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‫دانشكده مهندس ي پزشكي‬
State-space Models with
Embedded Integrator
Ref: Model Predictive Control System Design and Implementation Using
MATLAB, Liuping Wang.
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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 j2
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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