Auto-tuning: automatically find optimal PID parameters

[darioalessandro]

Problem

Tuning PID parameters (Kp, Ki, Kd) is the hardest part of using a PID controller. Users must manually adjust gains through trial and error, which is time-consuming and requires control theory expertise. Poorly tuned controllers lead to oscillation, slow response, or instability.

Pidgeon should be able to tune itself.

Proposal

Add an auto-tuning module to pidgeon that can automatically determine near-optimal PID parameters for a given system.

Phase 1: Relay Feedback Auto-Tuning (Classical)

The most proven and widely-used approach in industrial controllers (Siemens, Omron, ABB):

1. Run a relay test — the controller forces controlled oscillations in the system
2. Measure the ultimate gain and oscillation period from the response
3. Apply Ziegler-Nichols or Cohen-Coon formulas to compute Kp, Ki, Kd

This is deterministic, well-understood, and works without a system model. It would fit naturally as a pure function:

pub fn auto_tune(oscillation_data: &[RelayTestSample]) -> Result<ControllerConfig, PidError>

Phase 2: Optimization-Based Tuning

Use optimization algorithms to search for gains that minimize a cost function (e.g., ISE, ITAE):

• Particle Swarm Optimization (PSO) — simple, parallelizable, no gradients needed
• Genetic Algorithms — evolutionary search over parameter space

These require a simulation loop or real system interaction, so the API would take a user-provided evaluation function:

pub fn optimize_gains<F>(evaluate: F, bounds: GainBounds) -> Result<ControllerConfig, PidError>
where F: Fn(&ControllerConfig) -> f64  // returns cost

Phase 3 (Future): Learning-Based Tuning

• Reinforcement learning (e.g., PPO) to learn tuning policies across operating conditions
• Gain scheduling — automatically switch between pre-tuned parameter sets based on system state
• Neural network-based prediction of optimal gains from system characteristics

Design Considerations

• Phase 1 should be no_std-compatible (pure math, no allocations needed)
• Phases 2+ will require std (iterative optimization, closures)
• Auto-tuning should produce a standard ControllerConfig — no special controller type needed
• Should integrate with the existing debugging feature for telemetry during tuning runs

References

• Ziegler & Nichols (1942) — oscillation-based tuning formulas
• Åström & Hägglund — relay feedback method
• Wikipedia: PID Controller Tuning