Fractional-order electromagnetic modeling and identification for PMSM servo system.

An accurate electromagnetic model is essential for an optimal controller tuning of the high-performance servo system. This paper proposes a fractional-order electromagnetic model of a permanent magnet synchronous motor (PMSM) servo system and an identification methodology of this model. The reason why the investigated electromagnetic model should be a fractional-order one is addressed with a detailed explanation. The influence of voltage source inverter nonlinearity, which may cause system identification error, is analyzed. An improved inverter nonlinearity model and compensation method are proposed to promote the accuracy of the model parameter identification. Compared with the existing typical electromagnetic models of the PMSM servo system, the current open-loop and closed-loop experiments prove that the proposed fractional-order electromagnetic model with time delay is more accurate for the actual physical system. The effectiveness of the proposed nonlinearity modeling and compensation scheme of the inverter is also verified on an experimental PMSM servo system.

A fractional order friction model.

A new dynamic model for friction is proposed based on the commonality between frictional order dynamics and friction behavior. The model can achieve accurate modeling both in the sliding and the pre-sliding region with fewer parameters. Simulation results of the FOFM are illustrated with the parameters identification using the particle swarm optimization algorithm. The simulation shows that the fractional order friction model (FOFM) can capture most of the friction behavior accurately, including the hysteresis, non-local memory, Stribeck effect, and friction lag with only 7 parameters. Experimental results are also carried out to demonstrate the superiority of the proposed FOFM in terms of modeling accuracy and complexity, comparing with the well-known GMS model.

An analytical synthesis of fractional order PIλDµ controller design.

This paper proposed a comprehensive synthesis of fractional order PIλDµ (FOPIλDµ) controller analytical design, which is illustrated through the typical first order plus normalized time delay (FOPNTD) systems, with fulfilling five frequency-domain specifications simultaneously: phase margin (ϕm), gain margin (Am), phase crossover frequency (ωpc), gain crossover frequency (ωgc) and a "flat phase" constraint. The control loop shape can be adjusted with wide freedom according to the five design specifications, which can all be beneficial on optimizing the control system: ωgc represents the system control bandwidth and response speed, ϕm and Am guarantee the stability, and flat phase constraint keeps the system with iso-damping property on robustness of loop gain variations. The impact of ωpc adjustment is thoroughly discovered via frequency-domain analysis and also time-domain analysis with low-frequency disturbance and high-frequency noise. The frequency response functions are presented to show the loop-shaping advantages of the proposed synthesis scheme. A further in-depth study on designing guideline is also presented: the feasible region of four specifications, e.g. ωgc, ωpc, ϕm and Am, can all be collected and visualized in the multi-dimensional graphics. This feasible region gives users prior information and great flexibility before the controller design. Simulation results using the designed FOPIλDµ controller are carried out to demonstrate the performance advantages over the optimized integer-order PID, three-parameter FOPID, fractional filter-fractional order PID and Ziegler-Nichols FOPID controllers.

Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System.

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (Kp, Kd, µ)-space corresponding to the observer bandwidth ωo can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral- Derivative (PID) controller. For example, the JITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the JITAE of IOADRC and PID controller, respectively. Besides, the JITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the JITAE of IOADRC and PID controller, respectively.

Optimal robust fractional order PIλD controller synthesis for first order plus time delay systems.

In this paper, a practical and systematic tuning procedure combining both frequency-domain (FD) and time-domain (TD) specifications is proposed to obtain an optimal robust fractional order (FO) PIλD (FOPIλD) controller for the first order plus time delay (FOPTD) processes. The FD specifications (i.e. phase margin (PM), gain crossover frequency (ωgc) and flat phase constrain (FPC)) guarantee the systemic stability and robustness to plant gain variations. Meanwhile, the TD specification (i.e. the smallest JITAE) achieves optimal dynamic performance. Furthermore, the entire feasible regions of two frequency-domain specifications ωgc and PM have been obtained with a synthesis scheme and visualized in three-dimensional plots which can be used as prior knowledge before the controller design. The comparisons of feasible region with FOPI and integer order PID (IOPID) controllers clearly present the superiority of proposed FOPIλD controller. Simulation illustration for delay dominant systems, lag dominant systems and high order system with one zero, using the proposed optimal robust FOPIλD controller is presented to demonstrate the significant performance improvement over FOPI controller, three-parameter FOPID controller, Ziegler-Nichols FOPID controller, fractional filter-FOPID controller and SIMC-PI controller.

Fractional order active disturbance rejection control with the idea of cascaded fractional order integrator equivalence.

This paper presents a fractional order (FO)-active disturbance rejection control (ADRC) with a FO extended state observer (FOESO) design. Applying this FOESO, a typical second order motion plant can be converted into a cascadedfractionalorderintegrator(1∕s2r;0