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

Abstract

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.

An optimal robust design method for fractional‐order reset controller

“…Fractional calculus is used to extend the order of calculus from the integer to any real number. The definition of the fractional differential-integral operator [41] can be described as:…”

“…Fractional calculus is used to extend the order of calculus from the integer to any real number. The definition of the fractional differential‐integral operator [41] can be described as: $$$$ {}_{t_0}{D}_t^{\alpha }f(t)=\left\{\begin{array}{cc}\frac{d^{\alpha }}{d{t}^{\alpha }}f(t),\kern0.30em & \alpha >0\\ {}f(t),\kern0.30em & \alpha =0\\ {}{\int}_{t_0}^tf\left(\tau \right)d{\tau}^{-\alpha },\kern0.30em & \alpha <0\end{array}\right., $$$$ where $$$ t $$$ is the time variable, $$$ {t}_0 $$$ is the start time of the integral, which can be omitted when $$$ {t}_0=0 $$$, and $$$ \alpha $$$ is the order of calculus, which can be any real number.…”

“…To the best of the authors' knowledge, there is no published result on this controller's analytical design tuning method. Existing PI + CI tuning procedures [11,22,27,41], usually consist of two steps: designing a linear base controller (i.e., PI controller) and giving the reset ratio. Moreover, the reset ratio is usually calculated by a time-domain method.…”

A Fractional-Order ADRC Architecture for a PMSM Position Servo System with Improved Disturbance Rejection

“…Ref. [29] proposed an optimal fractional-order ADRC method for the PMSM speed servo system, which met the requirement for frequency-domain indicators and achieved optimal performance in the time domain. A comparison of these versions of ADRC is presented in Table 1.…”

“…(3) Simulation and experimental comparison tests on a PMSM position servo system were conducted to verify the effectiveness of the proposed method. Linear GESO Fractional-Order PD [20] Linear Model-Aided ESO Model Predictive Control [25] Nonlinear Nonlinear ESO Fractional-order PD [29] Linear LESO Fractional-Order PD [26,27] Linear FOESO PID [28] Linear FOESO Fuzzy Self-Tuning PD…”