| Summary: | The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (<inline-formula><math display="inline"><semantics><msub><mi>ω</mi><mrow><mi>g</mi><mi>c</mi></mrow></msub></semantics></math></inline-formula>) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and <inline-formula><math display="inline"><semantics><msub><mi>ω</mi><mrow><mi>g</mi><mi>c</mi></mrow></msub></semantics></math></inline-formula> as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and <inline-formula><math display="inline"><semantics><msub><mi>ω</mi><mrow><mi>g</mi><mi>c</mi></mrow></msub></semantics></math></inline-formula> when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.
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