Robust Fractional Order PID Controller Research Articles

Robust Fractional Order PID Controller Coupled with a Nonlinear Filtered Smith Predictor for Solar Collector Fields

This work introduces a Fractional Order PID (FOPID) controller associated with a nonlinear Filtered Smith Predictor (FSP) to control a Solar Collector Field (SCF) system. The combined approach enhances the control performance by decoupling model uncertainties. First, the FOPID addresses linear model uncertainties through optimal robust design across the operational conditions, while the FSP compensator adeptly manages the system’s varying time delays. Rigorous tuning in the frequency domain considering closed-loop, robustness, and disturbance rejection performances is developed using a bi-level optimization approach to obtain the FOPID control parameters. Experimental results of the FOPID + nonlinear FSP demonstrate low rise time for reference tracking and robust stability across several operating conditions, even in the face of high-frequency disturbances in the solar irradiance due to passing clouds. Moreover, the nonlinear FSP effectively handles variations in time delays undergone by the water flow variation during the experiment. The achieved outcomes of the overall control structure, comprising the FOPID + FSP, demonstrate a promising approach for SCF system control, obtaining robust behavior in the presence of model uncertainties and disturbances while offering satisfactory reference tracking capabilities across an extensive range of plant operations.

Robust fractional order PID controller synthesis for the first order plus integral system

The fractional order PID (FOPID) controller has been found to have the potential to provide more flexibility in the design options than the integer order PID (IOPID) controller. However, in the FOPID controller design practice, investigations are still required in selecting the achievable design specifications and controller parameters. In order to obtain a practical tuning method for the FOPID controller, taking the first order plus integral systems as the plants, the complete achievable regions of the design specifications are collected and analyzed. In addition, the selectable integral and derivative orders of the FOPID controller are also collected and modeled. With the prior knowledge obtained, a synthesis method for the FOPID controller is proposed to make the control system achieve the desired flat-phase characteristic. To verify the effectiveness of the proposed method, the synthesis method is applied to design the FOPID controller for the permanent magnet synchronous motor (PMSM) speed servo system. Simulation and experimental results show that system with the FOPID controller can achieve satisfying tracking performance and disturbance rejection performance.

Design of an improved robust fractional order PID controller for magnetic levitation system based on atom search optimization

Design of an improved robust fractional order PID controller for magnetic levitation system based on atom search optimization

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

SummaryIn this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters kp, ki, kd can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.

English

English

Bode shaping-based design methods of a fractional order PID controller for uncertain systems

This paper deals with robust fractional order PID controller design via numerical optimization. Three new frequency-domain design methods are proposed. They achieve good robustness to the variation of some parameters by maintaining the open-loop phase quasi-constant in a pre-specified frequency band, i.e., maintaining the iso-damping property of the controlled system. The two first methods are extensions of the well-known Monje-Vinagre et al. method for uncertain systems. They ameliorate the numerical optimization algorithm by imposing the open-loop phase to be flat in a frequency band not only around a single frequency. The third method is an interval-based design approach that simplifies the algorithm by reducing the constraints number and offers a more large frequency band with an iso-damping property. Several numerical examples are presented to show the efficiency of each proposed method and discuss the obtained results. Also, an application to the liquid carbon monoxide level control is presented.