Decoupled double‐loop FOIMC‐PD control architecture for double integral with dead time processes

Abstract

A novel double‐loop control configuration with two controllers is suggested for double integrating processes with dead‐time. The stabilizing range of the inner‐loop proportional‐derivative (PD) controller is obtained using the Routh stability criteria. From this range, the exact PD settings are obtained by following a graphical approach where the integration of absolute error (IAE) is plotted for different PD settings. The PD settings resulting in the minimum IAE are chosen. In addition to stabilizing the plant, the inner‐loop also rejects the disturbances. A fractional‐order internal model controller (FOIMC) is designed for satisfactory set‐point tracking response in the outer‐loop. The suggested strategy has four adjustable parameters (proportional and derivative time constants, outer closed‐loop adjustment parameter, and fractional‐order of the FOIMC low‐pass filter). Based on extensive simulations, the tuning ranges for the above‐mentioned adjustable parameters are specified. The simulation study is done with the help of benchmark double integrating plant models with large dead‐time. Quantitative performance measures are also computed for comparing the suggested and previously reported schemes. The suggested FOIMC‐PD control architecture yields enhanced control performance than some recently reported techniques.

Modified Smith predictor‐based optimal fractional PD‐PD controller for double integrating processes with considerable time delay

“…In case of G 00 p2 s ð Þ, offset is observed in process response for MSP scheme developed by Kumar et al 14 Table 5 shows the performance indices (IAE, ITAE, ISE, ITSE, and TV) which further validate the supremacy of the proposed scheme in comparison with the settings provided in earlier studies. 14,15 Through simulation experiments, it is found that maximum 10% delay perturbation is allowable for the proposed scheme. Small gain theorem 35 is employed towards robust stability analysis (Table 2) while incorporating positive perturbations as shown in Figure 12.…”

“…Responses clearly reveal that the proposed scheme provides superior closed-loop performance, especially during load rejection phases. It is to note that the settings by Kumar et al 14 fail to regain the desired output with the perturbed model G 00 p1 s ð Þ subsequent to the load change. Robust stability analysis results are exhibited in Table 2 with small gain theorem 35 in the presence of positive perturbations (ΔK p and Δθ m ).…”

“…Closed-loop performance of the proposed MSP-FO (PD-PD) controller is validated through simulation study for three well-known DIPTD processes in comparison with recent relevant works. 14,15 Kumar et al 14 implemented MSP-based FOIMC PD scheme whereas in Karan and Dey, 15 MSP-based conventional PD-PD controller structure is reported. In the subsequent sections, relative closed-loop performance of the proposed work is evaluated against both the integer and fractional order controllers.…”

“…Proposed controller is found to exhibit improved closed-loop response especially during load rejection phase compared with that of Karan and Dey. 15 It is already mentioned that unstable behavior is found for the settings by Kumar et al 14 in each case. Corresponding performance indices are provided in Table 6 with reduced value of the error indices for the proposed scheme.…”

“…With Rao-1 optimization algorithm tuning parameters are found to be K p1 ¼ 0:5994, K d1 ¼ 0:9598, μ 1 ¼ 0:8738 and K p2 ¼ 0:0215, K d2 ¼ 0:2998, and μ 2 ¼ 1:1970. Relative performance (Figure 16a) for the proposed scheme is evaluated against the recent settings by Kumar et al 14 and Karan and Dey. 15 Unstable behavior for Model III is reported for the settings by Kumar et al 14 Mathematical expressions of the controllers are provided in Table 1.…”