Migrate to new Gitea instance (gitea.wbd-rd.nl)
- Update all submodule URLs from gitea.centraal.wbd-rd.nl to gitea.wbd-rd.nl - Add settler as proper submodule in .gitmodules - Add agent skills, function anchors, decisions, and improvements - Add Docker configuration and scripts - Add manuals and third_party docs - Update .gitignore with secrets and build artifacts - Remove stale .tgz build artifact Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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third_party/docs/pid-control-theory.md
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third_party/docs/pid-control-theory.md
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# PID Control for Process Applications
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> **Used by**: `mechanical-process-engineer` agent, `node-red-runtime` agent, `generalFunctions/src/pid/`
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> **Validation**: Verified against Astrom & Hagglund (ISA, 2006) and MATLAB/Simulink documentation
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## Continuous PID Controller
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### Standard (ISA/Ideal) Form
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```
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u(t) = K_p · [e(t) + (1/T_i) · ∫e(τ)dτ + T_d · de(t)/dt]
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```
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Where:
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- u(t) = controller output
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- e(t) = error = setpoint - process variable (SP - PV)
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- K_p = proportional gain
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- T_i = integral time (seconds)
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- T_d = derivative time (seconds)
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### Parallel Form
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```
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u(t) = K_p · e(t) + K_i · ∫e(τ)dτ + K_d · de(t)/dt
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```
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Where K_i = K_p/T_i and K_d = K_p · T_d
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## Discrete PID Implementation
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### Positional Form (absolute output)
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```
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u[k] = K_p · e[k] + K_i · Δt · Σe[j] + K_d · (e[k] - e[k-1]) / Δt
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```
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- Computes the absolute output value each cycle
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- Requires tracking of the integral sum
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- Subject to integral windup
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- Used when the controller output directly sets an actuator position
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### Velocity Form (incremental output)
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```
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Δu[k] = K_p · (e[k] - e[k-1]) + K_i · Δt · e[k] + K_d · (e[k] - 2·e[k-1] + e[k-2]) / Δt
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u[k] = u[k-1] + Δu[k]
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```
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- Computes the **change** in output each cycle
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- Inherently bumpless on mode transfers (auto→manual→auto)
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- Less prone to windup (but still needs anti-windup for output limits)
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- Preferred for incremental actuators (VFDs, variable valves)
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## Anti-Windup Strategies
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Integral windup occurs when the controller output saturates (hits actuator limits) but the integral term continues to accumulate, causing large overshoot when the error changes sign.
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### 1. Clamping (Conditional Integration)
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Stop integrating when the output is saturated **and** the error has the same sign as the integral term:
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```
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if (u_raw > u_max || u_raw < u_min) && sign(e) == sign(integral):
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freeze integral (do not accumulate)
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else:
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integral += e * Δt
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```
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- Simple to implement
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- Effective for most process control applications
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- The approach used in the EVOLV generalFunctions PID implementation
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### 2. Back-Calculation
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When the output saturates, feed back the difference between the saturated and unsaturated output to "unwind" the integrator:
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```
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integral += (K_i · e + K_b · (u_saturated - u_raw)) · Δt
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```
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Where K_b = 1/T_t (tracking time constant, typically T_t = √(T_i · T_d) or T_t = T_d).
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- More sophisticated than clamping
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- Better performance for systems with large disturbances
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- Recommended by Astrom & Hagglund for demanding applications
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### 3. Integrator Reset
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Reset the integrator to a value that would produce the saturated output:
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```
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if u_raw > u_max:
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integral = (u_max - K_p · e) / K_i
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```
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- Simple but can be aggressive
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- May cause discontinuities
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## Derivative Filtering
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The derivative term amplifies high-frequency noise. Always filter it:
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### First-Order Low-Pass Filter on D-Term
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```
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D_filtered[k] = α · D_filtered[k-1] + (1-α) · D_raw[k]
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```
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Where α = T_f / (T_f + Δt) and T_f = T_d / N (N typically 5-20, default 10).
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### Derivative on PV (not Error)
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To avoid derivative kick on setpoint changes:
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```
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D = -K_d · (PV[k] - PV[k-1]) / Δt (instead of using error)
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```
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This is the standard approach for process control.
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## Cascade PID
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Two nested loops where the outer (master) loop's output is the setpoint for the inner (slave) loop.
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```
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[SP_outer] → [PID_outer] → [SP_inner] → [PID_inner] → [Actuator] → [Process]
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↑ ↑
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[PV_outer] ←──── [Process] ←── [PV_inner]
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```
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### Design Rules
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- Inner loop must be **5-10x faster** than outer loop
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- Tune inner loop first (with outer loop in manual)
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- Then tune outer loop
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- Anti-windup on outer loop essential (its output is bounded by inner loop's SP limits)
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### EVOLV Application
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- Outer: Level controller → outputs flow setpoint
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- Inner: Flow controller → outputs pump speed
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- pumpingStation node coordinates this cascade
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## Tuning Methods
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### Ziegler-Nichols (Ultimate Gain Method)
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1. Set I and D to zero, increase K_p until sustained oscillation
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2. Record ultimate gain K_u and ultimate period T_u
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3. Apply: K_p = 0.6·K_u, T_i = T_u/2, T_d = T_u/8
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### Cohen-Coon (Process Reaction Curve)
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1. Apply step change, record process reaction curve
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2. Identify: gain K, dead time L, time constant τ
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3. Apply formulas based on K, L, τ
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### Lambda Tuning (IMC-based)
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1. Identify process as FOPDT: K, L, τ
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2. Choose closed-loop time constant λ (typically λ = max(3·L, τ))
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3. K_p = τ/(K·λ), T_i = τ
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- **Preferred for process control** — gives non-oscillatory response
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- Directly specifies desired closed-loop speed
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- Robust to model uncertainty when λ is chosen conservatively
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## Authoritative References
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1. Astrom, K.J. & Hagglund, T. (2006). "Advanced PID Control." ISA — The Instrumentation, Systems, and Automation Society.
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2. Astrom, K.J. & Hagglund, T. (1995). "PID Controllers: Theory, Design, and Tuning." 2nd ed., ISA.
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3. Seborg, D.E. et al. (2011). "Process Dynamics and Control." 3rd ed., Wiley. (Chapter on PID control)
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4. MATLAB/Simulink documentation — "Anti-Windup Control Using PID Controller Block"
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5. Smith, C.A. & Corripio, A.B. (2005). "Principles and Practices of Automatic Process Control." 3rd ed., Wiley.
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