PID Tank Level Control

Simulation Control

Simulation Speed

t_end — Simulation Time (s)

Type the simulation time and press Enter to apply.

PID Controller Gains

Kp — Proportional 2.0

Ki — Integral 0.5

Kd — Derivative 0.0

Controller Options (HYSYS-style)

β — P Setpoint Weight 1.00

γ — D Setpoint Weight 0.00

PV Noise σ (m) 0.000

α — Derivative Filter (0 = off) 0.00

Anti-reset windup (back-calculation)

β < 1 softens the setpoint response (2-DOF). γ = 0 uses derivative-on-measurement. Turn windup off to see integral windup during saturation.

System Settings

Setpoint (m) 5.0

Tank Area (m²) 2.0

Flow Resistance (R) 1.0

Disturbance (m³/s) 0.0

Setpoint Step (live)

Step the setpoint while running to watch the transient response.

Presets

Transfer Function G(s) = 1 / (A·s + 1/R)
Controller: u = u_bias + Kp(β·SP − h) + Ki·∫(SP − h)dt + Kd(γ·dSP/dt − dh/dt)

Tank Schematic

LIVE

PV Tank Level h — process variable

MV Inflow q_in — manipulated variable

e Error (SP − h)

Current Level

0.00 m

Control Input

0.00

Error

0.00 m

Overshoot

Settling Time

— s

SSE

—

Parameters & Equations

Everything this simulation uses, written out for study.

Process Model

Tank mass balance A · dh/dt = q_in − h/R + d h — level (m) · q_in — inflow (m³/s) · A — cross-section (m²) · R — outflow resistance · d — disturbance inflow (m³/s)

Steady state (open loop) h_ss = R · (q_in + d) Time constant τ = A·R. With A = 2, R = 1 → τ = 2 s.

Controller — 2-DOF PID 2-DOF

Control law q_in = clamp[ K_p(β·SP − h) + K_i∫(SP − h)dt + K_d(γ·dSP/dt − dh/dt), 0, 20 ] error e = SP − h. Integral uses the full error; derivative uses the weighted setpoint minus the measurement.

β (beta) is the proportional setpoint weight. β = 1 is a standard PID; β < 1 reacts more gently to setpoint changes (less overshoot) while still rejecting disturbances at full gain.

γ (gamma) is the derivative setpoint weight. γ = 0 gives derivative-on-measurement (no derivative "kick"); γ = 1 gives derivative-on-error.

Parameters

Symbol	Meaning	Default
A	Tank cross-section area	2.0 m²
R	Outflow resistance	1.0
SP	Level setpoint	5.0 m
d	Disturbance inflow	0.0 m³/s
K_p	Proportional gain	2.0
K_i	Integral gain	0.5
K_d	Derivative gain	0.0
q_in	Inflow (actuator, clamped)	0–20 m³/s

Controller Options

Symbol	Meaning	Default
β 2-DOF	Proportional setpoint weight	1.00
γ 2-DOF	Derivative setpoint weight	0.00
α filter	Derivative filter (0 = off)	0.00
σ noise	PV sensor noise std-dev	0.00 m
AW windup	Anti-reset windup (back-calculation)	on

Anti-reset windup (back-calculation): when the inflow saturates at its limit, the integral is bled by the over-drive I ← I + (Δt/T_t)(u_sat − u), so it cannot "wind up". Turn it off to see the slow recovery caused by windup.

PV noise: a zero-mean Gaussian noise of standard deviation σ is added to the measured level only (the true level stays clean): h_meas = h + σ·N(0,1).

Derivative filter (α): the raw derivative is smoothed by a first-order filter D_f[k] = a·D_f[k−1] + (1−a)·D_raw[k] with a = exp(−Δt/τ), where τ is a physical time constant set from α. α = 0 disables filtering; larger α suppresses noise amplification at the cost of a small lag.