On Sampled-Data PI Control for Nonlinear Systems

This paper studies sampled-data proportional-integral (PI) control for a basic class of nonlinear uncertain systems. The authors claim that a process with the first-order dynamics can achieve zero steady-state error through a sampled-data PI controller whenever the sampling period T < T₀(k_p, k_i, L), where T₀(k_p, k_i, L) is a number determined by the parameters k_p, k_i and the Lipschitz constant L of the system. On the other hand, once the sampling period T is given, the two parameters k_p and k_i of the sampled-data PI controller are apparently restricted by T, or the setpoint tracking error diverges.