Function File: P = augw (G, W1, W2, W3)

Extend plant for stacked S/KS/T problem. Subsequently, the robust control problem can be solved by h2syn or hinfsyn.

Inputs

G

LTI model of plant.

W1

LTI model of performance weight. Bounds the largest singular values of sensitivity S. Model must be empty [], SISO or of appropriate size.

W2

LTI model to penalize large control inputs. Bounds the largest singular values of KS. Model must be empty [], SISO or of appropriate size.

W3

LTI model of robustness and noise sensitivity weight. Bounds the largest singular values of complementary sensitivity T. Model must be empty [], SISO or of appropriate size.

All inputs must be proper/realizable. Scalars, vectors and matrices are possible instead of LTI models.

Outputs

P

State-space model of augmented plant.

Block Diagram

    |W1 |-W1*G |    z1 = W1 r  -  W1 G u
    |0  | W2   |    z2 =          W2   u
P = |0  | W3*G |    z3 =          W3 G u
    |----+-------|
    |I  |   -G |    e  =    r  -     G u

                                                      +------+  z1
            +---------------------------------------->| W1  |----->
            |                                        +------+
            |                                        +------+  z2
            |                +---------------------->| W2  |----->
            |                |                      +------+
 r   +    e |  +--------+  u |  +--------+  y       +------+  z3
----->(+)---+-->| K(s)  |----+-->| G(s)  |----+---->| W3  |----->
       ^ -      +--------+        +--------+    |    +------+
       |                                       |
       +----------------------------------------+

               +--------+
               |       |-----> z1 (p1x1)          z1 = W1 e
 r (px1) ----->| P(s)  |-----> z2 (p2x1)          z2 = W2 u
               |       |-----> z3 (p3x1)          z3 = W3 y
 u (mx1) ----->|       |-----> e (px1)            e = r - y
               +--------+

               +--------+  
       r ----->|       |-----> z
               | P(s)  |
       u +---->|       |-----+ e
         |    +--------+     |
         |                   |
         |    +--------+     |
         +-----| K(s)  |<----+
               +--------+

References
[1] Skogestad, S. and Postlethwaite I. (2005) Multivariable Feedback Control: Analysis and Design: Second Edition. Wiley.

See also: h2syn, hinfsyn, mixsyn.

Package: control