SB10LD

Closed-loop system matrices for a system with robust controller

Purpose

  To compute the matrices of the closed-loop system

           | AC | BC |
       G = |----|----|,
           | CC | DC |

  from the matrices of the open-loop system

            | A | B |
        P = |---|---|
            | C | D |

  and the matrices of the controller

           | AK | BK |
       K = |----|----|.
           | CK | DK |

      SUBROUTINE SB10LD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC,
     $                   D, LDD, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK,
     $                   AC, LDAC, BC, LDBC, CC, LDCC, DC, LDDC, IWORK,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDAC, LDAK, LDB, LDBC, LDBK, LDC,
     $                   LDCC, LDCK, LDD, LDDC, LDDK, LDWORK, M, N,
     $                   NCON, NMEAS, NP
C     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), AC( LDAC, * ), AK( LDAK, * ),
     $                   B( LDB, * ), BC( LDBC, * ), BK( LDBK, * ),
     $                   C( LDC, * ), CC( LDCC, * ), CK( LDCK, * ),
     $                   D( LDD, * ), DC( LDDC, * ), DK( LDDK, * ),
     $                   DWORK( * )

Input/Output Parameters

  N       (input) INTEGER
          The order of the system.  N >= 0.

  M       (input) INTEGER
          The column size of the matrix B.  M >= 0.

  NP      (input) INTEGER
          The row size of the matrix C.  NP >= 0.

  NCON    (input) INTEGER
          The number of control inputs (M2).  M >= NCON >= 0.
          NP-NMEAS >= NCON.

  NMEAS   (input) INTEGER
          The number of measurements (NP2).  NP >= NMEAS >= 0.
          M-NCON >= NMEAS.

  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
          The leading N-by-N part of this array must contain the
          system state matrix A.

  LDA     INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

  B       (input) DOUBLE PRECISION array, dimension (LDB,M)
          The leading N-by-M part of this array must contain the
          system input matrix B.

  LDB     INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

  C       (input) DOUBLE PRECISION array, dimension (LDC,N)
          The leading NP-by-N part of this array must contain the
          system output matrix C.

  LDC     INTEGER
          The leading dimension of the array C.  LDC >= max(1,NP).

  D       (input) DOUBLE PRECISION array, dimension (LDD,M)
          The leading NP-by-M part of this array must contain the
          system input/output matrix D.

  LDD     INTEGER
          The leading dimension of the array D.  LDD >= max(1,NP).

  AK      (input) DOUBLE PRECISION array, dimension (LDAK,N)
          The leading N-by-N part of this array must contain the
          controller state matrix AK.

  LDAK    INTEGER
          The leading dimension of the array AK.  LDAK >= max(1,N).

  BK      (input) DOUBLE PRECISION array, dimension (LDBK,NMEAS)
          The leading N-by-NMEAS part of this array must contain the
          controller input matrix BK.

  LDBK    INTEGER
          The leading dimension of the array BK.  LDBK >= max(1,N).

  CK      (input) DOUBLE PRECISION array, dimension (LDCK,N)
          The leading NCON-by-N part of this array must contain the
          controller output matrix CK.

  LDCK    INTEGER
          The leading dimension of the array CK.
          LDCK >= max(1,NCON).

  DK      (input) DOUBLE PRECISION array, dimension (LDDK,NMEAS)
          The leading NCON-by-NMEAS part of this array must contain
          the controller input/output matrix DK.

  LDDK    INTEGER
          The leading dimension of the array DK.
          LDDK >= max(1,NCON).

  AC      (output) DOUBLE PRECISION array, dimension (LDAC,2*N)
          The leading 2*N-by-2*N part of this array contains the
          closed-loop system state matrix AC.

  LDAC    INTEGER
          The leading dimension of the array AC.
          LDAC >= max(1,2*N).

  BC      (output) DOUBLE PRECISION array, dimension (LDBC,M-NCON)
          The leading 2*N-by-(M-NCON) part of this array contains
          the closed-loop system input matrix BC.

  LDBC    INTEGER
          The leading dimension of the array BC.
          LDBC >= max(1,2*N).

  CC      (output) DOUBLE PRECISION array, dimension (LDCC,2*N)
          The leading (NP-NMEAS)-by-2*N part of this array contains
          the closed-loop system output matrix CC.

  LDCC    INTEGER
          The leading dimension of the array CC.
          LDCC >= max(1,NP-NMEAS).

  DC      (output) DOUBLE PRECISION array, dimension (LDDC,M-NCON)
          The leading (NP-NMEAS)-by-(M-NCON) part of this array
          contains the closed-loop system input/output matrix DC.

  LDDC    INTEGER
          The leading dimension of the array DC.
          LDDC >= max(1,NP-NMEAS).

  IWORK   INTEGER array, dimension (2*max(NCON,NMEAS))

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0, DWORK(1) contains the optimal
          LDWORK.

  LDWORK  INTEGER
          The dimension of the array DWORK.
          LDWORK >= 2*M*M+NP*NP+2*M*N+M*NP+2*N*NP.
          For good performance, LDWORK must generally be larger.

  Error Indicactor

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value;
          = 1:  if the matrix Inp2 - D22*DK is singular to working
                precision;
          = 2:  if the matrix Im2 - DK*D22 is singular to working
                precision.

  The routine implements the formulas given in [1].

  [1] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and
      Smith, R.
      mu-Analysis and Synthesis Toolbox.
      The MathWorks Inc., Natick, Mass., 1995.

  The accuracy of the result depends on the condition numbers of the
  matrices  Inp2 - D22*DK  and  Im2 - DK*D22.

  None

Program Text

  None

  None

  None