Taking a difference operation on both sides New
Taking a difference operation on both sides:
New state variable vector:
Example 1:
Characteristic equation:
Prediction of State and Output Variables
The future control trajectory: Future state variables:
Optimization
Example 2:
We can verify this by increasing Nc to 9, while maintaining rω = 10 First four parameters in U are slightly different from the previous case
Receding Horizon Control
Example 4:
Receding horizon control
Closed-loop Control System
Standard form of linear time-invariant state feedback
Example 5 closed-loop feedback gain matrices in Ex. 2
State Estimation
Basic Ideas About an Observer
Example 7: Linearized equation of motion of a simple pendulum
(a) Estimation without observer
Model alone is not sufficient to predict the angle of the pendulum
(b) Estimation with observer
Example 8 DC motor
Discrete-time model is observable ?
Second pole at λ = 1 cannot be moved no matter what choice we make for j 2
Kalman Filter
State Estimate Predictive Control
Closed-loop state-space equation:
Example 9. The augmented model for a double integrated plant (see Example 1) is given by
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