Control Systems - Week 12

EM412 - CONTROL SYSTEMS Week 12 – State Space Design • Chapter 9: State Space Design State Feedback Stabilizability Observer Design Integral Design Text : Design of Feedback Control Systems 4th (Edition) R.T. Stefani, C.J. Savant, B. Shahian, G.H. Hostetter INSTRUCTOR: MAJ DR. KUNWAR FARAZ AHMED

State Space Design State Feedback and Pole Placement Consider the simple 1st Order system This procedure is formalized as the State Feedback x  x  u, x(0)  x0 , y  x Control law where u is the plant input This system is unstable since pole is 1 • Reference input is set to 0 To stabilize the system we feed the system some gain k where u = - k x Therefore the compensated system becomes x  x  kx  (1  k ) x Which has a pole at (1-k) which results in an asymptotically stable system for k > 1

u   Kx  [k1

k1

 x1  x   k1n ] 2      xn 

 x  ( A  BK ) x

• Choose K so that eigenvalues of (A-BK) are in desirable locations, e.g., LHP (2)

State Space Design State Feedback and Pole Placement

(3)

State Space Design Stabilizability

(4)

State Space Design Observer Design

(5)

State Space Design Observer Design

(6)

State Space Design Separation Principle

(7)

State Space Design Observer Based Controller

(8)

State Space Design Integral Control

(9)

State Space Design Integral Control

(10)