As decentralized money market protocols continue to grow in value locked, there have been a number of optimizations proposed for improving capital efficiency. One set of proposals from Euler Finance and Mars Protocol is to have an interest rate curve that is a proportional-integral-derivative (PID) controller. In this paper, we demonstrate attacks on proportional and proportional-integral controlled interest rate curves. The attack allows one to manipulate the interest rate curve to take a higher proportion of the earned yield than their pro-rata share of the lending pool. We conclude with an argument that PID interest rate curves can actually \emph{reduce} capital efficiency (due to attack mitigations) unless supply and demand elasticity to rate changes are sufficiently high.

翻译：随着去中心化货币市场协议锁仓价值持续增长，学界提出了多项优化方案以提升资本效率。Euler Finance与Mars Protocol提出的方案之一，是采用比例-积分-微分（PID）控制器作为利率曲线。本文展示了针对比例控制与比例积分控制利率曲线的攻击方法。该攻击使攻击者能够操纵利率曲线，从出借池中获取超出其按比例份额的收益。我们最终论证：除非借贷双方对利率变化的弹性足够高，否则PID利率曲线实际上会因攻击缓解措施而降低资本效率。