BlockWerk Documentation
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PID

PID Controller

Continuous

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.

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Mathematical Model

u(t)=Kpe(t)+Ki∫0te(τ)dτ+Kdddte(t)u(t) = K_p e(t) + K_i \int_{0}^{t} e(\tau) d\tau + K_d \frac{d}{dt} e(t)

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.

Inputs & Outputs

Direction ID Label Type Status
→ In error Error number Required
→ In reset Reset number Optional
← Out out Output number Output

Parameters

Parameters Label Type Default Description
kp Proportional Gain (Kp) number 1 Controls immediate response to error
ki Integral Gain (Ki) number 0.1 Eliminates steady-state error over time
kd Derivative Gain (Kd) number 0.1 Dampens oscillations by responding to error rate of change
n Filter Coefficient (N) number 100 Derivative filter cutoff frequency. Higher = less filtering
form PID Form select parallel Parallel: u = Kp·e + Ki·∫e + Kd·de/dt. Series: u = Kp·(1 + 1/(Ti·s) + Td·s)·e
min Saturation Min number -1000000000000000 Lower output limit for anti-windup protection
max Saturation Max number 1000000000000000 Upper output limit for anti-windup protection

Usage 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 & Best Practices

  • 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

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