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

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 [e-mail] to discuss about the file and model !

[Sam Chak]

Hi @ChoonHan,

To debug this, you will need to provide the mathematical model of the Buck–Boost Converter. Additionally, it would be helpful if you could demonstrate how you obtained the Observer gain matrix L = [-6803.4; 4293.6].

[ChoonHan]

Hello @Sam Chak thank you for your assiatance,

the matrix L was calcluted with the below codes by using matrix A, C, 10 times the value of original pole value at [-220 -220]:

additonally, the current measurement at the inductor is shown to be:

do let me know if more information is needed, thank you for the assiatance once again.

[Sam Chak]

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]

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

Answer 1

[Sam Chak]

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

[ChoonHan]

Hello @Sam Chak, thank you for sharing the file but would it possible to implement the full state observer on an actual buck boost converter cicuit as one of the given parameter given was vin = 20V as shown in the picture figure below:

[Sam Chak]

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]

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.