The plant is a stable, discrete LTI state-space model with four states, three inputs, and three outputs. The manipulated variables are inputs 1 and 2. Input 3 is an unmeasured disturbance. Outputs 1 and 3 are measured. Output 2 is unmeasured.
Fix the number generator seed to ensure repeatable results.
Create a model of the plant and specify the signals for MPC.
The last command forces the plant to satisfy the assumption of no direct feedthrough.
Calculate the default model predictive controller for this plant.
-->"PredictionHorizon" is empty. Assuming default 10.
-->"ControlHorizon" is empty. Assuming default 2.
-->"Weights.ManipulatedVariables" is empty. Assuming default 0.00000.
-->"Weights.ManipulatedVariablesRate" is empty. Assuming default 0.10000.
-->"Weights.OutputVariables" is empty. Assuming default 1.00000.
for output(s) y1 y3 and zero weight for output(s) y2
Obtain the parameters to be used in state estimation.
-->The "Model.Disturbance" property is empty:
Assuming unmeasured input disturbance #3 is integrated white noise.
-->Assuming output disturbance added to measured output #1 is integrated white noise.
Assuming no disturbance added to measured output #3.
-->"Model.Noise" is empty. Assuming white noise on each measured output.
Based on the estimator state equation, the estimator poles are given by the eigenvalues of A - L*Cm
. Calculate and display the poles.
Poles = 6×1
-0.5409
-0.0026
0.2358
0.7628
0.8595
0.9718
Confirm that the default estimator is asymptotically stable.
This value is less than 1, so the estimator is asymptotically stable.
Verify that in this case, L = A*M
.
ans = 6×2
10-15 ×
0.1665 -0.1249
-0.4718 0.0833
-0.5690 0.3331
0.4441 0.0278
-0.0278 0.0069
0.1249 0.0139