# Performance Improvement for PMSM Driven by DTC Based on Discrete Duty Ratio Determination Method
## 1 Introduction  
The performances of the servo motor and the motor control strategy determine the quality of the servo system. Permanent magnet synchronous motor (PMSM) has lots of merits, including high reliability and good control performance. Additionally, it has been applied in industrial robot application widely [1; 2; 3; 4; 5; 6; 7]. Field-oriented control (FOC) and direct torque control (DTC) are the two widely applied high-performance control strategies for the PMSM [8; 9; 10; 11; 12; 13]. Torque is the variable in DTC that is controlled directly, so the quickest dynamic response can be obtained in the PMSM driven by DTC [14; 15; 16]. Therefore, the servo system that is composed by the permanent magnet synchronous motor (PMSM) driven by direct torque control owns many merits than other servo systems.  
The torque error and the flux error are compensated by a single active vector comprehensively in single vector error compensational strategy (SV-DTC). Therefore, the PMSM driven by SV-DTC suffers from some drawbacks, such as large torque and flux linkage ripples as the errors of flux linkage and torque in conventional DTC (CDTC) are compensated by only one active vector [17; 18; 19; 20]. On the other hand, in order to improve the steady-state performance of the PMSM, the novel direct torque control(NDTC) utilizing composite active vectors has been proposed in [2]. Despite the better steady-state and dynamic-state performance of the PMSM system can be obtained, the computation burden is inevitably increased with the using of the adaptive sector division criterion, therefore, the fixed sector division criterion is proposed for the control system (FS-DTC) in [3].  
In order to simplify the complexity of the control system, the determination method of the duty ratio value is studied in this paper.The analytical relationship between the sector angle of the synthetic vector and the error rate is deduced first. It should be noted that the applied master vector and slave vector during each control period in FS-DTC are the adjacent vectors, therefore, the direction of the equivalentsymthetic vector is between from the directions of the two active vectors. The precondition of the accurate duty ratio value determination is the selection of the suitable discrete duty ratio value. The complexity of the control system will be increased while the discrete duty ratio value is much accurate, on the other hand, the required error compensation results cannot be obtained while the discrete duty ratio value is inaccurate. The proposed discrete duty ratio determination method can solve the existing problems in FS-DTC effectively.  
The rest of this paper comprises the following sections. The calculations of the accurate active factors are described in Section 2. The scheme diagram of the discrete duty ratio determination method is illustrated in Section 3. The calculation for the synthetic vector, the discrete sector angle, the discrete error angle, and the duty ratio scale are also described in this Section, which are the indispensable integral parts of the discrete duty ratio determination method. The description of experimental setup and discussions on experimental results are given in Section 4. The conclusion is analyzed in Section 5.