引言

随着电力电子技术、微型计算机技术、稀土永磁材料和控制理论的飞速发展，PMSM具有体积小、重量轻、效率高、转动惯量小、可靠性高等优点已获得越来越广泛的应用，将DTC策略应用于PMSM控制中，以提高电机的快速转矩响应，成为研究者关注的课题。

直接转矩控制理论于20世纪80年代由德国学者M.Depenbrock和日本学者I.Takahashi首先针对异步电动机提出，90年代由Zhong.L,RahmanMF,Hu.YW等学者提出PMSMDTC理论[6]。其基本思想是将电机给定转速和实际转速的误差，经PI调节器输出作为转矩的给定信号；同时系统根据检测的电机三相电流和电压值，利用磁链模型和转矩模型分别计算electric motor 的磁链和转矩大小；结合electric motor 转子的位置，以及磁链与实际值之间误差信号合理选择逆变器开关矢量，以达到electric motor 调速目的。

由于electric motor 转速变化以及负载突变，对control system 性能影响较大，因此为了获得满意的是transfer function 计算，simulation 研究是最有效的手段。 本文利用MATLAB/Simulink simulation 工具对PMSMDTC system 进行了详细介绍，为permanent magnet synchronous machine (PMSM) 交直流伺服系统数字化control 提供了基础。

1 PSM Direct Torque Control Theory

1.1 Permanent Magnet Synchronous Motor Mathematical Model

假设：

Stator winding is symmetrical and each phase winding has a mutual angle of 120 degrees in space.

The rotor on the permanent magnet has no damping winding, and the magnetic field does not have any damping effect.

Neglecting magnetic saturation, eddy current, and hysteresis losses.

Using these assumptions, we can derive the α-β coordinate system equations for PSM:

v_a = R_s * i_a + L_s * di_a/dt - ω_e * L_s * i_b,

v_b = R_s * i_b + L_s * di_b/dt + ω_e * L_s * i_a,

where v_a and v_b are stator voltage components in the α-β coordinates; i_a and i_b are stator current components; R_s is stator resistance; p is differential operator; ω_e is rotor mechanical angular speed.

The flux equation can be derived by integrating both sides of Equations (2) to get:

λ_mα = λ_m0cos(θ_r) - Δω_e / ω_e,

λ_mβ = λ_m0sin(θ_r),

where λ_mα and λ_mβ are magnetic flux components in α-β coordinates; θ_r is rotor position angle.

The electromagnetic torque equation can be expressed as:

T_em = (3/2)(p_persistentλ_msi_qs),

where T_em is electromagnetic torque; p_persistent represents the number of pole pairs of electric motor ; λ_ms denotes airgap flux linkage per unit time period related to one pole pair ;i_qs indicates q-axis component of stator current vector.

Power dynamic motion equation for electric machine can be written as:

Jdω_me/dt + Bω_me + T_load = T_em,

where J denotes moment inertia coefficient representing electrical inertial force constant for electric machine ;B represents viscous friction coefficient between rotating parts ;T_load signifies external load torque acting on shaft axis .

1.2 DTC System Construction

The DTC control principle diagram consists mainly of an input voltage source converter, a PSM, voltage calculation module, three-phase current sampling circuitry with 3s/2 transformation process utilizing discrete-time data obtained from sampled currents , estimation models for magnetic flux linkages , estimation model for electromagnetic torque , estimation model for rotor position based on measured values from sensors or encoder readings . A PI controller that compares error signals produced by desired rotational speed deviation with actual rotational speed value then adjusts output PWM signal which controls switching actions at appropriate instants via switch table selection logic .

Figure 5 shows how this entire setup works within Simulink environment using MATLAB toolboxes where it's implemented numerically through algorithmic implementation steps :

figure5: Direct Torque Control System Block Diagram

Step-by-step guide to create this block diagram:

Start with defining input parameters such as desired rotation rate n_d(n), initial conditions like initial angular displacement theta_0(rad), initial angular velocity omega_0(rpm).

Next set up basic blocks including PI controllers & integrators along side other necessary functions such as sampling circuits converting raw sensor measurements into digital form before feeding them back into your main loop routine. Finally use logical gates to make decisions about when certain events should occur during execution depending upon threshold comparisons made against predefined constants stored elsewhere within codebase itself.