High-order Sliding Mode Control For Brushless DC Motor Speed Servo System

Brushless DC motor(BLDCM)has been more and more widely used in More Electric/All Electric Aircraft(MEA/AEA),Hypersonic Vehicles,Electric Vehicles,Robots and other industrial applications,due to its several advantages such as simple structure,excellent performance,high power density,high efficiency,high reliability.The performance requirements of BLDCM control system are becoming more and more high.BLDCM speed servo system is the core system in these applications.Strengthen the robustness of BLDCM speed servo system is a key point to improve the dynamic and static performance of the system.In this dissertation,under the condition of comprehensively grasping the research actuality of BLDCM control technology and high-order sliding mode control(HOSM)theory,and based on the BLDCM nonlinear modeling,the research emphasis of improving the robustness of BLDCM speed servo system is focused on the design of the speed servo control laws,which would be designed based on the second-order sliding mode(SOSM)algorithm of Super-Twisting Algorithm(STA)and Prescribed Convergence Law(PCL)Algorithm,taking into account the research of the methods which would improve the system’s overall performance,such as reducing the torque ripple,the copper los and the speed overshoot.Firstly,a pure feedback nonlinear model of the BLDCM based on the two-phase conduction circuits is established,then,a kind of two-stage sliding mode backstepping self-adaptive SOSM BLDCM speed servo control method is proposed.Compared with the traditional SOSM control method,the proposed method needs no derivative of the sliding mode variable,avoiding the negative impact on the system from the noise and interference caused by the derivation.In the whole control law design process,a novel self-adaptive STA(SSTA)is proposed for the first stage speed control.Compared with the original STA,the SSTA can make the system be more robust to the step load disturbance and has a smaller speed overshoot.For the second stage current control,the effective compensation measures is designed to eliminate the adverse effect on torque control caused by the non-ideality of back-EMF and the freewheeling of the off-phase,consequently,the torque ripple is reduced,and the torque control accuracy is improved.In order to simplify the control law further,the second-order model of BLDCM is decomposed into two first-order elements as the outer speed loop and the inner torque loop,on this basis,a first-order and second-order sliding mode cascaded dual-closed loop BLDCM speed servo control method is proposed.For the outer loop speed STA control,the analysis shows that the proportional of sliding mode variable does not destroy the stability of the STA control system,then,a novel STA with the proportional of sliding mode variable(PSTA)is proposed.Compare with the original STA,PSTA improves the convergence rate and the robustness against the step load disturbance,it also reduces the speed overshoot.For the inner loop torque control,aiming at reducing the torque ripple and improving the dynamic performance of torque control,the first-order sliding mode(FOSM)direct torque control(DTC)without the flux linkage control is presented combined with non-ideal trapezoidal wave back-EMF,FOSM algorithm,two-phase conduction non-zero voltage vectors and the zero voltage vector.The results show that,compared with the traditional speed and current dual closed-loop PI control method,both the above-mentioned two methods proposed for speed servo control can improve the system’s robustness against uncertain load disturbance and the speed control precision,also reduce the speed overshoot and the torque ripple.But compared with each other,the control law of the first-order and second-order sliding mode cascaded control has more simple formula and fewer control parameters,besides,it still possesses the advantage of no need for derivation.Although the above mentioned FOSM DTC can eliminate the torque ripple caused by the non-ideality of back-EMF,it still belongs to the two-phase conduction control mode,causing the commutation torque ripple cannot be eliminated when the BLDCM running at high speed.Besides,without flux linkage closed-loop,the performance of the BLDCM-DTC system cannot be improved by designing the flux linkage tracking trajectory.To solve the above two problems,the relevant coordinate transformations and the maximum torque per ampere(MTPA)vector control principle of BLDCM are combined to create the BLDCM-MTPA flux linkage tracking-DTC with three-phase conduction voltage vectors.The mechanism of the stator flux linkage MTPA tracking trajectory changing with load torque is revealed.Compared with the traditional current PI control and the BLDCM-flux linkage uncontrolled-DTC,the proposed novel BLDCM-DTC can eliminate the torque ripple caused by the non-ideality of back-EMF,but also the commutation torque ripple,the torque control precision is correspondingly improved.Besides,the stator copper loss is minimized by MTPA flux linkage tracking control,consequently,the running efficiency of the BLDCM is improved.Lastly,to solve the common problem of speed overshoot which exists in both the traditional dual closed-loop PI control and the proposed two control methods based on STA,the BLDCM-MTPA-PCL SOSM speed servo control method is created in combination with the PCL algorithm to the BLDCM-MTPA vector control principle.In the process of designing control law,the PCL algorithm cannot be directly applied to BLDCM-MTPA vector control resulting from that the space vector pulse width modulation(SVPWM)technique cannot be used to make the discontinuous output of PCL algorithm work,this problem is solved by modeling the three-phase full bridge inverter and using relevant coordinate transformation.Besides,by designing the special sliding mode variables,the matching design problem of direct axis current channel and speed channel between which the relative degree is unequal is solved.In addition,for solving the current uncontrolled problem in the BLDCM-MTPA-PCL SOSM speed servo control method,a current indirectly limiting method based on electromagnetic torque FOSM control is presented.The proposed BLDCM-MTPA-PCL control method is a speed torque integrated control method,there is only one control parameter need to be adjusted,which greatly simplifies the control structure and reduces the number of control parameters.The results show that,by using the proposed BLDCM-MTPA-PCL control method,the system has stronger robustness with no speed overshoot,and the torque ripple and the stator copper loss are effectively reduced,consequently,the running efficiency of the BLDCM is improved.