In this study, a PI‐PD controller tuning method is presented using the weighted geometrical center method, which is based on the calculation of the weighted geometric center of the stability region obtained by the stability boundary locus method. The proposed method for tuning of PI‐PD controller parameters (kd,kf,kp and ki) is performed in three steps. In the first step, the (kd,kf) parameter region for the inner loop with PD controller is obtained, and then the weighted geometric center of this region is calculated. In the second step, the inner PD loop is reduced to a single block using the numerical values of (kd,kf) that are obtained in the first step. Then, the (kp,ki) values of the external loop with PI controller are determined by the same procedure. This tuning method has some advantages over other tuning methods in terms of simplicity and robustness. The simulation examples show that a PI‐PD controller designed using the proposed method provides good performance results when compared to other tuning methods presented in the literature.
The paper present extensions of some results developed in the parametric robust control to fractional order interval control systems (FOICS). Computation of the Bode and Nyquist envelopes of FOICS are studied. Using the geometric structure of the value set of fractional order interval polynomials (FOIP), a technique is proposed for computing the Bode and Nyquist envelopes of transfer functions whose numerator and denominator polynomials are fractional order polynomials with interval uncertainty structure. The results obtained are useful for the analysis and design of FOICS. Numerical examples are included to illustrate the benefit of the method presented.
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