机电传动控制第四周仿真作业

题目要求：

结合本周学习的交流电机原理及启动、调速、制动特性，用Modelica设计和仿真一个用三相交流异步电机带动起重机起升机构运行。具体要求如下：

1）实现如下机械运动周期：

控制电机带重物上升，从静止加速到800r/min
保持800r/min匀速运动0.5s，
减速到静止，保持静止状态0.5s，
带重物下降，从静止达到600r/min
保持600r/min匀速运动0.6s，
减速到静止。
(为了便于仿真，匀速和静止持续时间较短)

2) 升降机构和重物折算到到电机转子轴上的等效负载惯量为1Kg.m^2，折算到到电机转子轴上的等效负载转矩是15N.m。

3）使用统一的电机模型,如果控制策略中用到转子串电阻，允许将该电机的转子改为绕线式转子（参数不变）。

4）参照教材中给出的交流电机启动、调速和制动方法，设计控制策略，用Modelica实现控制策略并与电机模型实现联合仿真。

5）可以采用定子串电阻、转子串电阻、定子调压、定子调频等手段，但必须具备工程上的可实施性。

6）评价指标：快速启动、制动，冲击转矩和冲击电流小，能耗小，兼顾实施的经济性。

仿真分析：

为实现高启动转矩和低启动电流的较好启动特性，仿真选取了绕线异步电动机的逐级切除启动电阻法实现电机的启动，同时选取转子串接电阻法作为调速方法，以反接制动作为制动方式，控制全过程中转矩大小不大于85N·m，全过程电流大小不超过25A，最终仿真全过程用时6690ms，仿真使用电机模型参数为：额定电压（相电压）220 V，额定频率50 Hz，极对数p=3，电机转动惯量0.1 kg.m^2，负载转动惯量1 kg.m^2，定子电阻：0.531 Ohm，转子电阻：0.408 Ohm，定子漏感：2.52 mH，转子漏感：2.52 mH，互感：8.47 mH，仿真过程中使用辅助参数来实现对过程时间点的定位。

仿真代码及结果：

model SACIM "A Simple AC Induction
Motor Model"

type Voltage=Real(unit="V");

type Current=Real(unit="A");

type Resistance=Real(unit="Ohm");

type Inductance=Real(unit="H");

type Speed=Real(unit="r/min");

type Torque=Real(unit="N.m");

type Inertia=Real(unit="kg.m^2");

type Frequency=Real(unit="Hz");

type Flux=Real(unit="Wb");

type Angle=Real(unit="rad");

type
AngularVelocity=Real(unit="rad/s");

constant Real Pi = 3.1415926;

Real y1;

Real y2;

Real z;

Current i_A"A Phase Current of
Stator";

Current i_B"B Phase Current of
Stator";

Current i_C"C Phase Current of
Stator";

Voltage u_A"A Phase Voltage of
Stator";

Voltage u_B"B Phase Voltage of
Stator";

Voltage u_C"C Phase Voltage of Stator";

Current i_a"A Phase Current of
Rotor";

Current i_b"B Phase Current of
Rotor";

Current i_c"C Phase Current of
Rotor";

Frequency f_s"Frequency of
Stator";

Torque Tm"Torque of the Motor";

Speed n"Speed of the Motor";

Flux Psi_A"A Phase Flux-Linkage of
Stator";

Flux Psi_B"B Phase Flux-Linkage of
Stator";

Flux Psi_C"C Phase Flux-Linkage of
Stator";

Flux Psi_a"a Phase Flux-Linkage of
Rotor";

Flux Psi_b"b Phase Flux-Linkage of
Rotor";

Flux Psi_c"c Phase Flux-Linkage of
Rotor";

Angle phi"Electrical Angle of
Rotor";

Angle phi_m"Mechnical Angle of
Rotor";

AngularVelocity w"Angular Velocity of
Rotor";

