Continuous

PIDController Block

Standard PID (Proportional-Integral-Derivative) controller for closed-loop control

Description

The PID Controller block implements a standard Proportional-Integral-Derivative controller for closed-loop feedback control. It combines three control terms to regulate a process: proportional correction for immediate response, integral for eliminating steady-state error, and derivative for damping overshoot.

Mathematical Model

P term:  p(t) = Kp × e(t)
I term:  i(t) = Ki × ∫₀ᵗ e(τ) dτ
D term:  d(t) = Kd × N × s/(s+N) × e(t)   (filtered derivative)

Output:  u(t) = p(t) + i(t) + d(t)
Saturated: u = clamp(u, u_min, u_max)

Discrete approximation:

I[n] = I[n-1] + Ki × e[n] × Δt                              (Forward Euler)
D[n] = (Kd × N × (e[n] - e[n-1]) + D[n-1]) / (1 + N × Δt)  (Backward Euler filter)

The derivative filter transfer function is Kd × N × s / (s + N), where N is the filter coefficient. This low-pass filters the derivative action to reduce noise amplification. Higher N means less filtering (N → ∞ gives pure derivative). Typical values: N = 10–100.

Parameters

proportionalGain (Kp)

Proportional gain. Controls immediate response to error.

Type: number
Symbol: Kp
Range: 0 to 10000
Default: 1.0
Tooltip: Controls immediate response to error

integralGain (Ki)

Integral gain. Eliminates steady-state error by accumulating error over time.

Type: number
Symbol: Ki
Range: 0 to 1000
Default: 0.1
Tooltip: Eliminates steady-state error over time

derivativeGain (Kd)

Derivative gain. Dampens oscillations by responding to error rate of change.

Type: number
Symbol: Kd
Range: 0 to 1000
Default: 0.0
Tooltip: Dampens oscillations by responding to error rate of change

filterCoefficient (N)

Derivative filter coefficient. Controls the cutoff frequency of the derivative low-pass filter.

Type: number
Symbol: N
Range: 1 to 10000
Default: 100
Tooltip: Derivative filter cutoff frequency. Higher = less filtering

saturationMin

Lower output limit for anti-windup protection.

Type: number
Default: -10
Tooltip: Lower output limit for anti-windup protection

saturationMax

Upper output limit for anti-windup protection.

Type: number
Default: 10
Tooltip: Upper output limit for anti-windup protection

reset (optional)

Reset trigger. Set > 0 to reset the controller state.

Type: number
Required: false

Anti-Windup Behavior

The anti-windup mechanism prevents integral accumulation when the output would saturate:

Before updating the integral, a candidate output is computed with the new integral value
If this candidate output would exceed the saturation limits AND the error drives it further into saturation, the integral update is blocked
If the error drives the output *away* from saturation (unwinding), integration is always allowed
This ensures fast recovery when the setpoint changes direction

Examples

Temperature Control (1 second)

Setpoint = 50°C, measured temperature ramps from 20°C. PID controller outputs heating signal, reducing error over time.

Motor Speed Regulation

Reference speed vs measured speed error fed to PID. Output drives motor command signal.

Remarks

Tuning: Start with Kp only (Ki=0, Kd=0), tune P for good response, add I to remove offset, add D for stability
Anti-Windup: Uses conditional integration — integral only accumulates when doing so would not cause or worsen saturation
Derivative Filter: The filtered derivative avoids noise amplification inherent in pure differentiation
Sample Rate: All gains work correctly independent of simulation sample time (Δt is handled internally)
Error Input: Connect (reference - measured) or similar error signal
Classic Control: Foundation for most industrial feedback systems