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In order to obtain faster and more accuracy transient tracking performances for non-positive plants, a fast proportional integral difference (PID) type parameter optimal iterative learning control algorithm is proposed. In the algorithm, the PID type operators are introduced to enhance convergence speed and a suitable set of basis functions is added to avoid the algorithm plunge into local optimal when the plant is not positive. Theoretic proof shows that the algorithm monotone convergence to zero no matter the system plant is positive or not. Finally, simulations show that the algorithm also has a faster convergence speed compare with other similar algorithms.