PID Controller

See PIDController.sol and PIDRateSetter.sol for more details.

1. Introduction

The PID Controller is a smart contract that fine-tunes the system's redemption rate by analyzing the deviation, which is the discrepancy between the market and redemption prices. It performs the following tasks:

  • Computes and stores the system's proportional and integral deviations.
  • Applies a decay factor to the integral deviation.
  • Adjusts the redemption rate by applying proportional and integral gains to the deviation.

The PID Rate Setter schedules and triggers the PID Controller's redemption rate adjustments.

2. Contract Details

2.1 PID Controller

Key Methods:

Authorized

  • computeRate: Computes the new redemption rate, applying the proportional and integral gains to the deviation (can only be called by the PID Rate Setter contract).

Contract Parameters:

  • Seed Proposer: Authorized address for initiating redemption rate updates.
  • integralPeriodSize: Minimum duration required to calculate integral deviation.
  • perSecondCumulativeLeak: Decay constant for the integral deviation.
  • noiseBarrier: Lowest deviation percentage considered for redemption rate adjustment.
  • feedbackOutputUpperBound: Maximum limit for the redemption rate.
  • feedbackOutputLowerBound: Minimum limit for the redemption rate.
  • proportionalGain: Gain factor for proportional deviation.
  • integralGain: Gain factor for integral deviation.

2.2 PID Rate Setter

Key Methods:

Public

  • updateRate: Retrieves market and redemption prices from the Oracle Relayer and prompts the PID Controller to compute the new redemption rate.

Contract Parameters:

  • updateRateDelay: Time gap between successive redemption rate adjustments.

3. Key Mechanisms & Concepts

Deviation Metrics

The PID Controller monitors the gap between market and redemption prices and stores both the proportional and integral deviations. Whenever the deviation changes, its integral component is decayed to mitigate the impact of historical deviations on future rates.

Proportional Deviation (pTerm)

It is computed as:

pTerm = (redemptionPrice - marketPrice) / redemptionPrice

Integral Deviation (iTerm)

It is calculated iteratively:

iTerm_n = (iTerm_(n-1) * decayFactor) + ((pTerm_n - pTerm_(n-1)) / 2)

Gain Parameters

The system owner can configure the gain parameters for proportional (pGain) and integral (iGain) deviations. The redemption rate is then adjusted as follows:

redemptionRate = 1 + (pTerm * pGain + iTerm * iGain)

Notice: All of pTerm, iTerm, pGain, iGain can be negative, so the redemption rate can be lesser than 1 (decrease the rate). Yet the redemption rate can never be 0 or negative.

4. Gotchas

5. Failure Modes

  • Invalid seedProposer risks stale redemption rate.
  • High noiseBarrier hampers redemption rate adjustment.
  • High integralPeriodSize lowers PID responsiveness.
  • Over-the-top feedbackOutputUpperBound is likely disregarded.
  • Null feedbackOutputUpperBound constrains positive control range.
  • Excessive feedbackOutputLowerBound may be overlooked.
  • Null feedbackOutputLowerBound limits negative control range.
  • High perSecondCumulativeLeak quickens integral decay.
  • Low perSecondCumulativeLeak amplifies integral's historical effect.
  • High kp makes controller jittery to current deviations.
  • High ki overemphasizes historical deviations.