Plant identification to FOPDT in open loop system. 

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... Some controllers, especially older models have a proportional band (PB) setting instead of a controller gain. The PB is defined as the percentage error that results in a 100% change in controller output (Johnson, 1993; Äström, 1995). The Ziegler-Nichols (ZN) design methods are the most popular heuristic methods used in process control for determining the parameters of a P(I) and a PID controller. Although these methods date back to early 40s for analogue controllers, they are still appropriate for modern digital control systems. It was the year 1942, when the first method of Ziegler and Nichols was published which is known as the continuous cycling method . In this method, the controller gain is increased until a sustained oscillation takes place at gain K u . If the corresponding period of oscillation be T u , then the parameters of the controllers, as suggested by Ziegler and Nichols (Ziegler-Nichols, 1942), are shown in Table 1. In their second paper, published in 1943, Ziegler and Nichols proposed an alternative method, commonly known as the process reaction curve method. In this method, the open loop unit step response of the plant is measured which usually the form has shown in Fig. 1. The response is approximated by straight lines, with τ d , T and K indicated as shown, by the unit step response of a first-order plus time delay (FOPTD) model given in eq. (5). The rules of Ziegler and Nichols (Ziegler-Nichols, 1943) are shown in Table 2. G ( s ) = K e − τ d s (5) Ts + 1 Table 1: ZN (Continuous Cycling Method) tuning rules Controller ...