机电传动控制第四周仿真作业

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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;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000);

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3);

elseif time <= 3560 then

f_s = f_N;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000);

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3);

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);

elseif time <= 4060 then

f_s = f_N;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000);

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3);

elseif time <= 4901 then

f_s = f_N;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000);

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3);

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);

else

f_s = f_N;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000);

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3);

end if;

 

if time<=160 then

R1=17;

elseif time<=930 then

R1=10;

elseif time<=1640 then

R1=6;

elseif time<=1930 then

R1=3;

elseif time<=2430 then

R1=12.2;

elseif time<=3300 then

R1=20.5;

elseif time<=3560 then

R1=12.2;

elseif time<=4060 then

R1=62.4;

elseif time<=4600 then

R1=10.5;

elseif time<=4901 then

R1=6;

elseif time<=5501 then

R1=100;

elseif time<=6280 then

R1=17;

elseif time<=6690 then

R1=12.2;

else

R1=62.4;

end if;

if n>=800 then

y1=1000;

elseif n>=0 then

y1=0;

else y1=-1000;

end if;

if n>=-600 then

y2=800;

else y2=-800;

end if;

if time<=1930 then

z=900;

elseif time<=3560 then

z=-900;

elseif time<=4060 then

z=900;

elseif time<=4901 then

z=-900;

elseif time<=6690 then

z=900;

else

z=-900;

end if;

end SACIM;

simulate(SACIM,startTime=0,stopTime=8000)

plot(n)

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plot({y1,y2,z})

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plot({i_a,imax,imin})

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plot({Tm,Tmax,Tmin})

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