This book describes a computational system for designing linear feedback control laws and filters for linear time-variant multivariable differential or difference equation state vector models. It presents numerical examples to illustrate the use of ORACLS to solve selected design problems.
Preface
One/The Oracles System
I/ Overview of Oracles
References
Two/Programs for Input/Output
I/ Introduction
II/ Subroutine Descriptions
A/ Input Hollerith Data; define COMMON Block Data (RDTITL)
B/ Accumulate Line Count; Page Output (LNCNT)
C/ Input Numerical Data (READ)
D/ Output Numerical Data (PRNT)
References
Three/ Programs for Vector/Matrix Operation
I/ Introduction
II/ Subroutine Descriptions
A/ Equation (Equate)
B/ Matrix Transpose (TRANP)
C/ Scalar Multiplication (SCALE)
D/ Form Identity Matrix (UNITY)
E/ Form Null Matrix (NULL)
F/ Trace of Matrix (TRCE)
G/ Matrix Addition (ADD)
H/ Matrix Subtraction (SUBT)
I/ Matrix Multiplication (MULT)
J/ Maximum of Matrix Elements (MAXEL)
K/ Selected Matrix Norms (MAXEL)
L/ Matrix Juxtaposition by Columns (JUXTC)
M/ Matrix Juxtaposition by Rows (JUXTR)
References
Four/ Programs for Analysis of Constant Linear Systems
I/ Introduction
II/ Subroutine Descriptions
A/ Factor Nonnegative Definite Matrix (FACTOR)
B/ Eigensystem Computation (EIGEN)
C/ Solve AX =B, A Positive Definite (SYMPDS)
D/ Solve AX=B, A Nonsingular (GELIM)
E/ Singular value Decomposition (SNVDEC)
F/ Solve Discrete Liapunov Equation (SUM)
G/ Solve Continuous Liapunov Equation (BILIN)
H/ Solve General Equation AX + XB = C (BARSTW)
I/ Examine Matrix for Relative stability (TESTSTA)
J/ Matrix Exponential by Series Method (EXPSER)
K/ Matrix Exponential by Pade Method (EXPADE)
L/ Matrix Exponential and Integral (EXPINT)
M/ Steady-State Variance (VARANCE)
N/ Controllability (CTROL)
O/ Transient Response (TRANSIT)
P/ Transfer Matrix (LEVIER)
References
Five/ Programs for Control Law Design
I/ Introduction
II/ Subroutine Descriptions
A/ Evaluate Sampled-Data Regulator Coefficients (SAMPL)
B/ Eliminate Performance Index Cross-Products (PREFIL)
C/ Stabilize Continuous System (CSTAB)
D/ Stabilize Discrete System (DSTAB)
E/ Digital Transient Quadratic Regulator (DISCREG)
F/ Continuous Transient Quadratic Regulator (CNTNREG)
G/ Riccati Solution by Newton’s Method (RICTNWT)
H/ Asymptotic Quadratic Regulator (ASYMREG)
I/ Asymptotic Kalman-Bucy Filter (ASYMFIL)
J/ Explicit Model Following (EXPMDFL)
K/ Implicit Model Following (IMPMDFL)
L/ Eigenvalue Placement (POLE)
References
Six/ Supporting Programs
I/ Introduction
II/ Subroutine Descriptions
A/ Input Numerical Data (READL)
B/ Balance Square Matrix (BALANC)
C/ Upper Hessenberg Form (ELMHES)
D/ Eigenvalues (HQR)
E/ Eigenvectors (INVIT)
F/ Eigenvectors (ELMBAK)
G/ Eigenvectors (BALBAK)
H/ LU Factorization (DETFAC)
I/ Solve AX + XB = C (AVPXB)
J/ Solve AX + XB =C (AXPXB)
K/ Solve A’X +XA =C (ATXPXA)
L/ Solve A’X =XA =C (SYMSLV)
M/ Upper Hessenberg Form (HSHLDR)
N/ Upper Hessenberg Form (BCKMLT)
O/ Real Schur Form (SCHUR)
P/ Solve Ax = b (SYSSLV)
Q/ Solve AX = B (GAISEL)
Seven/ Design Problems
I/ Introduction
II/ Optimal Transient Regulator
A/ Problem Statement
B/ Executive Program
C/ Output from Oracls
III. Optimal Sampled-Data Regulator
A/ Problem Statement
B/ Executive Program
C/ Output from Oracles
IV/ Model Following
A/ Problem Statement
B/ Executive Program
C/ Output from ORACLS
V/ Kalman-Bucy Filter
A/ Problem Statement
B/ Executive Program
C/ Output from Oracls
VI/ Eigenvalue Placement
A/ Problem Statement
B/ Executive Program
C/ Output from Oracls
VII/ Transfer Matrix
A/ Problem statement
B/ Executive Program
C/ Output from Oracls
VII/ Transfer Matrix
A/ Problem Statement
B/ Executive Program
C/ Output from Oracles
References
Biography
Ernest S. Armstrong