Successful design of control systems depends mainly on a system model to achieve accurate control performance. The complexity of thermal systems, such as an air-conditioning system, makes it extremely difficult to obtain an exact system model to improve control quality. Thus, for tuning PID controllers to complex system dynamics, most systems under control are often approximated by a first-order lag plus deadtime system. PID controller tuning always involves a trade-off between performance and robust stability. This paper describes tuning PID controllers using optimization, subject to constraints on derivatives of control input, and considering model uncertainty caused by changes in system dynamics. Graphs by which optimal PID parameters can be obtained are presented as functions of a normalized deadtime and a perturbation of system parameters. To evaluate control performance, disturbance suppression and reference tracking properties are presented and compared to those by the partial model matching method and the H8 compensator designed for the same system. Moreover, to avoid making the control system sensitive to measurement noise, a PI controller with a relaxation filter is newly developed. It is found that there is very little difference in control performance between the PI controller and the H8 compensator.