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Time delay in bilateral control system seriously deteriorates performance and stability. Acceleration-based bilateral control (ABC) is hybrid of position and force control in the acceleration dimension using the disturbance observer. It can be divided into two modal spaces: common and differential. The sum of master and slave forces is controlled to be zero in the common modal space (1,+1) to realize the law of action-reaction. The difference of master and slave positions is controlled to be zero in the differential modal space (1,-1) for position tracking. This brief analyzes the stability of each modal space under time delay. Based on modal space analysis, this brief proposes a novel four-channel (4ch) ABC architecture using two degrees of freedom proportional derivative (PD) control for haptic communication under time delay. In the proposed 4ch ABC, the difference of position is controlled to be zero by P-D control (differential proactive PD control), and the sum of the forces is controlled to be zero by damping-injected force P control. Furthermore, this brief utilizes frequency-domain damping design to realize both high performance and stability based on delay-dependent robust H∞ stability. The proposed 4ch ABC improves the stability of each modal space under time delay. The validity of the proposed control system is confirmed by some experimental results.