Data based design of Digital PID Controller

In this paper, we present a procedure for designing a digital proportional-integral-derivative (PID) controller based on input-output data of an arbitrary stable plant without identifying plant models. Based on an impulse input to the plant, the response of the plant is obtained which is then used to directly find the stabilizing set of PID controllers. The method makes use of Tchebyshev representation for discrete- time systems and the set is determined by obtaining a set of linear inequalities with two unknowns while keeping the third parameter fixed. By sweeping on the third parameter, the entire set can be obtained. This result is useful because it does not depend upon knowing the model of the system and the operations performed are directly on the data obtained. It is also observed that the region becomes more and more accurate as more and more sample points are included. This is shown through illustrative examples.