Phase-constrained fractional order PIλ controller for second-order-plus dead time systems

In this paper we propose a phase-constrained fractional order PI lambda controller based on a second-order-plus dead time process and a new tuning method. The design is derived in several constraints: a flat phase constraint, a gain crossover frequency and a phase margin. With the specified phase margin, it can reach the corresponding upper boundary of gain crossover frequency and the stability region. The complete surface of stabilizing controllers is achieved by guaranteeing the open-loop system to fulfil the pre-set phase margin. Afterwards, a stability line on the relative stable surface can then be obtained. For a set of controllers on the stability line, the flat phase constraint is used to make sure the uniqueness of the designed controller. The effectiveness of the proposed method is illustrated with several numerical examples.