دانشگاه صنعتي اميركبير دانشكده مهندسي پزشكي State-space Models with Embedded Integrator استاد درس دكتر فرزاد توحيدخواه آبان 1388 کنترل پيش بين-دکتر توحيدخواه

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 r ω = 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 8DC 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