Digital Control Systems STATE FEEDBACK CONTROLLER DESIGN

Design via Pole Placement

Open loop control system

Design via Pole Placement Closed loop system

Design via Pole Placement Determination of feedback gain by using controllable canonical form

Design via Pole Placement Determination of feedback gain by using controllable canonical form

Design via Pole Placement Determination of feedback gain by Ackermann’s Formula Determination of feedback gain by a causal approach

Design via Pole Placement Example: Determination of feedback gain by using controllable canonical form: Determination of feedback gain by using Ackermann’s Formula: Determination of feedback gain bycausal method:

Design via Pole Placement Uncontrollable system: Kalman Controllable Form

Design via Pole Placement Uncontrollable system: Kalman Controllable Form State Feedback The modes of can be arbitrarily assigned. The modes of is not influenced by state feedback control

Design via Pole Placement Example: Kalman Controllable Form State Feedback The modes of can be arbitrarily assigned. The modes of is not influenced by state feedback control

Design via Pole Placement Example: Kalman Controllability Decomposition Desired closed loop poles: -1, -2.5, -2.5 Not: We do not feedback the uncontrollable mode

Design via Pole Placement Example: Kalman Controllability Decomposition Desired closed loop poles: -1, -2.5, -2.5 Not: We do not feedback the uncontrollable mode