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Fractional Order PID controller for Setpoint Tracking and Load Rejection
Published in Satyajit Chakrabarti, Ayan Kumar Panja, Amartya Mukherjee, Arun Kr. Bar, Intelligent Electrical Systems: A Step towards Smarter Earth, 2021
Sudipta Ghosh, Arijit Bhowmik, DipaBala Sarkar, Anirban Bhatta, Biswajit Chakraborty
PID controller has been considered a very popular and useful controller in most of the process industries for its easily tuneable scheme. Profuse researches have been focused on the tuning method of PID controllers amongst them Ziegler–Nichols (ZN) tuning rules are mostly acceptable. It has been revealed that Ziegler–Nichols (ZN) tuned PID controller cannot restrict the response within the acceptable limits throughout the process. To overcome the high overshoot in setpoint kick as well as in load disturbance, several techniques have been used. For this purpose, fixed setpoint weighting (FSPW), where a weighting factor is multiplied with setpoint and applied to the proportional gain, is used. Hence, it is observed that the usage of VSPW tuned PID controller is beneficial for decreasing high overshoot but failed to reduce the rise time. Therefore, for reducing the process rise time, variable setpoint (multi valued) weighting method is quite satisfactory. But this method shows extremum (maximum or minimum) value of Integral Time Absolute Error (ITAE), Integral Square Error (ISE), Integral Absolute Error (IAE). It is necessary to mention that both fixed and variable setpoint weighted PID controller cannot influence any change in load disturbance. For improving the performance under the load disturbance as well as at setpoint changes, the dynamic setpoint weighting method is introduced. But it has certain limitations for improving the transient response. For enhancing the performance in transient period and also in load rejection behaviour, fractional order PID (FOPID) (denoted by PIλDμ) has been improvised here. The idea of fractional order algorithms for the control of dynamical systems was first introduced by Podlubny over the classical PID controller. In this proposed strategy, two extra parameters have been implemented (λ > 0, μ > 0) for the improvement of response in load disturbance and also at the setpoint kick. The values of kp, ki, kd is predetermined by Ziegler-Nichols (ZN) tuning method. Moreover, the steady-state error can also be minimised by tuning these two parameters (λ and μ). On the other hand, from it can be noticed that the flexibility of fractional order Proportional Integral Derivative (FOPID) controller is more than the other existing techniques and provides more prospects for improving the dynamic properties of fractional order control system. The superiority of the proposed controller has been established by determining the performance indices such as percentage overshoot (% Os), rise time (tr), peak time (tp), delay time (td), Integral Absolute Error (IAE), Integral Square Error (ISE). The values of λ and μ are selected through trial and error procedure.
Combined frequency and voltage regulation in multi-area system using an equilibrium optimiser based non-integer controller with penetration of electric vehicles
Published in International Journal of Ambient Energy, 2023
Fractional order control is related to fractional calculus, which generalises the integer order (IO) integration and differentiation to a fractional number. The fundamental operator for this purpose is , where denotes the real number, and are the limits of the operation, which is defined mathematically as (6). Grnwald–Letnikov (GL), Riemann–Liouville (RL) and Caputo definitions are some popular processes to define fractional calculus (Debbarma and Dutta 2017). The RL formula for FO differential function is denoted in (7). where and represent gamma function and an integer, respectively.
Robust Load Frequency Control Using Fractional-order TID-PD Approach Via Salp Swarm Algorithm
Published in IETE Journal of Research, 2023
Mandeep Sharma, Surya Prakash, Sahaj Saxena
Although, numerous LFC approaches have been developed so far involving the concepts from classical control to modern control, however, finding a new optimal controller is still challenging. Various classical, adaptive, fractional-order (FO), intelligent, model-reduction based, state feedback, event-triggered control, and robust control approaches are present in [5–14]. FO-based control schemes are receiving huge consideration in recent years due to their bonus flexibility for the design and improvement of the performance. An FO-PID controller is considered for frequency regulation of isolated wind-biomass power system [15]. Fractional order control exhibits better performance due to its higher degree of flexibility. Different type of cascade controllers [16–19] and multi-stage/dual-stage controllers [20–25] considering amalgamation of FO and integer-order (IO) control are also reported in the literature to achieve optimal LFC. A fractional-order PI and PID controllers are cascaded as master and slave controllers, respectively for LFC of deregulated power systems having RES in both areas [18]. In [19] authors proposed a cascade controller having two control loops i.e. master (as PI) and slave (as PD). A dual-stage controller is proposed in [23] having the first stage as a PIDN controller and the subsequent stage as a PI controller. In [25] author used a multi-stage controller i.e. Fuzzy-PIDF combined with one plus PI (FPIDF-(1+PI)) for LFC.
An effective Smith predictor based fractional-order PID controller design methodology for preservation of design optimality and robust control performance in practice
Published in International Journal of Systems Science, 2022
As a summary, an inverse controller design methodology for the Smith predictor based FOPID controller was presented to achieve optimal and robust performance based on Bode’s ideal loop characteristics. In fractional order control system practice, the design optimality can be deteriorated due to the approximate implementation of the fractional order elements. At this point, the proposed design methodology can preserve the design optimality for non-ideal realisation of FOPID controllers in real control applications by taking into account an approximate implementation method in the controller design task. This is a major issue that is solved in the current study, and the presented FOPID design method can preserve practical optimality and control robustness based on Bode’s ideal loop characterisation in the control practices.