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.

Fractional order PIλDµ controller design for satisfying time and frequency domain specifications simultaneously.

In order to achieve a desired control performance characterized by satisfying specifications in both frequency-domain and time-domain simultaneously, an optimal fractional order proportional integral derivative (PIλDµ) controller design strategy is proposed based on analytical calculation and Differential Evolution algorithm for a permanent magnet synchronous motor (PMSM) servo system in this paper. In this controller design, the frequency-domain specifications can guarantee the system stability with both gain margin and phase margin, and also the system robustness to loop gain variations. The time-domain specifications can ensure the desired step response performance with rapid rising curve, constrained overshoot, and proper power consuming. Compared with the PIλ controller and the traditional PID controller, PIλDµ controller can get obvious benefits from two more degrees of freedom of the fractional orders λ and µ on satisfying multiple constraints simultaneously and achieving better servo tracking performance for the PMSM servo system. PMSM speed tracking simulations and experiments are demonstrated to show the significant advantages of using the proposed optimal PIλDµ controller over the optimal fractional order PIλ controller and traditional integer order PID controller.

Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm.

A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations.

PMSM sensorless control with separate control strategies and smooth switch from low speed to high speed.

This paper proposes a smooth switching scheme with separate control strategies on low speed mode and high speed mode for permanent magnet synchronous motor (PMSM) sensorless control to improve the overall performance in full speed range. Constant voltage/frequency tuning method is used on low speed mode because the rotor position can hardly be estimated precisely at low speed. Along with the increasing speed, the control strategy can be switched to high speed mode smoothly when current and speed meet the given requirements. In this high speed mode, the current tracking with a sliding mode observer (SMO) and speed tracking with a sliding mode controller (SMC) are handled, respectively. Experimental demonstration is presented to show the desired performance in full speed range of the PMSM sensorless control using the proposed control scheme in this paper.

Enhanced robust fractional order proportional-plus-integral controller based on neural network for velocity control of permanent magnet synchronous motor.

The traditional integer order proportional-integral-differential (IO-PID) controller is sensitive to the parameter variation or/and external load disturbance of permanent magnet synchronous motor (PMSM). And the fractional order proportional-integral-differential (FO-PID) control scheme based on robustness tuning method is proposed to enhance the robustness. But the robustness focuses on the open-loop gain variation of controlled plant. In this paper, an enhanced robust fractional order proportional-plus-integral (ERFOPI) controller based on neural network is proposed. The control law of the ERFOPI controller is acted on a fractional order implement function (FOIF) of tracking error but not tracking error directly, which, according to theory analysis, can enhance the robust performance of system. Tuning rules and approaches, based on phase margin, crossover frequency specification and robustness rejecting gain variation, are introduced to obtain the parameters of ERFOPI controller. And the neural network algorithm is used to adjust the parameter of FOIF. Simulation and experimental results show that the method proposed in this paper not only achieve favorable tracking performance, but also is robust with regard to external load disturbance and parameter variation.

Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor.

A fractional order sliding mode control (FROSMC) scheme based on parameters auto-tuning for the velocity control of permanent magnet synchronous motor (PMSM) is proposed in this paper. The control law of the proposed F(R)OSMC scheme is designed according to Lyapunov stability theorem. Based on the property of transferring energy with adjustable type in F(R)OSMC, this paper analyzes the chattering phenomenon in classic sliding mode control (SMC) is attenuated with F(R)OSMC system. A fuzzy logic inference scheme (FLIS) is utilized to obtain the gain of switching control. Simulations and experiments demonstrate that the proposed FROSMC not only achieve better control performance with smaller chatting than that with integer order sliding mode control, but also is robust to external load disturbance and parameter variations.

Fractional order ultra low-speed position servo: improved performance via describing function analysis.

In a reference of the previous work, a new systematic design method for fractional order proportional and derivative (FOPD) controller is proposed for a class of typical second-order plants. Simulation and experimental results in the reference show that, the dynamic performance and robustness with the designed FOPD controller outperforms that with the optimized traditional integer order proportional integral (IOPI) controller at normal speed. Furthermore, it is found that, for the ultra low-speed position tracking with a significant friction effect, the tracking performance using the designed FOPD controller is much better than that using the optimized IOPI controller. However, the reason of this advantage is unclear. In this paper, using the describing function method and Bode plots analysis, the observed advantage of the designed FOPD controller over the optimized IOPI controller, for the nonlinear low-speed position tracking system with friction effect, is explained with the theoretical analysis. This explanation for the priority of the designed FOPD controller is consistently demonstrated by the extended experimental results in this paper.

Cogging effect minimization in PMSM position servo system using dual high-order periodic adaptive learning compensation.

Cogging effect which can be treated as a type of position-dependent periodic disturbance, is a serious disadvantage of the permanent magnetic synchronous motor (PMSM). In this paper, based on a simulation system model of PMSM position servo control, the cogging force, viscous friction, and applied load in the real PMSM control system are considered and presented. A dual high-order periodic adaptive learning compensation (DHO-PALC) method is proposed to minimize the cogging effect on the PMSM position and velocity servo system. In this DHO-PALC scheme, more than one previous periods stored information of both the composite tracking error and the estimate of the cogging force is used for the control law updating. Asymptotical stability proof with the proposed DHO-PALC scheme is presented. Simulation is implemented on the PMSM servo system model to illustrate the proposed method. When the constant speed reference is applied, the DHO-PALC can achieve a faster learning convergence speed than the first-order periodic adaptive learning compensation (FO-PALC). Moreover, when the designed reference signal changes periodically, the proposed DHO-PALC can obtain not only faster convergence speed, but also much smaller final error bound than the FO-PALC.