Design of P and PI controllers for unstable first-order plus time delay systems

Explicit design formulae are derived for proportional (P), and proportional and integral (PI), controllers for unstable first-order plus time delay processes. A stability condition for the design of a PI controller is derived. The values of Kmax and τI from the proposed approximate analytical solutions are compared with the exact numerical solutions. The response of the controlled system with the proposed design settings is compared with that of the settings given by De Paor and O'Malley (1989). © 1994 Taylor & Francis Ltd.