The new type of the design method proposed in this paper is similar to the one using phase lead-lag compensator and has two particular characteristics. First, the approximate system described real order lag element with a dead time element is specially adopted to identify the controlled object. The principle of the identification derived from the frequency characteristics is presented. Secondly, the compensator is composed by an integral element and phase lead-lag elements having multiple zeros and multiple poles. The order of phase lead-lag elements is, in general, an integer but in this design it will be treated as a real number. In order to use practically the compensator, the impulse response function of the compensator is obtained in the form of a series expansion of a gamma function and it can be performed by the convolution method between the impulse response function of the compensator and a deviation error signal.The compensator parameters are determined by a rule of trial and error in order to obtain a quick response using manipulating variable under the maximum value assigned in advance. Since the order of the compensator can be adjusted finely through numerical treatment as to a real, the quick response by a relatively small manipulating variable has been performed. Then, the selection of the sampling time in the case of practical digital control is considered in detail. The effectiveness of this control design method is shown by examples.
The control system design method for the controlled object having such a higher order lag element and a dead time element as used in general for the process control system is treated in this paper. Two types of the transfer function with the real order element are used in the control system design method. One is the transfer function of the controlled object approximated the real order lag element and a dead time system to a higher order controlled object. The other is the transfer function of the compensator with the real order phase lead-lag element proposed previously to control this controlled object. The principle of the design for the system composed of these elements is based on frequency characteristics.In this design, parameters of the compensator for a given phase margin, a gain margin and a peak gain in Nichols chart are intended to decide. The derivation of parameters of the compensator to satisfy specifications of these frequency characteristics is described, and then the property of the control system is confirmed by the transient responses.From results of the unit step response and the consideration to specifications of the system design, a suitable range of the parameter of the compensator is researched in detail. And then a suitable combination of the peak gain and the phase margin is obtained for a given specification of the frequency characteristics. The usability of this control system design method is appreciated through some examples. Moreover, the application of the principle of this controll system design method to the control system using the most general PID compensator has shown.
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