An Analytic Study On the Mutual Relation between Method(1) and (2) of ZIEGLER-NICHOLS Control Parameter Tuning

지글러-니콜스 제어파라미터 조정법(1),(2)의 상호 연관성에 대한 해석적 연구

Parameter tuning methods by Ziegler-Nickels for control systems are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between methods of Z-N(1) and Z-N(2), or how Z-N(1) method can be originated from Z-N(2) method by analyzing one loop control system of P or PI controller and time delay process. The formulas of Z-N(1) consist of process parameters, L(time delay), $K_m$(gain) and $T_m$(time constant), but Z-N(2) method is based only on the ultimate gain $K_u$ and the ultimate period $T_u$ acquired normally by practical trial without any parameters of Z-N(1). In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into the formulas composed of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula. And a model system is adopted to compare the approximated formula to Z-N(1) and Z-N(2) methods, the results of which show the effectiveness of the proposals.