40013	Output current	R	0.1 A
40014	Fault code	R	Code per the manual

RS-485 wiring, CRC-16 calculation and a frame builder are in Modbus RTU · TCP (Thai). Remember: set the “communication timeout” in the drive so it stops if the PLC is silent for longer than the set time — otherwise, if the communication cable breaks, the drive keeps running at the last frequency.

Example P-2

The PLC sends 4–20 mA to a VFD ranged 20–50 Hz; 42 Hz is wanted

Invert P1: $I = 4 + 16\,(42 - 20)/(50 - 20) = 4 + 11.73 = 15.73$ mA
If the analog output is 0–27648 = 4–20 mA: raw value $= 27648 \times 11.73/16 = 20275$
Set the drive to treat AI below 2 mA as a broken wire and choose the response (stop / fallback speed)

Frequently asked questions

Is it better to run PID in the PLC or in the VFD?

For a single loop where the transmitter can be wired straight into the VFD, the drive's own PID is simple, responds quickly and keeps working even if the PLC fails. If several pumps must be coordinated, there are many conditions, or the loop must be logged and adjusted from SCADA, PID in the PLC is more flexible.

What value do I send over Modbus to command 35.5 Hz?

It depends on the register units in the drive manual. Many drives use 0.01 Hz units, so you send 3550. Some use a fraction of maximum frequency, e.g. 0–16384 or 0–10000 = 0–100 %. Always read the manual and test with a low value first.

Ajarn Mod · Teerawut Savangboon
Lecturer in Electrical Engineering, Dhonburi Rajabhat University, Samut Prakan · Profile