A set of general expressions is derived from a single asymmetrical relay feedback test for online plant identification. The expressions also remain valid for an odd symmetrical limit cycle test method. Using the expressions, the exact parameters of open-loop stable and unstable first-order plus time delay (FOPDT) and second-order plus time delay (SOPDT) transfer function models may be obtained from simple measurements made on the limit cycle. The approach can also be used to identify transfer functions of integrating processes. Conditions for the existence of limit cycles in unstable FOPDT and SOPDT processes are derived. The design of controllers for these processes is then considered and a simple, but very effective, approach using standard forms with a variable zero is presented. The advantages of using PI-PD control, compared with conventional PID or PI-D control, particularly for unstable and integrating processes is clearly shown. Examples are given to illustrate the value of the proposed general identification method and the improved system performance provided by the proposed controllers.