Precise and low-latency information transmission through communication systems is essential in the Industrial Internet of Things (IIoT). However

in an industrial system

there is always a coupling relationship between the control and communication components. To improve the system's overall performance

exploring the co-design of communication and control systems is crucial. In this work

we propose a new metric - Age of Loop Information with Flexible Transmission (AoLI-FT)

which dynamically adjusts the maximum number of uplink (UL) and downlink (DL) transmission rounds

thus enhancing reliability while ensuring timeliness. Our goal is to explore the relationship between AoLI-FT

reliability

and control convergence rate

and to design optimal blocklengths for UL and DL that achieve the desired control convergence rate. To address this issue

we first derive a closed-form expression for the upper bound of AoLI-FT. Subsequently

we establish a relationship between communication reliability and control convergence rates using a Lyapunov-like function. Finally

we introduce an iterative alternating algorithm to determine the optimal communication and control parameters. The numerical results demonstrate the significant performance advantagesof our proposed communication and control co-design strategy in terms of latency and control cost.