This paper proposes a simple tuning method based on partial model matching for PID controller.
In process control field, most of controlled objects are approximated by a 1st order lag plus dead time system. The partial model matching method can be applied to tuning PID controller for this typed system. Time scale factor σ has to be calculated as a minimum positive root of a 3rd order equation, and parameters of PID controller are calculated as functions of σ and process parameters, namely, process gain
K, time constant
T and dead time
L. Comparing with conventional methods, in which PID control parameters are calculated as relatively simple functions of process parameters, the partial model matching method is complex and nontransparent in being applied to PID controller.
This paper proposes a simple method to calculate σ when Kitamori model is used as a reference. In the method, σ is calculated by an approximate equation σ/L=1.37. And then this paper shows that σ/L is calculated as a function of
L/
T when Kitamori model and other models are used as a reference. Even though
L/
T changes, σ/L changes only a little when Kitamori model is used as a reference. Finally, it is showed that σ/L is calculated as a function of
L/
T in PI, I-PD and I-P controller, too. Since σ is response time constant of control system, rising time of above control systems which are tuned by the partial model matching method, can be easily compared.
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