Standard forms with two variable zeros and generalized optimal proportional integral derivative (PID) design for all pole systems

Other than the classical methods, the use of standard forms for control system design is well known. 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 zeros systems. In this study, for the first time, optimum values of standard form coefficients with five pole and two variable zeros are obtained for the integral squared time error (ISTE) and integral of the squared time error (IST 2 E) criteria. Again in this study, a generalized controller design approach using th degree all pole systems. In the proposed approach, a proportional integral derivative (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 standard form coefficients and the proposed simple mathematical operations. Comparative examples for the use of the proposed approach together with some well known methods are also given in the MATLAB.