Why am I not able to get desired output of -40V.

Question

ChoonHan 2024-3-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2098116-why-am-i-not-able-to-get-desired-output-of-40v

编辑： ChoonHan 2024-3-26

Hello to all readers,

I would like to seek your assiatance with my simulink model of the Buck Boost converter with pole state feedback and with state observer to obtain the desired output voltage of -40V. The model is shown as below:

When the model was implemented with only the controller, the desired output voltage of -40V was achieved but when implemented with an observer, the output votlage had dropped to -20V and I would like to seek your assitance and discussion in why this scenario might have happened.

the gain K and Kr used are [0.0709 0.0052] and -0.0181 respectively to obtain the desired output voltage of -40V

but when implementing the observer, the L was calcluated based on 10x times the value of the desired pole which was [-222 -222]

and L matrix was given calculated to be [-6803.4; 4293.6]

However, the output voltage was -20V instead. May I seek your help to debug on some of the reason this had happened?

Thank you very much for your kind attention.

Due to personal reasons, I had to remove the file and I apologise for that, do privately email me at choonchoon97@gmail.com to discuss about the file and model !

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Sam Chak 2024-3-24

在 MATLAB Online 中打开

Thanks @ChoonHan. Could you please provide the input matrix B and the computation of the control gain matrix, K = [0.0709 0.0052], and Kr = -0.0181? You can use the Indentation icon to copy/paste your code into the grey field as shown below.

A = [0, 1; 0, 0];
B = [0; 1];
C = [1, 0];
D =  0;
K = lqr(A, B, eye(2), 1)    % control gain matrix
K = 1x2
    1.0000    1.7321

ChoonHan 2024-3-24

Hi @Sam Chak, here is the code for the gain K and kr, it was done by using ackerman's formula:

>> A = [0 20.96; -709.22 -106.38];

>> B = [3771.21; 12765.96];

>> C = [0 1];

>> D =0;

>> P = [-220 -220];

>> k=acker(A,B,P)

k =

0.0709 0.0052

>> kr = -[C*(A-B*k)^(-1)*B]^(-1)

kr =

-0.0181

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Answer 1

Sam Chak 2024-3-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2098116-why-am-i-not-able-to-get-desired-output-of-40v#answer_1430191

在 MATLAB Online 中打开

Fullorder_StateObserver.slx

Hi @ChoonHan

I have constructed a full-order state observer in Simulink based on the information you provided, and it yields the expected output voltage of -40V. It appears that the observer is designed correctly.

However, in your original Simscape model for the Buck-Boost Converter, I suspect that the reason for the output voltage being -20V is due to a setting in the DC Voltage source in the Buck-Boost Converter, as shown below.

format long
A   = [0 20.96; -709.22 -106.38];   % state matrix
B   = [3771.21; 12765.96];          % input matrix
C   = [0 1];                        % output matrix
D   = 0;                            % direct matrix
p   = [-220 -220];                  % desired closed-loop poles
q   = 10*p;                         % 10 times faster than p
K   = acker(A, B, p)                % controller gain matrix
Kr  = - (C*(A - B*K)^(-1)*B)^(-1)   % reference gain
L   = acker(A', C', q)'             % observer gain matrix

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Sam Chak 2024-3-25

在 MATLAB Online 中打开

Hi @ChoonHan,

I'm not an expert in Buck-Boost Converters. I noticed that you implemented a state observer in your Simscape Buck-Boost Converter model. However, both your feedback controller and the state observer are designed based on the LINEAR state-space system mentioned in your comment. It's worth noting that Buck-Boost Converters are typically NONLINEAR and non-minimum phase systems when it comes to their output voltage.

Could you please verify if the Simscape Buck-Boost Converter remains relatively linear within the operating range of 20V to –50V? It is crucial to validate the linearization steps you have taken from the original derived nonlinear ODE to the linearized ODE (state-space).

A   = [0 20.96; -709.22 -106.38];   % state matrix
B   = [3771.21; 12765.96];          % input matrix
C   = [0 1];                        % output matrix
D   = 0;                            % direct matrix
BBC = ss(A, B, C, D)                % Buck-Boost Converter model
BBC =
 
  A = 
           x1      x2
   x1       0   20.96
   x2  -709.2  -106.4
 
  B = 
              u1
   x1       3771
   x2  1.277e+04
 
  C = 
       x1  x2
   y1   0   1
 
  D = 
       u1
   y1   0
 
Continuous-time state-space model.

ChoonHan 2024-3-25

Hello @Sam Chak thank you for the explanations, the team had concluded that the state space model you had given will be a better presentation to model the system itself. Thank you for all the assistance so far, really appreciate all your efforts.

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