PI/PID based multi-objective control design: an ILMI approach

In many real world control problems, we have to follow several control objectives, simultaneously. At the same time, it is usually desirable to meet all specified goals using the controllers with simple structures such as proportional-integral (PI) and proportional-integral-derivative (PID) which are useful in industry applications. Since, practically these controllers are commonly tuned based on classical or trial-and-error approaches, they are incapable of obtaining good dynamical performance to capture all design objectives and specification. With regard to above problem, this paper addresses a new method to design of multi-objective PI/PID controller. For this purpose, first the multi-objective control design is reduced to an H₂/H_∞ static output feedback control synthesis, and then the control parameters are easily carried out using an iterative linear matrix inequalities (ILMI) algorithm. As a numerical example, the proposed method is applied to a multi-area power system to design a set of PI-based robust load frequency controllers.