Determination of the Overshoot Scalar Control Systems with Transfer Zero and Binomial Law of Poles Distribution

Background/Objectives: One of the most popular approaches to the design of automatic control systems is the modal method of controller synthesis. Methods: Its peculiarity is that the requirements for management process quality are formalized by ensuring the desired location on a complex plane of a closed system poles. At that, the introduction of the modal controller makes no effect on the location of transmission zeros. Finding: However, it is known that many transition process quality indicators (e.g., overshoot value) depend not only on the poles but the zeros of the transfer function as well. In work presented here, we analyzed the dependence of overshoot value on the relative position of a dynamic system zeros and poles. Calculation formulas which allow determining the value of a positive or a negative overshoot without the development of transient response are obtained for a scalar system with one zero and the binomial pole distribution law. The dependence of overshoot value on the relative position of the transmission zero and the dynamic system poles is studied. The conditions are formulated, the implementation of which will provide in control system such an overshoot value which does not exceed a predetermined value. Conclusion: The obtained results can be used for further theoretical studies as well as in practice in solving problems of analysis and synthesis of control systems with a modal controller.