In industries controllers are conventionally and most commonly designed as a PID controller using a classical control method such as Evans' root locus method, etc. However, it is not easy to determine the three design parameters, i.e., proportional, integral and derivative gains, appropriately. Although design methods of a PID controller such as the ultimate sensitivity method by Ziegler and Nichols and its improved version by Kuwata have been proposed for some types of plant, engineers are often forced to do a tedious job of design iteration by trial-and-error.
In this paper, the author focuses on an I-PD type controller and proposes methods to determine its feedback gains based on the type-I optimal servomechanism. In an I-PD controller, integral action is applied to the control error and proportional and derivative actions to the output. Since the architecture of the control system is similar to the type-I optimal servomechanism, it is possible to design an I-PD controller from the gains of the optimal servo controller. The design procedure is summarized as follows. First the transfer function of a given single-input-single-output system is transformed into a state-space representation by choosing a state vector appropriately. Next a type-I optimal servo controller is designed for the system. Feedback gains of an I-PD (Integral-preceding Proportional Derivative) controller are determined from those of the servo controller. Furthermore, feedback gains of the I-PD controller provides those of a PID controller. Two design methods are presented according to the choice of the state vector. A controller determined from the feedback gains by the optimal servo controller is not necessarily an I-PD controller; in fact, it accompanies a filter unless the numerator of the transfer function is constant, and the derivative terms whose differential order is higher than one appears, when the plant order is higher than two. However, the resulting controller can be reduced to a typical I-PD controller by order reduction and gain adjustment. Numerical examples illustrate the effectiveness of the design methods and provide comparison with the results by the improved ultimate sensitivity method.
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