Design of an improved Fractional Order PID controller using Variable Set-Point Control Scheme

This paper presents a novel control strategy for Fractional Order PID (FOPID) controllers i.e., Variable Set-Point Weighted Variable Fractional Order PID (VSPWVFOPID) controller. To implement this control scheme, three different values of set-point weighting factor ($\beta$), integral order ($\lambda$) and differential order ($\mu$) are selected for three different regions of output response and applied to set-point, integral action, and differential action, respectively. The key focus of this control scheme is to provide satisfactory results in both, initial transient and load rejection phases as well as superior robust control. The effectiveness of the proposed VSPW-VFOPID controller is demonstrated considering two different process models and their 10% perturbed systems in MATLAB simulation platform. The performance of the proposed control scheme is compared with existing control techniques like Ziegler Nichols (ZN) tuning, Fixed Set Point Weighting (FSPW), Variable Set Point Weighting (VSPW), and Fractional Order PID (FOPID). In this context, VSPW-VFOPID can provide better response during both phases. For the purpose of this paper, various performance indices are considered like Percentage Overshoot (OS%), Rise-Time $(\mathrm{t}_{\mathrm{r}})$, Peak-Time $(\mathrm{t}_{\mathrm{p}})$, Settling-Time $(\mathrm{t}_{\mathrm{s}})$, Integral Absolute Error (IAE), Integral Square Error (ISE), and Integral Time Absolute Error (ITAE). From the results of the proposed scheme, it can be concluded that, apart from enhanced robust control, VSPW-VFOPID shows excellent performance during initial set-point tracking and load rejection phases which makes it superior to other existing control schemes.