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Function Reference: augw

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

Source Code: augw