Improved Optimal Controller Designs for All Pole Systems and Standard Forms with One/Two Variable Zeroes

Abstract

Use of the standard forms for controller design is known for a long time. Since first introduced in 1950s, many new contributions have been proposed in the literature. In these contributions, the standard forms are obtained for all poles and with no zero, one zero and two zeroes systems. In this study, for the first time, optimum values of standard form coefficients with two variable zeroes are obtained using only one constrained for the Integral Squared Time Error (ISTE) and Integral of the Squared Time Error (IST2E) criteria. Again in this study, an improved generalized controller design approaches using standard forms with all pole and two variable zeroes have been given for nth degree all pole systems. By improving the previously proposed approaches, stabilities of the overall transfer functions have been guaranteed. In the proposed approaches, a PI or PID controller in the feed forward path and a polynomial controller, which its degree changes according to system degree in the inner feedback path, have been used. Parameters of these controllers are obtained using the standard form coefficients and the proposed simple mathematical operations without the restrictions of the previously proposed approaches. Comparative examples for the use of the proposed approaches and the obtained standard forms together with the previously proposed methods are also given in the MATLAB.

DOI: http://dx.doi.org/10.5755/j01.eee.20.2.4135