how to define mpc object's plant as state space ?

how to define the mpc object's plant as state space rather than transfer function. i tried to run this code but not working.

% Define system matrices (Ad, Bd, Cd, Dd) for the quadruple tank system
Ad = [-0.0173190, 0, 0.026219, 0; 0, -0.0113455, 0, 0.017708; 0, 0, -0.026219, 0; 0, 0, 0, -0.017708];
Bd = [0.0395, 0; 0, 0.03598; 0, 0.076375; 0.06378, 0];
Cd = [1, 0, 0, 0; 0, 1, 0, 0];
Dd = [0, 0; 0, 0];

% Define prediction and control horizons
predictionHorizon = 10;  % Adjust as needed
controlHorizon = 3;      % Adjust as needed

% Define constraints (input and state constraints)
inputConstraints = [-10, 10; -10, 10];  % Adjust as needed
stateConstraints = [0, 40; 0, 40; 0, 40; 0, 40];  % Adjust as needed

% Define cost function weights
Q = eye(4);  % State weight matrix (adjust as needed)
R = eye(2);  % Input weight matrix (adjust as needed)

% Initial state
x0 = [10; 10; 10; 10];  % Adjust the initial state as needed

% MPC setup
mpcobj = mpc(Ad, Bd, Cd, Dd, 'PredictionHorizon', predictionHorizon, 'ControlHorizon', controlHorizon);

Answer 1

[Sam Chak]

Hi @AMAN

There was an incorrect syntax issue with mpc(), but it is now fixed below:

% Define system matrices (Ad, Bd, Cd, Dd) for the quadruple tank system
Ad  = [-0.0173190, 0, 0.026219, 0; 0, -0.0113455, 0, 0.017708; 0, 0, -0.026219, 0; 0, 0, 0, -0.017708];
Bd  = [0.0395, 0; 0, 0.03598; 0, 0.076375; 0.06378, 0];
Cd  = [1, 0, 0, 0; 0, 1, 0, 0];
Dd  = [0, 0; 0, 0];
sys = ss(Ad, Bd, Cd, Dd)    % <-- added this

sys =
 
  A = 
             x1        x2        x3        x4
   x1  -0.01732         0   0.02622         0
   x2         0  -0.01135         0   0.01771
   x3         0         0  -0.02622         0
   x4         0         0         0  -0.01771
 
  B = 
            u1       u2
   x1   0.0395        0
   x2        0  0.03598
   x3        0  0.07637
   x4  0.06378        0
 
  C = 
       x1  x2  x3  x4
   y1   1   0   0   0
   y2   0   1   0   0
 
  D = 
       u1  u2
   y1   0   0
   y2   0   0
 
Continuous-time state-space model.

% Define prediction and control horizons
predictionHorizon = 10;  % Adjust as needed
controlHorizon    = 3;   % Adjust as needed

% Define constraints (input and state constraints)
inputConstraints = [-10, 10; -10, 10];  % Adjust as needed
stateConstraints = [0, 40; 0, 40; 0, 40; 0, 40];  % Adjust as needed

% Define cost function weights
Q = eye(4);  % State weight matrix (adjust as needed)
R = eye(2);  % Input weight matrix (adjust as needed)

% Initial state
x0 = [10; 10; 10; 10];  % Adjust the initial state as needed

% MPC setup
ts     = 0.1;                                               % <-- added this
mpcobj = mpc(sys, ts, predictionHorizon, controlHorizon)    % <-- fixed this

-->"Weights.ManipulatedVariables" is empty. Assuming default 0.00000.
-->"Weights.ManipulatedVariablesRate" is empty. Assuming default 0.10000.
-->"Weights.OutputVariables" is empty. Assuming default 1.00000.
 
MPC object (created on 19-Oct-2023 17:07:26):
---------------------------------------------
Sampling time:      0.1 (seconds)
Prediction Horizon: 10
Control Horizon:    3

Plant Model:        
                                      --------------
      2  manipulated variable(s)   -->|  4 states  |
                                      |            |-->  2 measured output(s)
      0  measured disturbance(s)   -->|  2 inputs  |
                                      |            |-->  0 unmeasured output(s)
      0  unmeasured disturbance(s) -->|  2 outputs |
                                      --------------
Disturbance and Noise Models:
        Output disturbance model: default (type "getoutdist(mpcobj)" for details)
         Measurement noise model: default (unity gain after scaling)

Weights:
        ManipulatedVariables: [0 0]
    ManipulatedVariablesRate: [0.1000 0.1000]
             OutputVariables: [1 1]
                         ECR: 100000

State Estimation:  Default Kalman Filter (type "getEstimator(mpcobj)" for details)

Unconstrained

Use built-in "active-set" QP solver with MaxIterations of 120.

[AMAN]

thank you sir

[Sam Chak]

You are welcome, @AMAN.