In the near future, robots are expected to work with humans or operate alone and may replace human workers in various fields such as homes and factories. In a previous study, we proposed bilateral control-based imitation learning that enables robots to utilize force information and operate almost simultaneously with an expert's demonstration. In addition, we recently proposed an autoregressive neural network model (SM2SM) for bilateral control-based imitation learning to obtain long-term inferences. In the SM2SM model, both master and slave states must be input, but the master states are obtained from the previous outputs of the SM2SM model, resulting in destabilized estimation under large environmental variations. Hence, a new autoregressive neural network model (S2SM) is proposed in this study. This model requires only the slave state as input and its outputs are the next slave and master states, thereby improving the task success rates. In addition, a new feedback controller that utilizes the error between the responses and estimates of the slave is proposed, which shows better reproducibility.