Resistance R1;

parameter Torque Tl =15 "Load
Torque";

parameter Torque Tmax = 85;

parameter Torque Tmin = -85;

parameter Current imax = 25;

parameter Current imin = -25;

parameter Resistance Rs = 0.531"Stator
Resistance";

parameter Resistance Rr = 0.408"Rotor
Resistance";

parameter Inductance Ls =
0.00252"Stator Leakage Inductance";

parameter Inductance Lr = 0.00252"Rotor
Leakage Inductance";

parameter Inductance Lm =
0.00847"Mutual Inductance";

parameter Frequency f_N = 50"Rated
Frequency of Stator";

parameter Voltage u_N = 220"Rated
Phase Voltage of Stator";

parameter Real p =3"number of pole
pairs";

parameter Inertia Jm = 0.1"Motor
Inertia";

parameter Inertia Jl = 1"Load
Inertia";

initial equation

Psi_A = 0;

Psi_B = 0;

Psi_C = 0;

Psi_a = 0;

Psi_b = 0;

Psi_c = 0;

phi = 0;

w = 0;

equation

u_A = Rs * i_A + 1000 * der(Psi_A);

u_B = Rs * i_B + 1000 * der(Psi_B);

u_C = Rs * i_C + 1000 * der(Psi_C);

0 = (Rr+R1) * i_a + 1000 * der(Psi_a);

0 = (Rr+R1) * i_b + 1000 * der(Psi_b);

0 = (Rr+R1) * i_c + 1000 * der(Psi_c);

Psi_A = (Lm+Ls)*i_A + (-0.5*Lm)*i_B +
(-0.5*Lm)*i_C + (Lm*cos(phi))*i_a + (Lm*cos(phi+2*Pi/3))*i_b +
(Lm*cos(phi-2*Pi/3))*i_c;

Psi_B = (-0.5*Lm)*i_A + (Lm+Ls)*i_B +
(-0.5*Lm)*i_C + (Lm*cos(phi-2*Pi/3))*i_a + (Lm*cos(phi))*i_b +
(Lm*cos(phi+2*Pi/3))*i_c;

Psi_C = (-0.5*Lm)*i_A + (-0.5*Lm)*i_B +
(Lm+Ls)*i_C + (Lm*cos(phi+2*Pi/3))*i_a + (Lm*cos(phi-2*Pi/3))*i_b +
(Lm*cos(phi))*i_c;

Psi_a = (Lm*cos(phi))*i_A +
(Lm*cos(phi-2*Pi/3))*i_B + (Lm*cos(phi+2*Pi/3))*i_C + (Lm+Lr)*i_a +
(-0.5*Lm)*i_b + (-0.5*Lm)*i_c;

Psi_b = (Lm*cos(phi+2*Pi/3))*i_A +
(Lm*cos(phi))*i_B + (Lm*cos(phi-2*Pi/3))*i_C + (-0.5*Lm)*i_a + (Lm+Lr)*i_b +
(-0.5*Lm)*i_c;

Psi_c = (Lm*cos(phi-2*Pi/3))*i_A +
(Lm*cos(phi+2*Pi/3))*i_B + (Lm*cos(phi))*i_C + (-0.5*Lm)*i_a + (-0.5*Lm)*i_b +
(Lm+Lr)*i_c;

Tm
=-p*Lm*((i_A*i_a+i_B*i_b+i_C*i_c)*sin(phi)+(i_A*i_b+i_B*i_c+i_C*i_a)*sin(phi+2*Pi/3)+(i_A*i_c+i_B*i_a+i_C*i_b)*sin(phi-2*Pi/3));

w = 1000 * der(phi_m);

phi_m = phi/p;

n= w*60/(2*Pi);

Tm-Tl = (Jm+Jl) * 1000 * der(w);

if time <= 100 then

u_A = 0;

u_B = 0;

u_C = 0;

f_s = 0;

elseif time <= 2430 then

f_s = f_N;