Proportional‐integral‐derivative (PID) control is one of the most widely used feedback control strategies because of its ability to follow step commands and reject constant disturbances with zero asymptotic error, as well as the ease of tuning. This paper presents an adaptive digital PID controller for sampled‐data systems with sensor, actuator, and feedback nonlinearities. The linear continuous‐time dynamics are assumed to be first‐order lag with dead time (ie, delay). The plant gain is assumed to have known sign but unknown magnitude, and the dead time is assumed to be unknown. The sensor and actuator nonlinearities are assumed to be monotonic, with known trend but are otherwise unknown, and the feedback nonlinearity is assumed to be monotonic, but is otherwise unknown. A numerical investigation is presented to support a simulation‐based conjecture, which concerns closed‐loop stability and performance. Numerical examples illustrate the effect of initialization on the rate of adaptation and investigate failure modes in cases where the assumptions of the simulation‐based conjecture are violated.