Simscape Electronical Technical Articles 2020-03-31

Simscape Electronical Technical Articles and Newsletters

1. Estimating Transfer Function Models for a Boost Converter

编程操作 >> Estimating Transfer Function Models for a Boost Converter
Apps操作 >> Estimating the Frequency Response of a Power Electronics Model
iddemo_boost_converter
Transfer Function Models

Find the transfer function from the PWM duty cycle set-point to the load voltage, Uout.

Apps操作

1. Specify which portion of the model requires frequency response estimation.
   打开Apps -> Linearization Manager，选中黑色simulink信号线点DutyCycle出线和Uout入线，分别选Cloosed-Loop内Input Perturbation和Output Measurent.
2. Find an operating point and initialize the model.
   打开Apps -> Model Linearizer -> Esitimation -> Operating Point -> Take Simulation Snapshot，输入一个稳态工作点，如0.01s。
   Initialize model到MATLAB Workspace;
3. Create a perturbation signal.
   Input Signal -> Create sinestream input绿色加号，200~20000rad/s内取30点，shift选中全部点，设置幅值等参数。
4. Compute the non-parametric frequency response.
   ESTIMATE -> Bode把生成的frd数据拖入MATLAB Workspace;
5. Obtain the parametric model
   help bode和help bodeoptions。使用tfest进行传递函数的参数识别。

Using the spa and tfest commands requires System Identification Toolbox™ software.
sys_np is a nonparametric identified model. sys_p is a parametric identified model.

sysA = tfest(estsys1,2) % estsys1是模型线性化得到的frd数据，2代表二阶系统

结果会得到估计的传递函数，匹配度等信息：

sysA =
 
  From input "DutyCycle" to output "PS-Simulink Converter":
  -4.442e06 s + 6.178e09
  -----------------------
  s^2 + 6941 s + 9.822e06
 
Continuous-time identified transfer function.

Parameterization:
   Number of poles: 2   Number of zeros: 1
   Number of free coefficients: 4
   Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                                                                                            
Estimated using TFEST on frequency response data "Frequency response estimation using the input signal "in_sine1"".
Fit to estimation data: 97.51%                                                                                     
FPE: 254.9, MSE: 194.9    

生成伯德图时记得把PhaseMathching打开，默认是关闭的，则Phase无法匹配。

bopt               = bodeoptions;
bopt.Grid          = 'on';
bopt.PhaseMatching = 'on';

figure,bode(estsys1,'r*',sysA,bopt)

红色是在模型线性化中得到的离散的点，蓝色是参数估计得到的伯德图。

6. Verify the results.
   Perform a time-domain verification in a Simulink® simulation with the switch-mode boost converter and a Transfer Function block implementing the parametric estimation. We measure and compare the response of both systems to the same small perturbation signal, that is, a 2% positive step superimposed on the steady-state duty cycle.
   一定要在开环（固定给定）的情况下验证！
   
   对参数估计得到的传递函数进行验证和修正。

t=0.06s给定D加入了2%的阶跃信号。

使用命令tf2ss可以把传递函数变为状态空间方程，这样可以定义初始状态。

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Related：
>> 电力电子电路小信号分析
>> Design Controller for Power Electronics Model Using Frequency Response Data

• Validate Controller
  You can examine the tuned controller performance using a simulation with line and load disturbances. To examine the controller dynamic performance, the Simulink model uses the following disturbances:

• Line disturbance at t = 0.075 sec, which increases the input voltage, from 5V to 10V. 使用模型step配合Controlled Voltage Source；
• Load disturbance at t = 0.1 sec, which increases the load resistance, from 3 ohms to 6 ohms. 使用模型step配合Variable Resistor；

https://ww2.mathworks.cn/help/slcontrol/ug/design-controller-for-power-electronics-model-using-simulated-io-data.html

>> Design PID Controllers for Three-Phase Rectifier using Closed-Loop PID Autotuner Block

2. 各种变换器模型

power_converters

Three Types of Models:

1. Switching Devices: Converters are modeled using standard SPS power switches and diodes(see in simscape -> Electrical -> Specicalized Power Systems -> Fundamental Blocks -> Power Electronics) controlled by firing pulses produced by PWM generators.

2. Switching Function: Converters are modeled using a switching-function model. Two model types can be used depending on the nature of the firing signals sent to the g input:
   a) Switching Function controlled by firing pulses (0/1) produced by PWM generators. 结果比较接近第一种方法。
   b) Switching Function (PWM averaging) controlled by firing pulses averaged over a specified period. The g input then expects signals values between 0 and 1.

3. Average Model (Uref-controlled or D-controlled): Converters are modeled using a switching-function model directly controlled by the reference signal (Uref) or duty cycle (D). PWM generators are not required.

Technique 1 is the most accurate, while technique 3 yields to the fastest simulation. Techniques 2a and 2b are well-suited for real-time simulation.

这几种变换器模型中（Zero-Order Hold）采样时间不同：

%% Sample times
Ts_PWM = 5e-6;           % PWM generators sample time(s)
Ts_Control = 50e-6;      % Control systems sample time(s)
Ts_Power1= 5*Ts_PWM;     % Simscape(TM) Electrical(TM) Specialized Power Systems time step(s) for modeling technique "Switching Function (PWM averaging)"
Ts_Power2 = Ts_Control;  % Simscape Electrical Specialized Power Systems time step(s) for modeling technique "Uref-Controlled" 平均模型
Ts_Power = Ts_PWM;       % Default value

power_converters/Control Systems/PWM Gen Boost

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主回路：

• 三相电网线路阻抗和电参数测量

  
  
  图中有误！应该是背景颜色改为黑色。

• 变压器可以使用Three phase Transformer也可以使用多个单独的Linear Transformer配合Series RLC Branch连接。

• PWM 产生

  
  
  PWM Gen子模块

• 负载

  
  
  可变负载设置