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
Highlights
Nowadays classical controllers are still popular in spite of many proposed modern control methods due to the robust performance and easiness in the design steps
Optimal standard form coefficients have been calculated for c2 values changing 1 to 50 and since the results are linear it became possible to be used for higher values of c2 than 50
In this study standard forms with two variable zeros have been obtained for only constraining the c2 value
Summary
Nowadays classical controllers are still popular in spite of many proposed modern control methods due to the robust performance and easiness in the design steps. Dorf and Bishop [4] proposed the ISE criterion; the standard form coefficients have not been given in their study They gave obtained standard form coefficients for the systems with one zero using the ITAE criteria for a ramp input. Dorf and Bishop [4], [5] and some textbooks, which are devoting a separate section for the subject, propose and use c0 = d0 and c1 = d1 to get a zero steady-state error for a ramp input to obtain the closed loop transfer functions of n poles standard forms with one zero This case restricts the independently chosen control parameters. Another study has been presented by Sari and Boz in 2011 about for the first time obtaining optimum values of standard form coefficients with five pole and two variable zeros for ISTE and IST2E criteria [16]. The simulation results of the method with some well-known design methods have been presented graphically for comparison
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