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Tactile Internet based Cyber-Physical Systems (TCPS) are highly sensitive to component and communication latencies and packet drops. Building a high performing TCPS, thus, necessitates experimenting with different hardware, algorithms, access technologies, and communication protocols. To facilitate such experiments, we have developed TCPSbed, a modular testbed for TCPS. TCPSbed facilitates the integration of different components, both real and simulated, to realize different TCPS applications and evaluate their latency and control performances. TCPSbed's latency analyzer tool employs a novel method to isolate latencies of individual TCPS components such as the latencies contributed by actuation, sensing, algorithms, and by the network, all in an online fashion. TCPSbed's method of analyzing stability is also novel. It involves the use of the step response analysis method, a classic control-theoretic method used for analyzing the stability of generic control systems. TCPSbed's support for edge intelligence modules enables prediction of command and feedback signals at the network's edge allowing TCPS applications to perform well in adverse network conditions. TCPSbed's source-code, made available through our GitHub page TactileInternet, allows developers to extend its features and functionalities further. In this paper, we describe the architecture and implementation details of TCPSbed and demonstrate its features through several proof-of-concept experiments.