Difference between matlab ss function and Simulink State-Space block

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Raymond Wong 2022-7-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1753875-difference-between-matlab-ss-function-and-simulink-state-space-block

编辑： Paul 2023-4-19

采纳的回答： Raymond Wong

out.mat

在 MATLAB Online 中打开

I want to do induction motor state space model simulation, so I built it with ss function and set the zero initial conditions, but after I fed it with input by lsim function, the output diverged. When I built it with simulink state-space block, fed the same input, and set the same initial conditions, it converged and got pretty good result, which made me think what's the difference between these two state space modeling methods. What aspects should I pay attention if I want to make ss in matlab converge?

Update: I attached code in matlab and SImulink block for better understanding

Simulink Block and Solver setting:

The simulink block configurations are the same in matlab

Simulink solver setting:

MATLAB code:

%% Basic Setting
f = 10000; % Sampling Frequency
Ts = 1/f; 
%% Data Preparation(Not Important
out1 = out;
ab0_voltage1 = out1.voltage_ab0;
ab0_current1 = out1.current_ab0;
rotation_f1 = out1.speed;
start_time = 0;
sampling_time = 5;
start_point = start_time*f+1;
sampling_points = sampling_time*f-1;
t_ind = start_point:start_point+sampling_points; 
u = ab0_voltage1(t_ind,2:3); %Input
i = ab0_current1(t_ind,2:3); 
flux_init = out.flux_ab(start_point,2:3);
w = mean(out.w_e(end,2));
%% Parameterization of State Space A B C D
x = [6.14,0.037874419,0.387125581,4.987617956]; 
Rs = x(1);
lls_dot = x(2); 
Lm_dot = x(3);
Rr_dot = x(4);
%% State Space modeling
A = [-Rr_dot/Lm_dot, -w, Rr_dot,0;
     w, -Rr_dot/Lm_dot,  0,Rr_dot;
     Rr_dot/(Lm_dot*lls_dot), w/lls_dot, -(Rr_dot+Rs)/lls_dot, 0;
     -w/lls_dot, Rr_dot/(Lm_dot*lls_dot), 0, -(Rr_dot+Rs)/lls_dot];
 B = [0, 0;
      0, 0;
      1/lls_dot, 0;
      0, 1/lls_dot];
  C = [zeros(2),eye(2)];
  D =zeros(2);
sys = ss(A,B,C,D,Ts)
%% Response
t = 0:Ts:sampling_time-Ts;
x0 = [flux_init,i(1,1:2)]; % initial conditions setting
y = lsim(sys,u,t,x0) 

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Sam Chak 2022-7-6

Got this error mesage:

error: 'out' undefined

Raymond Wong 2022-7-6

@Sam Chak I forgot to upload the data file named by 'out.mat'. Sorry about that. See attached.

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采纳的回答

Raymond Wong 2022-7-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1753875-difference-between-matlab-ss-function-and-simulink-state-space-block#answer_1001380

编辑：Raymond Wong 2022-7-6

在 MATLAB Online 中打开

I found the issue. It turned out the model I built in MATLAB at first is the Discrete-time state-space model, which I didn't pay attention to. After I made it Continuous-time state-space model, it converged. In the code, the chage is shown below. @Sam Chak Technically they're the same model, but I'm not sure why the continuos version converge and the discrete version diverge.

% sys = ss(A,B,C,D,Ts)   Discrete-time state-space model
sys = ss(A,B,C,D) % Continuous-time state-space model

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Paul 2022-7-6

编辑：Paul 2023-4-19

在 MATLAB Online 中打开

load(websave('out', 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/1056590/out.mat'));
f = 10000; % Sampling Frequency
Ts = 1/f; 
%% Data Preparation(Not Important
out1 = out;
ab0_voltage1 = out1.voltage_ab0;
ab0_current1 = out1.current_ab0;
rotation_f1 = out1.speed;
Warning: Unrecognized field name "speed".
start_time = 0;
sampling_time = 5;
start_point = start_time*f+1;
sampling_points = sampling_time*f-1;
t_ind = start_point:start_point+sampling_points; 
u = ab0_voltage1(t_ind,2:3); %Input
i = ab0_current1(t_ind,2:3); 
flux_init = out.flux_ab(start_point,2:3);
w = mean(out.w_e(end,2));
%% Parameterization of State Space A B C D
x = [6.14,0.037874419,0.387125581,4.987617956]; 
Rs = x(1);
lls_dot = x(2); 
Lm_dot = x(3);
Rr_dot = x(4);
%% State Space modeling
A = [-Rr_dot/Lm_dot, -w, Rr_dot,0;
     w, -Rr_dot/Lm_dot,  0,Rr_dot;
     Rr_dot/(Lm_dot*lls_dot), w/lls_dot, -(Rr_dot+Rs)/lls_dot, 0;
     -w/lls_dot, Rr_dot/(Lm_dot*lls_dot), 0, -(Rr_dot+Rs)/lls_dot];
 B = [0, 0;
      0, 0;
      1/lls_dot, 0;
      0, 1/lls_dot];
  C = [zeros(2),eye(2)];
  D =zeros(2);

The continuous model is:

sysc = ss(A,B,C,D);

Its poles are all in the LHP, so sysc represents a stable system.

pole(sysc)
ans = 
   1.0e+02 *

  -1.3931 + 3.0338i
  -1.3931 - 3.0338i
  -1.6737 + 0.6997i
  -1.6737 - 0.6997i

The discretized model, assuming a ZOH, is

sysd = c2d(sysc,Ts);

All poles are inside the unit circle, so also stable

abs(pole(sysd))
ans = 4×1
    0.9862
    0.9862
    0.9834
    0.9834

What is the code that lead to the statement "the discrete model is not stable"?

Raymond Wong 2022-7-7

Thanks a lot.

Paul 2022-7-7

You've got it. Use c2d() to develop the discrete-time approximation to a continous-time model. Check the c2d doc page for the available options for the conversion. Good luck with rest of your project.

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更多回答（2 个）

Fangjun Jiang 2022-7-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1753875-difference-between-matlab-ss-function-and-simulink-state-space-block#answer_1000820

编辑：Fangjun Jiang 2022-7-5

https://www.mathworks.com/help/control/ref/lti.lsim.html

There are limited number of settings when calling lsim(sys,u,t,x0,method). You need to change the settings in Simulink to match the MATLAB simulation time vector. Most likely, choose discrete solver with fixed step size in Simulink. This is just to make the two simulation results match.

If the outputs in Simulink converge using the default settings, then the system is stable. Most likely, the step size in MATLAB is too large which caused it to diverge.