The paper introduces a constrained, model-free time-delay adaptive control (td-cMFAC) algorithm, designed to address the challenges of longitudinal cooperative platooning control for heavy trucks. Unlike traditional model-based approaches, this method eliminates the need for precise mathematical modeling of vehicle dynamics. At the heart of the algorithm is a time-varying pseudo-gradient (PG) dynamic linearization technique. This approach allows the system to adaptively estimate and compensate for time delays and nonlinearities using only input/output (I/O) data, without relying on an explicit dynamic model. The control framework combines: model-free adaptive controller (MFAC) to handle nonlinearities and uncertainties and tracking differentiator (TD) to improve transient performance and smooth reference signals. To ensure realistic and safe operation, the algorithm incorporates input/output constraints, limiting critical vehicle parameters such as acceleration, speed, and inter-vehicle spacing. These constraints prevent unrealistic or dangerous control actions. In addition, the effectiveness of its algorithm was verified experimentally through the powerful MATLAB-Simulink and TruckSim joint simulation platform.